DENSITY FUNCTIONAL STUDY OF NO DECOMPOSITION WITH CU-EXCHANGED ZEOLITES

BY R. RAMPRASAD B.Tech., Indian Institute of Technology, Madras, 1990

M.S., Washington State University, 1992

THESIS Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Materials Science and Engineering

in the Graduate College of the University of Illinois at Urbana-Champaign, 1997

Urbana, Illinois

iii DENSITY FUNCTIONAL STUDY OF NO DECOMPOSITION WITH

CU-EXCHANGED ZEOLITES

R. Ramprasad, Ph.D. Materials Science and Engineering University of Illinois at Urbana-Champaign, 1997

James B. Adams, Advisor

Cu ions exchanged into zeolites like ZSM-5 show high catalytic activity for the decomposition of environmentally harmful NO to harmless N

and O

. The present work

is an attempt to study this phenomenon using a first-principles quantum mechanicsbased density functional method. A small cluster model is proposed and used to examine the properties of zeolite-bound Cu ions, and their interactions with various species relevant to the decomposition process. Vibrational frequencies of the adsorbed species are compared with measured frequencies in an effort to assess the models and to help interpret infrared spectroscopy results. In addition, an orbital symmetry analyses coupled with transition state and intrinsic reaction coordinate searching techniques are used to assess the plausibility of proposed reaction mechanisms, and to elicit novel insights into other likely reaction pathways. According to conventional belief, the Cu-bound N-down gem-dinitrosyl species decomposes to N

and O

through a series of steps. We, however, find evidence for a more likely pathway

initiated by the formation of a short-lived and difficult to detect O-down intermediate, and have mapped out a multi-step reaction pathway. The redox mechanism proposed here has reasonable energetics and activation barriers for each individual mechanistic step, and involves two successive O-atom transfers to an isolated zeolitebound Cu

center, yielding sequentially N

O and Cu-bound O, followed by N

and

Cu-bound O

. We believe that the generic redox mechanism proposed here could

play a role in other non-zeolitic nitrogen oxide transformation reactions as well.

iv To the memory of my mother

and my ever-patient father

v Acknowledgments My greatest debt is to my advisor Prof. James B. Adams. But for his invaluable counsel, immense interest, enthusiasm and mentoring, this work would not be anywhere as close to what it is right now.

I am deeply indebted to Dr. Kenneth C. Hass, Ford Research Laboratory (FRL), who has contributed greatly towards my intellectual development and scientific thinking over the past few years. I have benefitted immensely from his mentoring, suggestions and criticisms.

In Dr. William F. Schneider (FRL), I found a great teacher and friend. I have learnt several aspects of what can only be termed `chemical intuition' from him. If my thesis has a flavor of good chemistry, the credit goes to him.

Special thanks are due to Dr. Keith M. Glassford, Dr. Sang Yang and Prof. David A. Drabold, who provided me with the initial impetus when I came to the Adams' group as a novice in electronic structure theory. I have also benefitted from interactions with Brian Goodman, Karland Kilian, Kyusang Lee, Dong Xiang Liao, Benjamin Liu, Dr. Miki Nomura, David Richards, Donald Siegel, Blair Tuttle and Dr. Wei Xu. Brian Goodman and Blair Tuttle read through parts of my thesis and made some very useful suggestions.

I would like to thank Profs. Richard Masel, Murray Gibson and Kenneth Schweizer for their advice and willingness to serve in my doctoral committee.

Thanks are due to David Richards for providing the L

X style files for typesetting this thesis, Dr. William Schneider for making Figures 4.1-4.4 and providing the ADF/GAMESS hybrid program which made determinations of transition states and intrinsic reaction coordinates possible, Dr. Kenneth C. Hass for making Figures 7.4 and 7.5, Ref. [3] from which Figure 2.2 was obtained, and T. A. Barckholtz for assistance with the EFFF method.

Kinkini S. Banerjee deserves an extra special thanks; by just being herself, she made me realize how fast time can pass.

This work was mainly supported by the National Science Foundation (Grant No. NSF-1-5-30897 (8)). I would also like to acknowledge the FRL where I spent three summers as an intern, and which partially supported this work. The present study is the result of a fruitful collaborative effort between our group and the FRL.

vi Contents Chapter 1 Introduction : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1

1.1 General comments on catalysts . . . . . . . . . . . . . . . . . . . . . 1 1.2 Three-way catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Lean-burn catalysts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.4 NO decomposition catalysts . . . . . . . . . . . . . . . . . . . . . . . 3 1.5 Current problems with zeolite-based Cu catalysts . . . . . . . . . . . 4 1.6 Goals of present study . . . . . . . . . . . . . . . . . . . . . . . . . . 4

2 Background : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 6

2.1 Zeolites--"Boiling Stones" . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 Cu-exchanged zeolites . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.3 Scope of theoretical techniques in understanding catalytic phenomena 12

3 Theoretical Methods : : : : : : : : : : : : : : : : : : : : : : : : : : : : 14

3.1 General comments on quantum mechanics-based calculations . . . . . 14 3.2 Density functional theory (DFT) . . . . . . . . . . . . . . . . . . . . 16 3.3 Performance of approximate density functional methods . . . . . . . . 20 3.4 Implementation used in the present study . . . . . . . . . . . . . . . 20

4 Models of Cu sites and their interaction with CO and NO : : : : : 23

4.1 Properties of zeolite-bound Cu ions . . . . . . . . . . . . . . . . . . . 23 4.2 Interaction of CO with Cu sites . . . . . . . . . . . . . . . . . . . . . 31 4.3 Interaction of NO with Cu sites . . . . . . . . . . . . . . . . . . . . . 39 4.4 Extension beyond the H

O Model . . . . . . . . . . . . . . . . . . . . 51

4.5 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 52

5 Dicarbonyl and dinitrosyl species in Cu exchanged zeolites : : : : 54

5.1 Cu-dicarbonyl complexes . . . . . . . . . . . . . . . . . . . . . . . . . 56 5.2 Cu-dinitrosyl complexes . . . . . . . . . . . . . . . . . . . . . . . . . 60 5.3 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 73

vii 6 Vibrational spectra of adsorbed CO and NO in Cu-exchanged zeolites : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 75 6.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . 76 6.2 Cu

-bound monocarbonyl complexes . . . . . . . . . . . . . . . . . . 83

6.3 Cu

-bound dicarbonyl [Cu(H

(CO)

]

complexes . . . . . . . . 88

6.4 Cu

-bound mononitrosyl complexes . . . . . . . . . . . . . . . . . . 90

6.5 Cu

-bound dinitrosyl [Cu(H

(NO)

]

complexes . . . . . . . . . 93

6.6 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 96

7 Orbital symmetry analysis of Cu-dinitrosyl complexes : : : : : : : 98

7.1 Free NO decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . 100 7.2 Free NO dimers vs. Cu-bound dinitrosyl species . . . . . . . . . . . . 102 7.3 NO decomposition and N-N bond formation on zeolite bound Cu ions 107 7.4 Summary and Conclusions . . . . . . . . . . . . . . . . . . . . . . . . 110

8 The mechanism of catalytic decomposition of NO by Cu-exchanged

zeolites : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 111 8.1 Computational details . . . . . . . . . . . . . . . . . . . . . . . . . . 112 8.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114 8.3 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128 8.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131

9 Summary : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 132 Appendix A Errors in decoupled EFFF frequencies : : : : : : : : : : : : : : : : : 136 B Natural Internal Coordinates : : : : : : : : : : : : : : : : : : : : : : : 139

B.1 Natural internal coordinates for bare model . . . . . . . . . . . . . . 140 B.2 Natural internal coordinates for water-ligand model . . . . . . . . . . 141 B.3 Natural internal coordinates for T-site model . . . . . . . . . . . . . . 142

Bibliography : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 145 Vita : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 158

viii List of Tables

3.1 Comparison of Calculated and Experimental Molecular Parameters for

CO, NO, and H

O. Distances in

* A, angles in degrees, energies in kcal

mol

\Gamma 1

and frequencies in cm

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . 22

4.1 Selected geometric parameters and Mulliken charges [LSDA], and binding energies [BP86] of [Cu(H

]

complexes. Distances in

* A, angles

in degrees, and energies in kcal/mol. . . . . . . . . . . . . . . . . . . 26 4.2 BP86 binding energies for addition of H

O, CO and NO to [Cu(H

]

complexes, in kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . 30

4.3 Selected geometric parameters [LSDA] and binding energies [BP86] for

[Cu(H

(CO)]

complexes. Distances in

* A, angles in degrees and

energies in kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . 33

4.4 Selected geometric parameters [LSDA] and binding energies [BP86] for

[Cu(H

(NO)]

complexes. Distances in

* A, angles in degrees, and

energies in kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . 40

5.1 Selected geometric parameters [LSDA] and binding energies [BP86] for

[Cu(H

(CO)

]

complexes. Distances in

* A, angles in degrees and

energies in kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . 57

5.2 Successive BP86 binding energies of CO, NO for N-down binding, and

relative energies, in kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . 59

5.3 Calculated properties [BP86] for the cis- and trans forms of free (NO)

\Gamma

and N

2\Gamma

. Bond lengths in

* A, bond angles in degrees and

energies in kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . 60

5.4 Selected geometric parameters, Cu d population [LSDA] and fragmentation energies [BP86] for [Cu(H

(NO)

]

complexes. Bond

lengths in

* A, bond angles in degrees and energies in kcal mol

\Gamma 1

. . . . 63

5.5 Selected geometric parameters, Cu d population [LSDA] and fragmentation energies [BP86] for [Cu(H

(ON)

]

and [Cu(H

]

complexes. Bond lengths in

* A, bond angles in degrees and energies in

kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

ix 6.1 Selected geometric parameters and scaled EFFF CO stretch frequencies for larger model carbonyl complexes. Distances in

* A and frequencies in cm

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78

6.2 Selected geometric parameters and scaled EFFF NO stretch frequencies for larger model nitrosyl complexes. Distances in

* A, angles in

degrees, and frequencies in cm

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . 79

6.3 C-O bond length and scaled EFFF and full normal mode (in parenthesis) CO vibrational stretch frequencies for [Cu(H

(CO)]

complexes. Distances in

* A and frequencies in cm

\Gamma 1

. . . . . . . . . . . . . 80

6.4 N-O bond length and scaled EFFF and full normal mode (in parenthesis) NO vibrational stretch frequencies for [Cu(H

(NO)]

complexes. Distances in

* A and frequencies in cm

\Gamma 1

. . . . . . . . . . . . . 81

6.5 C-O bond length and scaled EFFF and full normal mode (in parenthesis) antisymmetric and symmetric CO vibrational stretch frequencies for [Cu(H

(CO)

]

complexes. Distances in

* A and frequencies

in cm

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82

6.6 N-O bond length and scaled EFFF and full normal mode (in parenthesis) antisymmetric and symmetric NO vibrational stretch frequencies for [Cu(H

(NO)

]

complexes. Bond lengths in

* A and frequencies

in cm

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

6.7 Calculated equilibrium bond lengths and calculated and experimental

vibrational frequencies of diatomic molecules in the gas phase. Bond lengths in

* A and frequencies in cm

\Gamma 1

. . . . . . . . . . . . . . . . . . . 84

8.1 Geometries, frequencies and total energies for the transition state complexes involved in the NO decomposition reactions. Atom indices are consistent with those in Figure 8.1. BP86/LSDA stands for LSDA geometries and single-point BP86 energies at LSDA geometries. Values in parenthesis are LSDA energies. All bond lengths in

* A, bond and

dihedral angles in degrees, frequencies in cm

\Gamma 1

and energies in kcal

mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115

x 8.2 Geometries and total energies for reactant and product complexes involved in the NO decomposition reactions. O

refers to framework O.

Atom indices for ZCuONNO

are consistent with those in Figure 8.1.

BP86/LSDA stands for LSDA geometries and single-point BP86 energies at LSDA geometries. Values in parenthesis are LSDA energies. All bond lengths in

* A, bond and dihedral angles in degrees and energies

in kcal mol

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

8.3 Reaction and activation energies (in kcal mol

\Gamma 1

) for various reactions. 119

A.1 Various degrees of approximations in vibrational frequency calculations. All frequencies are in cm

\Gamma 1

. . . . . . . . . . . . . . . . . . . . . 137

xi List of Figures

2.1 TO

units in zeolites. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

2.2 (a) Secondary building unit (SBU) of silicalite; (b) chains formed by

linking the SBUs; (c) schematic of silicalite layers formed by sidelinking the chains; and (d) schematic of the three-dimensional intracrystalline pore structure of silicalite or ZSM-5. Figure adapted from Ref. [3]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

4.1 Molecular structures used in the Cu(H

calculations (first column), the linearly coordinated CO and NO structure calculations (second column), and the bent CO and NO structure calculations (third column). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 4.2 Molecular orbital diagrams for Cu(H

, x = 1-4. For ease of interpretation, the orbitals are shifted vertically so that the centroids of the d bands are approximately the same energy. . . . . . . . . . . . . 28 4.3 Molecular orbital diagrams for CO on the bare Cu atom and ions. For

ease of interpretation, the orbitals are shifted vertically so that the tops of the spin-up d orbital manifolds have the same energy. . . . . . 32 4.4 Molecular orbital diagrams for NO on bare Cu atom and ions. For ease

of interpretation, the orbitals are shifted vertically so that the tops of the spin-up d orbital manifolds have the same energy. . . . . . . . . . 41

5.1 Schematic of Cu-bound dicarbonyl [Cu(H

(CO)

]

complexes for

x = 0, 1, 2 or 4. Complexes may have overall charge (n = 0, 1 or 2) and are all constrained to C

symmetry except x = 0, which has a

ground state. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

5.2 Schematic structures of Cu-bound dinitrosyl [Cu(H

(NO)

]

(X = N,

Y = O) and [Cu(H

(ON)

]

(X = O, Y = N) complexes for x = 0,

1, 2 or 4. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

xii 5.3 Molecular orbital diagrams for dicarbonyl binding to bare Cu

(n = 0),

(n = 1) and Cu

(n = 2). For ease of interpretation, the orbitals

are shifted vertically so that the top of the Cu d orbital manifolds have the same energy. Levels below those indicated by arrows are all occupied, those above are empty. . . . . . . . . . . . . . . . . . . . . 58 5.4 Schematic molecular orbital diagrams for cis-(NO)

(left), cis-N

\Gamma

(center) and cis-N

2\Gamma

(right). Levels below those indicated by arrows

are all doubly occupied, and those above are empty. . . . . . . . . . . 61 5.5 Molecular orbital diagrams for N-down dinitrosyl binding to bare Cu

(a), Cu

(b) and Cu

(c). For ease of interpretation, the orbitals are

shifted vertically so that the top of the Cu d orbital manifolds have the same energy. Levels below those indicated by arrows are all doubly occupied, those above are empty, and those with a dominant Cu d component are indicated by bold lines. . . . . . . . . . . . . . . . . . 65 5.6 Molecular orbital diagrams for O-down dinitrosyl binding to bare Cu

(a), hyponitrite-like binding to bare Cu

(b) and hyponitrite-like binding to bare Cu

(c). For ease of interpretation, the orbitals are shifted

vertically so that the top of the Cu d orbital manifolds have the same energy. Levels below those indicated by arrows are all doubly occupied, those above are empty, and those with a dominant Cu d component are indicated by bold lines. . . . . . . . . . . . . . . . . . . . . . . . . 71

6.1 Basic geometries assumed for (a) 1-coordinated Cu and (b) 4-coordinated

Cu, for larger cluster models of YO (Y = C or N) ligated Cu(I) and Cu(II) sites in zeolites. Tetrahedral sites (T) may be occupied by Si, Al or J atoms. Terminating X species in 1-coordinated Cu complexes may be H or OH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 6.2 Calculated CO frequencies (*, from EFFF method, scaled by 0.98) vs.

C-O bond lengths (r) for monocarbonyl complexes. Linear fit to data and ranges of experimental values (from Table 6.3) are also shown. . . 86 6.3 Calculated symmetric and antisymmetric CO stretch frequencies (from

EFFF method, scaled by 0.98) vs. C-O bond lengths for dicarbonyl [Cu(H

(CO)

]

complexes. Linear fit to monocarbonyl results (from

Figure 4) and ranges of experimental values (Table 6.5) are also shown. 89

xiii 6.4 Calculated NO frequencies (*, from EFFF method, scaled by 0.97) vs.

N-O bond lengths (r) for mononitrosyl complexes. Linear fit to data and ranges of experimental values (from Table 6.4) are also shown. . . 92 6.5 Calculated symmetric and antisymmetric NO stretch frequencies (from

EFFF method, scaled by 0.97) vs. N-O bond lengths for dinitrosyl [Cu(H

(NO)

]

complexes. Linear fit to mononitrosyl results (from Figure 6.4) and ranges of experimental values (Table 6.6) are also shown. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

7.1 Orbital correlation (`Walsh') diagram for levels of the same C

symmetry associated with two isolated NO molecules (left), the cis-symmetric dimer (NO)

(center) and decoupled N

and O

(right). Levels below

those indicated by arrows are all doubly occupied, and those above are empty. Levels involved in forbidden crossings are connected by solid lines, and the levels themselves are darkened and pictured. The majority spin level crossing is indicated by a circle. . . . . . . . . . . 100 7.2 State correlation diagram for states of the same C

symmetry associated with two isolated NO molecules (left), the cis-symmetric dimer (NO)

(center) and decoupled N

and O

(right). . . . . . . . . . . . 101

7.3 Schematic interaction diagram for the formation of [Cu(NO)

]

from

and free (NO)

. The [Cu(NO)

]

orbitals are shown in the center

(labels as in Figure 5.5(b)), and those of the free (NO)

(labels as

in Figure 7.1) and Cu

fragments are shown in the left and right,

respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 7.4 Evolution of BP86 energy levels (a), BP86 total energy (b) and optimal

Cu-N-O angle (c) of [Cu(NO)

]

along a N-N separation coordinate.

All geometric parameters are optimized at each N-N bond length.The square indicates the forbidden crossing of levels of unlike symmetry during N-N bond formation. . . . . . . . . . . . . . . . . . . . . . . . 105

xiv 7.5 Evolution of BP86 energy levels (a) and BP86 total energy (b) of

[Cu(NO)

]

as a function of the Cu-N-O angle. The Cu-N bond

length, N-Cu-N angle and N-Cu-N-O dihedral angle are fixed at 1.95

* A, 95

ffi

and 0

ffi

, respectively (corresponding to a N-N bond length

of 2.87

* A), and the N-O bond length is optimized for a range of Cu-

N-O angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106

8.1 Schematic sketches of the bare (a), the water-ligand (b) and the T-site

sites, and the transition state structures

ZCuO

(d), ZCuONNO

(e) and ZCuOONN

(f). Dotted lines

indicate bonds that are being cleaved. Atom indices are used to define natural internal coordinates in Appendix B. . . . . . . . . . . . . . . 113 8.2 Schematic orbital correlation diagram for reactions (8.1) and (8.2)

along a planar reaction coordinate. Arrows indicate filling of highest occupied molecular orbitals, and solid and dashed lines indicate symmetric (a

) and antisymmetric (a

) orbitals, respectively. The diagram demonstrates smooth evolution of occupied and virtual orbitals, characteristic of an electronically allowed reaction pathway. . . . . . . 116 8.3 LSDA and BP86 energy profiles along the IRC for (a) reactions (8.3)

(open diamonds) and (8.5) (solid diamonds), (b) and reaction (8.6) (b) for the bare model. Arrows indicate transition from a long to short N-N bond length. Also shown are energies of reactants and products. 121 8.4 Relative energies of reactants, transition states and products involved

in reactions (8.3)-(8.7) within the water-ligand (a) and T-site (b) models: (i) ZCu

+ 2NO, (ii) ZCuO

, (iii) ZCuONNO

, (iv) ZCuO

(v) ZCuONNO

, (vi) ZCuO

+ N

O, (vii) ZCuOONN

, (viii) ZCuO

and (ix) ZCu

+ O

+ N

. . . . . . . . . . . . . . . . . . . . . . . 123

8.5 Schematic orbital correlation diagram for reactions (8.5) and (8.6)

along a planar reaction coordinate. Arrows indicate filling of highest occupied molecular orbitals. The diagram demonstrates smooth evolution of occupied and virtual orbitals, characteristic of an electronically allowed reaction pathway. All qualitative features are similar to those in Figure 8.2 except for the presence of the Cu d levels. . . . . . . . . 129

xv 8.6 The redox catalytic cycle for NO decomposition with Cu-exchanged

zeolites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

Chapter 1 Introduction

If I had to pick any one word that to me most captures

chemistry, it would be the word catalyst.

--Richard Zare

1.1 General comments on catalysts In 1836, Jakob Berzelius coined the term "catalysis" when he realized that changes in compositions of numerous substances that came in contact with small amounts of various ferments, liquids or solids could be classified by a single concept [1, 2]. Several centuries earlier, alchemists were aware of such actions of ferments and other substances, and were probably led to the belief that these could be used to convert base metals to gold.

In more modern terms, a catalyst can be described as a substance that speeds up a chemical reaction, and although participating in the reaction, is unchanged in the end. While the thermodynamics of the net reaction are unaltered by a catalyst, the kinetics can be very different. Heterogeneously catalyzed chemical reactions, the class of reactions relevant to this study, occur by a sequence of elementary steps that include adsorption of the reactants on the catalyst, chemical rearrangements (by bond breaking and formation, and molecular rearrangement) and desorption of the products. Thus, central to the concept of catalysis is the subject of reaction kinetics and reaction mechanisms.

The majority of biochemical and industrial chemical processes rely quite heavily on catalytic materials. Catalytic reactions take place in various phases: in solutions, within the solution-like confines of micelles and the molecular pockets of enzymes, within polymer gels, within the molecular scale cages and pores of crystalline solids like molecular-sieve zeolites, and on the surfaces of solids [3]. Classic examples of catalytic actions include the working of the D"oberiner's lamp, the Haber process, the

2 cracking of crude petroleum to fuels and chemicals and the metabolic processes in living beings.

1.2 Three-way catalysts In automotive industries, catalytic treatment of the automobile exhaust gases has been a standard feature since 1975 [4-6] to meet the federal government regulations limiting the amount of pollutants emitted. Due to incomplete combustion of fuel in the engines of vehicles, trace amounts of unburned hydrocarbons and carbon monoxide are emitted along with the combusted fuel [4]. Oxides of nitrogen-- primarily NO--are produced by high temperature combustion of nitrogen, and are also emitted along with the exhaust gases [4]. All three of the side-products of gasoline combustion--hydrocarbons, CO and NO

--are pollutants. Under certain

atmospheric conditions, in the presence of sunlight, hydrocarbons and NO

, through

a series of chemical and photochemical reactions in the lower atmosphere, lead to the formation of acid rain and photochemical smog, in addition to the formation of tropospheric ozone, which is harmful at low altitudes. CO, the other pollutant, is poisonous, as it displaces the vital O

from the human respiratory system.

Federal government regulations thus require the amounts of these effluents be decreased to acceptable levels [4]. In current automobiles which operate under stoichiometric air/fuel (A/F) ratio conditions (about 14.7 parts of air mixed with 1 part of fuel, by weight), this is accomplished by three-way catalysts (TWCs); the name reflects the simultaneous treatment by these catalysts of the two reducing pollutants, CO and uncombusted hydrocarbons, as well as the oxidizing pollutant, NO

. In the

United States, the very expensive noble metals Pt (1-2 g), Pd (0.5-1 g) and Rh (0.1-0.2 g) are used as vital ingredients of present day TWCs, costing $45-90 per vehicle [4,7]. Pt and Pd are primarily used for CO and hydrocarbon oxidation, while Rh is found to be most effective for NO

reduction. Cheaper base metal oxide catalysts

also show significant activity for the above reactions. However, despite their high cost, the noble metals are used in preference to base metal oxide catalysts because of (a) their tolerance to sulfur compounds (catalyst poisons) that are in the exhaust, (b) their high specific activity in the small catalyst volumes that are important for quick catalyst heating during vehicle start up, and (c) for the ease of packaging in the vehicle [7].

3 1.3 Lean-burn catalysts Although CO

, the inevitable product of gasoline combustion, is harmless, it is the

main "greenhouse" gas contributing to perhaps 50 % of the predicted global warming. The motor vehicle is identified as the contributor of about 15 % of the CO

emissions,

and this provides a motivation for low gasoline usage. It also turns out that engines which use high A/F ratios (in the 21-24 range)--the "lean-burn" engines--are more thermodynamically efficient than those which use a stoichiometric A/F mix [6, 8], and results in better fuel economy.

Lean burn operation results in an exhaust emission containing an excess of oxidants (more O

than when the engine operates under stoichiometric A/F conditions)

than reductants (NO

). Thus, although oxidation of unburned hydrocarbons and CO

is easy, reduction of the oxides of nitrogen under the prevailing extremely oxidizing conditions is much harder to achieve, even with TWCs. The twin goals of low and efficient fuel use and minimum emissions are increasingly being addressed by research in both the motor vehicle and catalyst industries of the world.

An additional motivation for the search for suitable nitrogen oxide reduction cataysts is that oxides of nitrogen are also produced in various stationary installation processes, like in power plants, nitric acid plants and in most fertilizer and petrochemical industries. NH

is the preferred reductant used in these cases in conjunction

with noble metal or vanadia/titania catalysts [6]. Much is, however, left to be desired at the present time, so far as these catalytic reduction processes are concerned. For one thing, NH

is expensive, and is itself environmentally objectionable, and causes

handling, transport and "slip" (of unreacted NH

) problems [6].

1.4 NO decomposition catalysts Copper-containing catalysts (oxide- and zeolite-based) are the most active for a wide range of reactions of transformation of nitrogen oxides [6, 9]. In particular, Cuexchanged zeolite catalysts show the highest activity both for the direct decomposition of NO (i.e., in the absence of any other reductant) and for the selective catalytic reduction (SCR) of NO (reduction in the presence of other reductants like NH

, hydrocarbons, CO, etc. under highly oxidizing conditions) [6, 9]. Copper is also the crucial component in the enzymes involved in the nitrogen cycle in living organ 4 isms [9]. There is thus a natural reason for choosing copper-based catalysts as a model system for understanding the mechanisms of the transformations of nitrogen oxide.

1.5 Current problems with zeolite-based Cu catalysts Although Cu-exchanged zeolites, particularly ZSM-5, show considerable promise for the removal of NO, several unresolved problems limit the outlook for the successful practical implementation of these catalysts [8, 9]. For instance, under realistic conditions, the catalyst shows poor activity for the direct decomposition process as it degrades rapidly due to dealumination in the presence of water vapor. The industrially more important SCR process has the following additional problems: (i) sensitivity to poisoning, (ii) limited temperature window, (iii) possible formation of harmful by-products, (iv) necessity of post-engine hydrocarbon additions to reach the optimum hydrocarbon/NO ratio, (v) difficulty of manufacturing of suitable shapes with sufficient mechanical resistance to thermal stress and vibrations, and (vi) inability to handle cyclic engine operation, specially varying hydrocarbon emission rates relative to NO

emission.

1.6 Goals of present study The goal of the present study is to investigate, using theoretical techniques, the catalytic decomposition of NO by Cu-exchanged zeolites. The direct decomposition of NO is a much simpler problem to study theoretically than the SCR process. This insight would help identify the important features of a successful NO decomposition-- and, perhaps, an SCR--catalyst, and would aid the rational design of more novel catalysts which are highly active and durable.

In the next Chapter, the structure of real zeolites (before and after cation exchange), and what is currently known about Cu-exchanged zeolites and their activity are discussed.

In Chapter 3, the theoretical methods that were adopted in the present study are outlined. Density functional theory [10-13] has been used entirely, in the determination of equilibrium (reactant and product) and transition state geometries and energies, reaction pathways and vibrational frequencies.

5 Our models of the active Cu sites in zeolites are described in Chapter 4. Binding of CO and NO to these active sites is examined in detail [14]; the electronic and geometric structure, and various binding modes of these adsorbates are thoroughly characterized.

An analogous discussion of Cu-bound gem-dicarbonyl (two CO molecules bound to the same site) and gem-dinitrosyl species [15] follows in Chapter 5. Gem-dinitrosyl species have been deemed important [6, 16-18] as these afford a way for two nitrogen containing species to be in close proximity, possibly facilitating the formation of the crucial N-N and/or the O-O bond.

Chapter 6 elaborates on the calculated vibrational spectrum of various adsorbed species [19]. Vibrational frequencies, which are the signatures of adsorbed species (for instance, reactant, product and transition state molecules, intermediates and spectator species), are measured experimentally by infrared (IR) spectroscopy techniques, and used as a means of characterizing these adsorbed species. In the present study, general factors which affect adsorbate frequencies are discussed, as well as experimental assignments of frequencies confirmed.

Dinitrosyl species are revisited in Chapter 7. An orbital symmetry analysis, based on the Woodward-Hoffmann rules of conservation of orbital symmetry [20-22], is performed on these dinitrosyl species [15] to examine their relevance as possible precursors for a single-step decomposition reaction. None of these species is shown to undergo such a decomposition, and only some of these species are shown to be relevant at all to any type of decomposition.

Chapter 8 addresses directly the important issue of the NO decomposition mechanisms [23]. It is shown that the NO decomposition occurs by a multi-step process, and an atomistically detailed mechanism of a plausible catalytic cycle is outlined.

All the results are summarized in Chapter 9.

6 Chapter 2 Background

. . . progress in catalysis can best be obtained by understanding the kinetic mechanisms of catalytic reactions as opposed to Edisonian research.

--Paul Emmett

2.1 Zeolites--"Boiling Stones" In 1756, the Swedish minerologist A. F. Cronstedt found a silicate mineral which fused readily on heating in a blowpipe flame. This led him to coin the term zeolite (zeo for boil, and lithos for stone, in Greek) to describe minerals that exhibited such behavior. Zeolites are crystalline, microporous aluminosilicates (i.e., composed primarily of Si, Al and O). These naturally occurring minerals can also be synthesized in the laboratory. The channels and cavities in these porous materials have molecular dimensions and bear catalytic sites, and have been compared to the molecular-scale clefts in enzymes, which also have catalytic sites. In addition to finding widespread application as shape-selective catalysts, these materials are also used as ion exchangers (for instance, in detergents) and molecular sieves [24-26].

Structure of zeolites The primary building blocks of zeolites are TO

tetrahedra (where the tetrahedral T

atom is Si or Al), with each apical O atom shared by adjacent tetrahedra, resulting in an overall stoichiometry of TO

. Tetrahedral Al introduces a charge imbalance in the

zeolite network (Figure 2.1); while each SiO

tetrahedron is charge neutral, each AlO

tetrahedron has a net negative charge associated with it, and is usually neutralized

by protons (H

), and in some cases by cations like Na

, K

, etc., depending on the

process by which the zeolite was synthesized. The protons (when the zeolite is in its H form) are the Bro/nsted acid sites [27], and show catalytic activity for various hydrocarbon conversion reactions [3]; the acidity of these Bro/nsted acid protons,

7 Al

O 1-

Si Al

O O O O

O-M +

O O

O 0

4+ OSi Si

O O O O

Figure 2.1: TO

units in zeolites.

which is a crucial factor in determining catalytic activity and selectivity, depends on a lot of factors, like the type of zeolite, Si/Al ratio, etc. Three of the best known purely siliceous varieties (i.e., when there is no Al in the zeolite framework) are quartz, cristobalite and silicalite; the last of these, viz silicalite, is closely related to the zeolite ZSM-5, which is most relevant to the present study.

Given only the constraint that the TO

tetrahedra should be corner sharing, these

tetrahedra can be combined in any of several ways to form the secondary building units (SBU). For instance, when they are arranged as shown in Figure 2.2(a), the SBU of silicalite results. The SBUs of silicalite (or ZSM-5) are linked to form chains, as shown in Figure 2.2(b), and these chains are linked to form layers, shown in Figure 2.2(c). The layers can be linked in two ways: neighboring layers related to each other either by an inversion or a reflection operation; the former results in silicalite or ZSM-5 (shown schematically in Figure 2.2(d)), and the latter in another zeolite called ZSM11. Five-fold (pentasil) and ten-fold rings are evident in Figure 2.2(c); the latter, which are lined by four-, five- and six-fold rings, form sinusoidal channels. A set of straight channels through ten-fold rings are also formed perpendicular to these sinusoidal channels (Figure 2.2(d)). In ZSM-5, the channels are 5-6

* A in diameter;

8 (a) (b)

(c) (d) Figure 2.2: (a) Secondary building unit (SBU) of silicalite; (b) chains formed by linking the SBUs; (c) schematic of silicalite layers formed by side-linking the chains; and (d) schematic of the threedimensional intra-crystalline pore structure of silicalite or ZSM-5. Figure adapted from Ref. [3].

the cavities formed at the intersection of the straight and sinusoidal channels are even larger (ss 9

* A) [6, 24, 28]. ZSM-5 crystallizes in the idealized orthorhombic system

with space group Pnma. It has a total of 288 atoms and 96 T sites in a single unit cell with dimensions 20:1 \Theta 19:9 \Theta 13:4

* A [6, 24, 28].

2.2 Cu-exchanged zeolites The Bro/nsted acid protons can be exchanged for other cations. Zeolites thus provide the framework and the possibility for having highly dispersed, isolated metal cations, analogous to dilute transition metal ion containing solutions in homogeneous cataly 9 sis.

Of particular interest to the present study is the Cu-exchanged form of zeolite ZSM-5--and of Zeolite Y, mordenite and erionite as well, although to a somewhat lesser extent. These are the zeolites that show the highest activities both for the direct decomposition of NO to N

and O

, and for the SCR of NO [6, 9]. Exchange

of Cu ions into ZSM-5 is accomplished by using copper nitrate or acetate solutions under well-specified conditions [29]. The exchanged Cu ions occupy extra-lattice positions in the zeolite framework, just as the Bro/nsted acid H

(or Na

) did before

the exchange. If the exchanged ion is Cu

, then it merely replaces a single Bro/nsted

acid H

(or Na

); each Cu

ion is thus charge compensated by a single framework

Al. Cu

ions, on the other hand, need to be charge compensated by two framework

Al. In high silica zeolites (typical Si/Al ratios ? 15 in ZSM-5), the Al centers may be too far apart on average to bind a dication. Hence, it has been suggested that some or all the Cu

may be present as extra-lattice [Cu

\Gamma

] or [Cu

\Gamma

] complexes

charge-compensating a single framework Al atom [6, 30]. In this connection, the socalled exchange level of Cu in zeolites is of importance. A 100% exchange level is defined as the case when one Cu

is exchanged for every two H

or Na

ions. Cu

exchanged zeolites with an exchange level that exceed the "stoichiometric" 100% are referred to as over-exchanged zeolites. There is general agreement in the literature that better NO decomposition performances are obtained with Cu-over-exchanged catalysts [31-33]. The possibility of such high levels of exchange, and high activity displayed by such over-exchanged catalysts imply that at least some of the Cu

ions

exist as [Cu

\Gamma

] or [Cu

\Gamma

] complexes in the zeolite framework, and that these

complexes are most likely involved in the NO decomposition process [17, 18].

Although the the location and nature of the Bro/nsted acid protons are well understood, large uncertainties exist regarding the location and nature of the active Cu ion sites in Cu-exchanged zeolites. One factor that complicates such investigations is that a variety of extra-lattice Cu sites may be possible, and these may vary with temperature, Cu oxidation state, preparation method (for instance, pH of the Cu solution), and the presence of other species either bound to the ion or to nearby pores [34]. Another factor is the relatively high Si/Al ratios, and hence low concentrations of Cu, in the materials of practical interest. What little is known about the location of Cu ions in ZSM-5 has been deduced from indirect spectroscopic

10 measurements [16-18, 30, 35-51]. For example, electron spin resonance (ESR), which detects only Cu

, provides evidence for at least two distinct sites in dehydrated

ZSM-5; these two are often referred to as "square planar" and "square pyramidal" although their exact nature is unclear [46, 47]. Other measurements [48-50], such as X-ray absorption near edge spectroscopy (XANES) and extended X-ray absorption fine structure (EXAFS), support the notion of highly coordinated Cu

in ZSM-5

and indicate a somewhat lower average coordination for Cu

. Electron paramagnetic resonance (EPR) and photoluminescence spectroscopy (of reduced Cu

ions)

indicates the presence of two types of Cu

, one in the vicinity of two Al atoms,

and another close to a single Al atom (and maybe with an extra-framework O

\Gamma

) [39]. Copper oxocations ([Cu

-O

2\Gamma

-Cu

]) have also been suggested to exist

in the zeolite framework, and, in fact, are believed by some to be the active sites for NO decomposition [37]. It has been shown that a certain manner of copper exchange and pretreatment conditions can result in such oxocations [50]; however, it is not established that these are the only possible catalytic sites.

Cu-exchanged zeolites are also known to undergo a process called autoreduction, a process by which part of the Cu

(presumably, the part that has an extra lattice

\Gamma

or OH

\Gamma

) get converted to Cu

, either by evacuation of the catalyst or at high

temperatures [47]. This spontaneous desorption of oxygen has been observed both directly with XANES [49] and flourescence [51], and indirectly using infrared (IR) vibrational spectroscopy [18,40,41,44] using CO and NO as probe molecules, and the following reaction has been proposed [47]:

2[Cu

\Gamma

]

\Gamma

* )

\Gamma

+ [Cu

\Gamma

]

\Gamma

+ H

O (2.1)

where Z stands for the zeolite.

Mechanisms of NO decomposition Considerable importance is attached to the exact mechanistic steps of catalytic reactions, each of which not only is thermodynamically feasible, but also kinetically favorable due to small activation barriers. Thus, characterization of a catalytic process involves identifying these individual steps.

Numerous IR measurements of the vibrational spectrum of various chemisorbed species on the catalyst have been performed [16-18, 35-39, 41, 44]. Vibrational frequencies corresponding to Cu

NO, Cu

\Gamma

NO, Cu

(NO)

, N

O, N

, other

higher oxides of nitrogen, as well as nitrito and nitrato species have been observed.

11 Several reaction mechanisms have been proposed [16-18, 41, 44, 52] using an analysis of the frequency spectrum of adsorbed species as a function of time, temperature and pressure of the gases, and using analysis from other experiments like photoluminescence, mass balance measurements, etc. Most proposed mechanisms are based on the autoreduction and redox capability of the Cu ions in zeolites, and involve the rearrangement of a Cu

-gem-dinitrosyl complex (i.e., two NO ligands bound to the

same Cu

site), resulting in N

O and [Cu

\Gamma

]

[16, 17, 41]. N

and O

are believed

to be formed by the interaction of N

O with Cu

(leaving behind [Cu

\Gamma

]

) followed by the evolution of O

from from two nearby [Cu

\Gamma

]

, regenerating the

active Cu

site [17]. Other Cu-N

species, like the Cu-nitroso-nitrosyl complex (Cu

(NO

)

\Gamma

(NO) formed by the interaction of a pair of nitrosyl ligands with

[Cu

\Gamma

]

) are also believed to participate in the decomposition process [16, 18, 41].

Of particular interest is also the mechanism proposed by Shelef, which argues in favor of a gem-dinitrosyl coupling mechanism for a single-step NO decomposition of Cu

(NO)

, involving only Cu

sites [52].

Several mechanisms for the SCR reactions of NO in the presence of NH

, CO or

hydrocarbons have also been proposed. These mechanisms are not discussed here, as the present study focuses only on the direct decomposition of NO. For information on SCR mechanisms, Ref. [6, 9] should be referred to.

We end this section with some comments about investigations involving catalysts closely related to Cu-ZSM-5. There have been several attempts at exchanging other transition metal ions like Ce, Pr, Co, into ZSM-5 [53-55, 57]. All such catalysts are extremely susceptible to deactivation by water. Unexchanged H-ZSM-5 has also been examined; it shows very poor activity for NO reduction under realistic exhaust conditions [56]. Adding co-cations like Mg

, Ce

, La

, Co

, Ni

, etc., have

been shown to promote the activity in some cases [57-59]. It has been suggested that the role of these cations is to stabilize the copper ions in zeolites, by occupying hidden sites [58]. It has clearly been felt that in the absence of a fundamental understanding of the role of Cu and the role of zeolites like ZSM-5, progress by an Edisonian approach, as has been customarily been adopted so far, will be slow.

12 2.3 Scope of theoretical techniques in understanding catalytic phenomena

Historically, catalysis has been an empirical science. Experimental techniques, especially surface science approaches, have greatly advanced our understanding of catalytic mechanisms [60-62], but even these techniques provide only incomplete information that may be misleading. For example, surface spectroscopic data tend to be dominated by long-lived species that may only be spectators for the reaction of interest but that are easily misidentified as key intermediates.

A powerful alternative to a purely experimental approach to catalysis is the complementary use of first-principles quantum mechanical calculations [63, 64]. Steady advances in computing power, fundamental theory, and computational algorithms have continually expanded the range of successful applications of these methods. Quantum calculations are already used almost routinely to determine equilibrium geometries, binding energies, and other adsorbate properties for many catalytic systems [63-65]. An even more promising aspect of this approach is its ability to probe entire reaction pathways inaccessible to current experimental methods and thereby assess directly the kinetic plausibility of proposed cataytic reaction mechanisms. A limited number of such studies have already been reported for various homogeneous reactions [66] and for simple heterogeneous reactions on metal surfaces [67, 69] and at Bro/nsted acid sites in zeolites [68, 70].

The chemistry of extra-lattice transition metal ions in zeolites is considerably more complex to study theoretically than that of extra-lattice protons (i.e., Bro/nsted acid sites), both because the former's location may not be well characterized, or even fixed [34], and also because the presence of d electrons makes the treatment of electron correlation effects more important. Thus, while a large body of literature which deals with aspects of zeolites like Bro/nsted acidity, adsorbate interaction with Bro/nsted acid sites, etc., exists [68, 70-77], hardly any calculations are available that focus on transition metal ion exchanged zeolites.

To the best of our knowledge, only four other groups have published calculations which focus on Cu exchanged zeolites [78-82]. All these groups have used cluster models of the Cu sites, and most of them [78, 81, 82] have addressed issues that are only indirectly related to the NO decomposition process.

Ref. [78] examines the interaction of the Cu ion with the zeolite framework and

13 found that the autoreduction reaction proposed earlier [47] (reaction (2.1) above) is feasible on thermodynamic grounds. On the topic of the coordination preference of Cu ions in zeolites, this study indicates that all Cu ions that participate in the autoreduction reaction prefer to be coordinated to two framework oxygens, while those that do not participate in the autoreduction (Cu

sites in the vicinity of two

Al atoms) prefer a low to high degree of coordination, depending on the type of zeolitic ring in which the Cu is present. Blint [81] examines the presence of hydrated Cu ions in zeolites, and points out that the catalytic mechanism in zeolites may have much in common with homogeneous catalysis. Ref. [82] investigates the interaction of CO and NO with Cu

and Cu

ion sites, and concludes that, contrary to experimental

observations, CO and NO bind only to Cu

and not to Cu

Trout et al [79] and Yokomichi et al [80] examine the thermodynamics of a number of plausible NO decomposition mechanistic steps. Studies based on just thermodynamic considerations are not expected to shed any new light on the decomposition mechanism. That a reaction pathway is thermodynamically favored may not prove anything about its feasibility. For instance, to explain the high activation barrier of the reaction 2N O ! N

+ O

, or to even identify the barrier theoretically, one has

to go beyond the favorable thermodynamics of that reaction. To date, no study has probed the kinetic pathways involved in the catalytic NO decompoisition process.

The reasons for the lack of extensive theoretical studies are: (i) difficulties associated with the large system sizes, (ii) several possible locations and oxidation states of Cu in the zeolite framework, and lack of reliable experimental data concerning these, and (iii) most importantly, the complex nature of the NO decomposition and SCR reactions.

14 Chapter 3 Theoretical Methods

The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known,

and the difficulty is only that the exact application of these laws lead to

equations much too complicated to be soluble.

--Paul Dirac

3.1 General comments on quantum mechanics-based calculations

Many physical properties of matter are related in some way to total energies. For instance, the equilibrium structure of a molecule or crystal at 0 K is the one that has the lowest total energy; surfaces, defects and other (meta)stable structures correspond to local minima in the total energy hypersurface in phase-space

; the curvatures of

the total energy hypersurface at energy minima are related to the vibrational and phonon frequencies, force constants and elastic moduli; activation energies of chemical reactions, diffusion and phase transitions are "passes" in the total energy hypersurface between the local minima ("valleys") corresponding to the reactants and products; and so on.

Thus, many predictive theories of matter rely on some prescription for calculating total energies. In searching for such a predictive theory, one would assume matter to be made of a large number of constituent parts and would postulate laws governing the behavior of these constituent parts, from which the laws of the matter in bulk could be deduced and its properties understood. However, this would not complete the explanation since the question of the structure and stability of the constituent

The dimensionality of the hypersurface is 3n \Gamma 6 (3n \Gamma 5 for linear systems), if n is the number

of particles (atoms) in the system under consideration.

15 parts is left untouched. To go into this question, it becomes necessary to postulate that each constituent part is itself composed of still smaller, more "fundamental" parts, in terms of which behavior of the larger parts is described. There is no end to this procedure, of course, and depending on the problem under study, and based on experience and prior knowledge, one decides on what the fundamental constituents should be.

It turns out that most of low-energy physics, chemistry, biology and materials science can be explained, in principle, by the quantum mechanics of electrons and ions. Although philosophical questions still remain concerning the interpretations and completeness of this theory, those things that modern quantum theory predicts are predicted with incredible accuracy. Quantum mechanics-based calculations have an additional appeal due to the fact that they are inherently parameter-free and do not rely on any experimental input other than the values of the electronic and ionic charges and masses, and so have been variously called as "First principles" or "ab initio" methods.

Quantum mechanics postulates that a certain entity, viz., the wavefunction, \Psi , contains all the information about the system; hence, a knowledge of the wavefunction implies complete knowledge of the system. Unfortunately, the wavefunction, being a function of several variables, i.e., of the positions of all the electrons and nuclei in the system, is very hard to be determined exactly for even systems as simple as the He atom. Any practical implementation of the equations of quantum theory involves a series of approximations, leading to a simplification of the many-body wavefunction. For instance, most implementations use the Born-Oppenheimer approximation [83], which is essentially a separation of the electronic and nuclear coordinates in the manybody wavefunction. This approximation is valid because of the large differences in mass between the electrons and nuclei, and the fact that the forces on all particles are approximately the same, implying that the electrons respond essentially instantaneously to the motion of the nuclei. Thus, for a given set of nuclear coordinates, the electronic problem is solved and the many-electron wavefunction determined; the nuclear problem is subsequently solved using the solution to the electronic problem. It is customary to treat the dynamics of the electrons quantum mechanically, and that of the nuclei classically.

Although considerably simplified, solution of the many-electron problem contin 16 ues to be formidable. Several techniques, such as configuration interaction (CI), pair and coupled-cluster, multiconfiguration self-consistent field (MCSCF) and Green's function methods, diffusional and variational quantum Monte Carlo (QMC) are available to treat many-electron systems [84, 85], either in terms of the many-electron wavefunction itself or in terms of one-electron wavefunctions (with the many-electron effects adequately incorporated). In recent years, density functional theory (DFT) has rapidly gained popularity because of its computational expedience, making it amenable to treat large-scale systems at an accuracy comparable to that of the other methods listed above, in a fraction of the time. Density functional methods have been used successfully in studying the electronic structure of a wide variety of solids, both crystalline and amorphous, defects in solids, molecular structures, and in determining transition-state structures and activation barriers. They have yielded reliable thermochemical data, force fields, dipole moments and frequencies, and have helped in assignments of NMR, photoelectron, ESR and UV spectra [86-89].

3.2 Density functional theory (DFT) Density functional theory was formulated by Hohenberg and Kohn [10], and later elaborated by Kohn and Sham [11]; it is an exact theory, in principle, and an alternative formulation of Schr"odinger Quantum Mechanics. While the chief element of the latter, as mentioned earlier, is the wavefunction, that of DFT is the electronic charge density (or the fictitious one-electron wavefunction, OE

, in the Kohn-Sham

version, discussed below). In what follows, the essence of DFT is outlined. For more details, Refs. [10-13] should be referred to.

Consider a set of N nonrelativistic, interacting electrons in a nonmagnetic (spinpaired) state in an external potential v(r) (for instance, Coulomb potentials due to point nuclei); electron spin and relativistic effects can be incorporated in the following discussion in a relatively straightforward manner. The (electronic) Hamiltonian for this system is:

^ H j

^ T +

^ U +

^ V (3.1)

where

^ T ,

^ U and

^ V are the total electronic kinetic energy operator, the repulsive interelectronic interaction energy operator and the attractive interaction energy operator between the electrons and the external potential, respectively, and are defined as

17 follows (in atomic units):

^ T j \Gamma

N X

;

^ U j

N X

ij;i6=j

1 jr

\Gamma r

;

^ V j

N X

v(r

) (3.2)

The first theorem of Hohenberg and Kohn [10] proves that the specification of the ground state charge density, ae(r), determines the external potential, v(r), uniquely (to within a trivial additive constant). Since v(r) fixes the Hamiltonian

^ H, and

since

^ H, via the Schr"odinger equation, fixes the ground state wavefunction, \Psi , ae(r)

determines all the ground state properties like the total energy, kinetic energy, force constants, electrical polarizability, etc. This theorem, thus, establishes ae(r) as the fundamental element of any electronic system. From a philosophical point of view, this fact has the following appeal: while \Psi is merely a mathematical abstraction, with no physical reality attached to it, ae(r) is very much an observable; a theory based on tangibles has always remained attractive.

The second theorem of Hohenberg and Kohn [10] establishes the equivalent of the variational theorem of Quantum Mechanics. It states that the total energy (which has been proved by the first theorem to be a functional of the charge density, ae(r)) is minimized by that ae(r) which corresponds to the true ground state.

The total energy is written in the following form:

E[ae(r)] = h\Psi j

^ Hj\Psi i = T [ae(r)] + U [ae(r)] +

v(r)ae(r)dr (3.3)

Both T [ae(r)] and U [ae(r)] have many-body and quantum effects buried in them; these terms are extracted and added, leaving behind just the one-electron and classical terms, viz., the kinetic energy of a set of non-interacting electrons with the same charge density, ae(r), and the classical Coulomb interaction due to ae(r), respectively. Thus,

T [ae(r)] + U [ae(r)] = T

[ae(r)] +

Z Z

ae(r)ae(r

)

jr \Gamma r

drdr

+ E

[ae(r)] (3.4)

where T

[ae(r)] is the kinetic energy of a set of non-interacting electrons with the same

ae(r), and E

[ae(r)] is the exchange-correlation energy, the sum total of all quantum

many-body contributions to the total energy. E

[ae(r)] (like T [ae(r)] + U [ae(r)]) is

a universal functional of ae(r), i.e., there is a rigorous one-to-one mapping between E

[ae(r)] and ae(r). Unfortunately, the functional dependence of E

[ae(r)] on ae(r) is

largely unknown. Most of the efforts at making DFT a more reliable and predictive tool centers around a search for better and better approximations for E

[ae(r)] (see

below).

18 The total energy functional can now be written in the following form:

E[ae(r)] = T

[ae(r)] + V

[ae(r)] (3.5)

where

[ae(r)] =

v(r)ae(r)dr +

Z Z

ae(r)ae(r

)

jr \Gamma r

drdr

+ E

[ae(r)] (3.6)

Now, E[ae(r)] in eqn. (3.5) is identical to that of a hypothetical system of noninteracting electrons with the same ae(r) as the real system, but moving in a different potential \Phi , given as:

\Phi (r) =

ffiV

[ae(r)]

ffiae(r)

= v(r) +

ae(r

)

jr \Gamma r

ffiE

[ae(r)]

ffiae(r)

(3.7)

Kohn and Sham noted [11] that the problem of a system of non-interacting electrons in an external potential \Phi is completely soluble. The solution of this problem is the Slater determinant of the single-particle wavefunctions, OE, which satisfy the Schr"odinger equation (\Gamma (1=2)r

+ \Phi (r))OE(r) = fflOE(r). Kohn and Sham thus obtained a set of single-particle Schr"odinger-like or Hartree-Fock-like equations for the system of interacting electrons:

\Gamma

+ v(r) +

ae(r

)

jr \Gamma r

+ v

(r)

(r) = ffl

(r) (3.8)

ae(r) =

N X

j=1

jOE

(r)j

(3.9)

(r) = ffiE

[ae(r)]=ffiae(r) (3.10)

These equations are, of course, similar to those in the Hartree or the Hartree-Fock approximation

, and like in these cases, the Kohn-Sham equations need to be solved

self-consistently. The total ground state energy for the real system, in terms of the "orbital" energies, ffl

, can be shown to be:

E =

N X

ffl

ae(r)ae(r

)

jr \Gamma r

drdr

\Gamma

(r)ae(r)dr + E

[ae(r)] (3.11)

where ffl

and ae(r) are all self-consistent quantities.

It may seem at first sight that the Kohn-Sham formulation literally undoes what the Hohenberg-Kohn theorems accomplished; while the latter tried to shift the emphasis from the wavefunction to the charge density, the former has brought back

Indeed, the Kohn-Sham equations reduce to the Hartree equations if v

or E

is ignored.

19 wavefunctions into the discussion. It should, however, be noted that the main result of the Hohenberg-Kohn theorems is the existence of a universal, although unknown, functional E

[ae(r)]. Having established that, the Kohn-Sham formalism sets up a

set of local equations merely as a computational procedure, that are much easier to solve than the non-local Hartree-Fock equations (which do not even treat the electron correlation effect).

Approximate density functional theory To put the Hohenberg-Kohn-Sham theory to practical use, one needs to have at least a good approximation for E

[ae(r)], as its exact form is unknown. It is dealt with

in the following manner. First, we define an exchange-correlation energy density functional, ffl

[ae(r)], as follows:

[ae(r)] =

ffl

[ae(r)]ae(r)dr (3.12)

The gradient series expansion of ffl

[ae(r)] for the case of a slowly varying ae(r) turns

out to be:

ffl

[ae(r)] = ffl

(ae(r)) + ffl

(ae(r))jrae(r)j

+ higher order terms (3.13)

Quantities like ffl

(ae(r)), ffl

(ae(r)), etc., are functions of ae(r). When only the zeroth

order (local) term is retained we have what is called the local density approximation (LDA):

LDA

[ae(r)] =

ffl

(ae)ae(r)dr (3.14)

ffl

(ae) is the exchange-correlation energy per particle of a uniform, interacting electron

gas of density ae, and is known nearly exactly [90, 91].

The next level of approximations are the so-called generalized gradient approximations (GGA) [92-95], which include the dependence of ffl

on the gradient of the

electron density as well. The functional form of this higher order term is determined seperately for exchange [92, 93] and correlation [94, 95] effects, so as to incorporate the known asymptotic behavior, in real- and reciprocal-space, of these quantities, and further analyses (random phase approximation (RPA), electronic polarizability and response function considerations, etc.).

The lack of knowledge of the exact exchange-correlation functional results in an intrinsic limitation of current DFT. Although more and more accurate forms of this functional are currently being developed, there seems to be no systematic way to achieve an arbitrarily high level of accuracy. This is in contrast to traditional

20 quantum chemistry methods, where such an accuracy is, in principle, possible, given a sufficiently powerful computer.

3.3 Performance of approximate density functional methods Notwithstanding the above limitation, approximate DFT has become extremely popular due to its remarkable performance. Unlike Hartree-Fock-based calculations, which typically scale as N

or N

, DFT-based methods scale as N

or better. Properties like equilibrium and transition state geometric structures, vibrational frequencies (at equilibrium and at transition states), charge moments and densities are described as well by LDA methods as by the best available post-HF schemes (within a few percent of experiments) [88, 89], in systems with "ordinary" chemical bonds (unusually long bonds, like those due to H-bonding and van der Waals interaction, excluded); bond energies, cohesive energies and relative energies (whenever calculated with respect to a system which has very non-uniform charge density, like in an atomic system), although grossly over-estimated (by about 20 %) at the LDA level, are described with almost chemical accuracy (\Sigma 5 kcal mol

\Gamma 1

) by GGA methods [88, 89].

Studies of potential energy surfaces, reaction pathways and activation energies are quite rare [66, 96]. Available data indicate that while reaction pathways are well described by both LDA and GGA, LDA performs poorly in describing reaction pathway energetics (including activation energies), but GGA results are more in accord with experiments [66, 97-99].

3.4 Implementation used in the present study Practical implementations involve expansion of the one-electron molecular orbitals, OE

, and charge density, ae(r), in terms of a known set of functions (like plane waves,

Gaussian-type functions, Slater-type functions, etc.), and conversion of the KohnSham equations (3.8)-(3.10) into a matrix eigen-value problem. Several LDA and GGA parametrizations are also available for E

[ae(r)] [91-95].

Calculations reported here were performed using the Amsterdam Density Functional (ADF) code [100], which employs Slater-type basis functions for expansion of the molecular orbitals and charge density. A split-valence plus polarization molecular orbital basis set was used for all atoms save Cu, for which a triple-zeta d orbital

21 representation was used. Atomic core orbitals were frozen in all calculations, including the 1s orbitals for C, N, and O and the 1s, 2s, and 2p orbitals for Cu. ADF employs a large charge density basis, and the charge fitting errors are uniformly small. The molecular grid used to perform numerical integration within ADF is controlled by a single accuracy parameter. An integration parameter of at least 4.5 was used in all calculations involving equilibrium geometries and a value of at least 5.5 in those involving transition state structures. These integration meshes were found to be more than sufficient to ensure convergence of geometries and energies to the precision quoted in this work.

Equilibrium geometries were obtained by gradient optimizations within the local (spin) density approximation [L(S)DA] parametrization of Vosko, Wilk and Nusair (VWN) [91], followed by single-point energy calculations using the gradient-corrected Becke exchange and Perdew correlation (BP86) functionals [92,94]. A limited number of calculations were performed using the full gradient-corrected potentials in the optimization procedure. In general, the gradient corrections tend to slightly increase the optimized bond lengths uniformly, but in all cases examined BP86 binding energies calculated at the VWN and BP86 geometries differ negligibly.

For reference against the larger Cu-containing clusters, and as simple benchmarks of the methods employed here, Table 3.1 contains comparisons of the calculated and experimental geometric, energetic, and vibrational properties of CO, NO, and H

O. As expected, the LDA method performs very well for both the structures and

vibrational spectra, but systematically overestimates the atomization energies. The BP86 functional also overestimates these energies, but by a smaller margin.

While equilibrium geometries were determined by optimization of the local internal coordinates of molecules, transition state searches were performed by optimization of natural internal coordinates [104, 105]; natural internal coordinates are suitable (symmetry-adapted) linear or non-linear combinations of the local internal coordinates. The reason for not preferring regular internal coordinates is that these coordinates are, in general, strongly coupled, leading to large off-diagonal Hessian (second energy derivative) matrix elements, which results in slow or no convergence during transition state geometry optimizations. Natural internal coordinates make the Hessian diagonally dominant, and so expedites the convergence process. As the option of using natural internal coordinates was not available in ADF, the optimizer

22 Table 3.1: Comparison of Calculated and Experimental Molecular Parameters for CO, NO, and H

O. Distances in

* A, angles in degrees, energies in kcal mol

\Gamma 1

and frequencies in cm

\Gamma 1

CO NO H

molecular geometries

LSDA r

: 1.131 r

: 1.154 r

: 0.980

HOH

: 104.5

exp 1.128

1.151

0.958

104.5 atomization energies

LSDA 294.7 191.0 251.5 BP86 270.6 164.1 230.6 exp

256.4 149.8 219.3

harmonic vibrational

frequencies

LSDA 2186 1941 a

: 1574, 3679

: 3772

exp 2170

1904

: 1653, 3825

: 3936

Ref. [101].

Ref. [102].

Ref. [103].

in GAMESS [106] (which had this utility built-in) was used. ADF was used to calculate the initial hessian, and energies and gradients at each optimization step [107].

In the following chapters, we present the results of our calculations performed using small cluster models of Cu-exchanged zeolites.

23 Chapter 4 Models of Cu sites and their interaction with CO and NO

In this chapter, we first examine the coordination preference of otherwise unligated isolated Cu ions in zeolite-like ligand environments, by calculating the binding energy, geometry and electronic structure as a function of the metal coordination number and oxidation state. We then study the interaction of CO and NO with our model Cu sites. Although CO is not involved in the direct decomposition of NO, it may play a role in the SCR of NO. Besides, CO has been employed extensively as a spectroscopic probe in studies of Cu-exchanged sites in zeolites [17, 38, 40, 108, 109], and the interaction of CO with transition metal ions is well understood theoretically. Model copper carbonyl complexes, thus, provide a ready reference system for our computational study.

4.1 Properties of zeolite-bound Cu ions In real zeolites, a Cu ion is envisioned to be coordinated to the aluminosilicate framework through an approximately equatorial band of sp

hybridized bridge O atoms.

The positively charged Cu ions are neutralized by nearby countercharges, like `tetrahedral' Al

\Gamma

, and perhaps by extra-lattice O

\Gamma

or OH

\Gamma

as well, especially in overexchanged zeolites [6, 30]. The zeolite lattice relaxes locally to accomodate the bare or ligated Cu ion, but the lattice structure itself remains essentially unaltered [110].

Because of the absence of detailed information as to the location of exchanged Cu ions, and the probable absence of unique Cu sites, a hierarchy of models of varying local coordination of Cu ions in zeolites are considered. The simplest of these models is, of course, a bare Cu

ion (n = 0-2). The next set of models focus primarily on

the immediate coordination environment of Cu in zeolites. Thus, the coordination of Cu

ions to its nearest neighbor framework oxygen atoms (terminated by H

atoms) is treated explicitly. These `water-ligand models' clearly neglect some of the

24 important features of the true zeolite coordination environment, such as the topology of the zeolite, the local zeolite charge introduced by Al substitution, and the longrange electrostatic field of the zeolite; it thus cannot be expected a priori to provide a quantitatively accurate description of the chemistry of zeolite-bound Cu ions. It thus seems natural to move on to the next level in the heirarchy of models, for instance, by explicitly considering framework Si and/or Al atoms. A recent study by some of our co-workers has focussed on such larger models, and has, in fact, shown that the water-ligand models actually provide a remarkably accurate description of local chemical properties at nominal Cu(0) and Cu(I) sites and at nominal Cu(II) sites with a sufficiently realistic (i.e., high) coordination [136]. In addition, it has also been shown that effects due to a more extended zeolite framework represent relatively minor perturbations on the dominant effects treated in simple cluster models like those considered here [14, 19, 78, 136-138]. The water-ligand models, which are the main foci of the present chapter, are thus exceedingly useful for exploring the trends in molecular and electronic structures and energetics that accompany variations in Cu coordination and oxidation state.

The simple models discussed in the present chapter are generically referred to as [Cu(H

]

, x = 0-4, n = 0-2. Symmetry constraints are imposed to maintain

`zeolite-like' coordination, and geometry optimizations within these constraints are performed to simulate the relaxation of the zeolite lattice and adsorbates. Figure 4.1 shows representative sketches of the various Cu-H

O cluster geometries considered.

In the one-coordinate case, which in our model corresponds to a Cu ion bound to a single bridge site within a zeolite, both planar (C

) and pyramidal (C

) geometries

were examined; while both types of minima were found, they differed very little in energetic and qualitative features, and we report only the lower energy C

results. In

the higher coordination cases, the clusters are optimized under the constraint of C

symmetry, with the water ligands pyramidalized at the oxygens.

In all cases it is possible to locate an LDA energy minimum satisfying the prescribed geometry constraints. These model structures are, in general, not global minima on their respective potential energy surfaces. In fact, in many cases they are saddle points with respect to relaxation of the symmetry constraints, for instance toward rotation of the H

O ligands. The purpose here is to construct generic models

of Cu coordination within zeolites, not of Cu-H

O complexes. That the Cu-H

25 Cu

O Cu

Y O

CuO O Cu

O O

Y O

Cu O O

Y O

CuO

Cu O O O

Y O

Cu O O O

O O O

Figure 4.1: Molecular structures used in the Cu(H

calculations (first column), the linearly

coordinated CO and NO structure calculations (second column), and the bent CO and NO structure calculations (third column).

structures reported here are not global minima, or are not necessarily minima at all, has no consequence for their use as models of Cu-ZSM-5.

Geometries. Table 4.1 contains the LDA-optimized results for the Cu-H

O complexes in the coordination geometries considered. Not surprisingly, as the charge on the system decreases, the optimal Cu-O bond length tends to increase, for example from 1.957

* A in Cu(H

to 2.102

* A in Cu(H

to 2.165

* A in Cu(H

. These

optimal distances are not unreasonable for coordination of a Cu ion within a zeolite; for instance, the distance from the center of a six-membered ring in ZSM-5 to the

26 Table 4.1: Selected geometric parameters and Mulliken charges [LSDA], and binding energies [BP86] of [Cu(H

]

complexes. Distances in

* A, angles in degrees, and energies in kcal/mol.

Cu-O

O-Cu-X

Mulliken BE

Cu charge Cu(II) systems (n = 2)

x = 1 1.912 1.499 \Gamma 128:9 x = 2 1.835 91.6 1.299 \Gamma 209:8 x = 3 1.946 84.0 1.112 \Gamma 252:0 x = 4 1.957 87.2 1.177 \Gamma 296:1 Cu(I) systems (n = 1)

x = 1 1.882 0.860 \Gamma 39:8 x = 2 1.861 88.1 0.733 \Gamma 80:9 x = 3 1.988 90.1 0.573 \Gamma 92:5 x = 4 2.102 89.9 0.602 \Gamma 96:3 Cu(0) systems (n = 0)

x = 1 2.048 \Gamma 0:071 \Gamma 2:4 x = 2 2.015 73.1 \Gamma 0:068 \Gamma 5:6 x = 3 2.006 87.9 0.135 \Gamma 0:4 x = 4 2.165 87.0 0.335 +1:5

Angle between Cu-O vector and vertical axis of symmetry;

Energy of reaction:

+ xH

O ! [Cu(H

]

, in kcal/mol;

Binding energy referenced to spherically averaged Cu

ion.

four nearest oxygen centers is approximately 2.27

* A, only slightly larger than the calculated relaxed distances in the water model. For a given overall charge, the optimal geometric parameters vary over approximately 0.20

* A as the coordination number is

changed. In each case, the optimal Cu-O bond distance decreases when a second water is added, but increases as the third and fourth waters are added, with the biggest variation in Cu-O bond distance found for Cu

. Hartree-Fock calculations on similar

[111-113] and Cu

[114] systems yield the same qualitative trends, but much

longer absolute bond lengths, while HF calculations on one- and two-coordinate Cu

agree reasonably well with the LDA results [115]. A limited number of geometry opti 27 mizations performed using gradient-corrected exchange-correlation functionals yield Cu-O bond lengths that are intermediate between the LDA and Hartree-Fock results, but in all cases the LDA length trends are reproduced.

In almost all cases in the water models the Cu ion chooses a location between the planes defined by the oxygen centers and the hydrogen centers. The one exception is Cu(H

, where the Cu ion resides above both the oxygen and hydrogen planes.

The greater pyramidalization at Cu in this case arises from strong mixing between the high lying, partially occupied d

\Gamma y

;xy

and d

xz;yz

orbitals permitted under C

symmetry.

Electronic Structure. The electronic structures of the Cu-H

O complexes are well

described in terms of a primarily electrostatic, ion-dipole interaction between water ligands and a Cu ion in an oxidation state equal to the overall charge of the cluster. As examples, molecular orbital diagrams for Cu(H

(x =1-4) are presented in

Figure 4.2. The atomic Cu

+ 1

S (d

) electron configuration is evident in the highest

energy orbitals of the complexes, and these predominantly d orbitals are split in fashions characteristic of the particular coordination geometries. For instance, in the four-coordinate case the d orbitals exhibit the characteristic square-planar crystal field splitting of one orbital above four, and in the 3-fold case the characteristic two above three trigonal splitting is evident. The molecular orbital analysis is essentially unchanged for the other net charges and oxidation states. Thus, atomic Cu

has a

D (d

) ground electronic configuration, and these d orbitals are split by the oxygen

crystal field just as in the Cu

case. As a result, C

Cu(H

has a Jahn-Telleractive (

E) ground state. Similarly, Cu

has a

S (d

) ground configuration, and

the high-energy 4s orbital remains the highest occupied orbital in the Cu

water

complexes. Mulliken population analysis confirms that, in both the Cu

and lowcoordinate Cu

cases, the majority of the spin density resides on the Cu center. The

relative energies of the d levels and the oxygen p manifold do vary with the formal oxidation state of the Cu ion, so that in the Cu

case, the metal and oxygen levels

are well separated, in the Cu

case they approach more closely, and in the Cu

case

they are strongly mixed. These interactions further contribute to the ligand field splitting of the Cu d levels.

The qualitative features of this electronic structure analysis are expected to carry over to actual zeolite systems. Binding of the Cu ions to the zeolite framework will

28 Figure 4.2: Molecular orbital diagrams for Cu(H

, x = 1-4. For ease of interpretation, the

orbitals are shifted vertically so that the centroids of the d bands are approximately the same energy.

occur primarily through electrostatic interactions, with secondary orbital interactions between oxygen p and metal ion d levels. Because of the importance of electrostatics, Cu ions in real zeolites will be strongly attracted to framework oxygens in negatively charged regions near Al-substituted sites. This localized attraction will provide an additional perturbation on the geometries, electronic structures, and binding energies of exchanged Cu ions, as well as their interactions with CO and NO. Nonetheless, we expect the qualitative trends predicted by the simple water model to be preserved. Further, the results in the next section suggest that both Cu

and Cu

can bind

strongly to a zeolite framework without aluminum immediately adjacent, although

29 proximity to aluminum is clearly desirable. The relatively large separations between aluminum atoms at high Si/Al ratios are thus not necessarily inconsistent with the binding of bare Cu

Binding Energies. Table 4.1 also contains the BP86 binding energies for formation of the Cu-H

O complexes from isolated Cu ions or atoms and water molecules. In

general, the absolute binding energies increase with the Cu charge, as one would expect for an interaction dominated by electrostatic effects. Thus, Cu

strongly

binds up to four water molecules, Cu

binds up to four but more weakly, and Cu

binds one or more than one water weakly or not at all.

Both experimental [118-120] and ab initio computational [111-113] results for successive binding of H

O to Cu

have previously been reported. Agreement between these earlier results and those reported here is excellent (within 3 kcal mol

\Gamma 1

compared to the best experiments [120] and calculations [113]) for the first three binding energies. Our calculated fourth binding energy is 10 kcal mol

\Gamma 1

less than the

experimental result, a discrepancy that disappears when our model square planar geometry is replaced with the experimental tetrahedral one. This remarkable level of agreement, while reassuring, is in part fortuitous, given the neglect here of zero-point vibrational energy and basis-set superposition errors (BSSE), among other factors. Agreement between ab initio calculations on one- and two-coordinated Cu

[111,115]

and the present work is not quite as impressive, with discrepancies as large as 30 kcal mol

\Gamma 1

for the first binding energy. No experimental data are available for the Cu

systems, so the relative accuracies of the calculations cannot be assessed. Clearly, further work is needed to resolve the discrepancies. We believe the BP86 binding energy results to be more than adequate for the qualitative analyses reported here.

Table 4.2 presents the BP86 binding energies in a more suggestive format useful for consideration of binding within zeolites. The second column of Table 4.2 contains the incremental energies for successive additions of H

O ligands to the Cu ions. In

general, the incremental binding energies are found to decrease as the number of substituents increases. For Cu

, the first and second added waters are each bound

by almost 40 kcal mol

\Gamma 1

, while the third and fourth are bound by a total of only

16 kcal mol

\Gamma 1

. Cu

is known to form primarily low-coordinate (four or fewer ligand)

complexes [121], and two-coordinate, linear structures are thought to be particularly stable because of the availability of favorable sd metal hybridization [113,118]. These

30 Table 4.2: BP86 binding energies for addition of H

O, CO and NO to [Cu(H

]

complexes, in

kcal mol

\Gamma 1

O +CO +NO

-129 -96 -159

Cu(H

-81 -55 -99

Cu(H

-42 -39 -73

Cu(H

-44 -30 -57

Cu(H

-5 -35

-40 -38 -35

Cu(H

-41 -42 -35

Cu(H

-12 -19 -15

Cu(H

-4 -21 -16

Cu(H

-19 -16

-2 -14 -27

Cu(H

-3 -16 -37

Cu(H

+5 -16 -35

Cu(H

+2 -20 -39

Cu(H

-15 -41

binding energies are somewhat sensitive to the chosen coordination geometry, but the general trends are constant. For instance, tetrahedral Cu(H

is more stable than

square planar Cu(H

, but only by 8 kcal mol

\Gamma 1

. Extrapolating these results to

Cu-exchanged zeolites, we expect Cu

to strongly bind to at least two bridge oxygens.

Higher coordination sites are energetically preferred, but only by a relatively small margin, and will be entropically less favorable. As we will show below, this preference for relatively low-coordination geometries persists when CO or NO is added to Cu+.

In contrast, the incremental H

O binding energies for Cu

are all very large,

with the fourth water ligand bound by 44 kcal mol

\Gamma 1

. Cu

is known to prefer to

form high-coordinate complexes with small ligands in aqueous solution, including the nearly octahedral Cu(H

[121]. In zeolites, we infer that Cu

will have

a strong preference for high-coordination sites and in hydrated samples will have a large affinity for extralattice H

O. These preferences are consistent with ESR and

31 other experimental data on Cu-exchanged zeolites, including ZSM-5 [34, 45, 46]. This preference for high coordination numbers persists when either CO or NO is bound to Cu

Finally, the calculations indicate that Cu

is only very weakly bound to up to two

water ligands and can bind no more than that. Energy decomposition analysis indicates that the binding is primarily electrostatic, arising from partial charge transfer from Cu to H

O, with only a small (28%) orbital relaxation contribution. Cu

is not

expected to interact strongly with a zeolite host.

4.2 Interaction of CO with Cu sites CO is both adsorbed by and active in the chemistry of Cu-exchanged zeolites. Hightemperature treatment of Cu

-exchanged zeolites with CO results in reduction of the

metal atoms to Cu

, and binding of CO to Cu sites within zeolites is well-known [122].

CO is known to be a reductant for NO over Cu-ZSM-5 [31], and may play a role in the selective catalytic reduction of NO. Further, CO is a sensitive spectroscopic probe for examination of binding sites; it has a distinct, readily detectable infrared absorption feature that is highly sensitive to its coordination environment.

For these reasons, and because the binding of CO to metal atoms is better understood than the binding of NO, it makes sense to consider first the binding of CO to zeolite-bound Cu ions. For this purpose, we build upon the Cu-H

O models by

introducing a CO ligand in the vacant axial coordination site and investigate the energetic and structural trends as a function of cluster charge and coordination number. Before discussing the Cu-H

O-CO model results, however, it is constructive to

consider CO binding to otherwise unligated Cu ions.

CuCO

Table 4.2 contains geometry and energy results for CuCO

(n = 0; 1; 2), and Figure 4.3 contains molecular orbital diagrams for the three. The binding of CO to metal ions is usually described in terms of donation from the occupied, antibonding 5oe orbital of CO into vacant metal orbitals and back-donation from occupied metal d orbitals into the vacant, antibonding CO 2ss orbitals [121]. These two interactions have opposite effects on the C-O bond length and strength, the former tending to shorten and strengthen the bond and the latter tending to lengthen and weaken it.

32 ds dd

ds, 5s1p

5s,ds

5s 1p

4s 4s

ds dd dp

1p 5s

dp dp ds, d ds, d

i`i' i^5s, 1p

4s, 2p 1 eV

Cu2+

1.99 A* 1.11 A*

Cu+

C O

1.80 A* 1.12 A*

Cu0

1.87 A*

1.15 A*

141o

Figure 4.3: Molecular orbital diagrams for CO on the bare Cu atom and ions. For ease of interpretation, the orbitals are shifted vertically so that the tops of the spin-up d orbital manifolds have the same energy.

The two are conveniently represented by the following resonance structures:

MCjO ! M=C=O The relative efficiency of these two modes is controlled by the spatial and energetic match between the metal and CO orbitals. The effects of oe donation and ss backdonation are evident in the molecular orbital diagrams in Figure 4.3: the oe donation resulting in destabilization of the d

orbitals and the ss back-donation resulting in a

stabilization of the d

orbitals. The magnitudes of these interactions vary considerably with the net charge, with the greatest amount of orbital interaction found in

33 Table 4.3: Selected geometric parameters [LSDA] and binding energies [BP86] for [Cu(H

(CO)]

complexes. Distances in

* A, angles in degrees and energies in kcal mol

\Gamma 1

C-O Cu-C Cu-C-O Cu-O BE

Cu(II) systems (n = 2)

x = 0 1.112 1.987 180.0 -95.7 x = 1 1.112 1.886 179.5 1.886 -184.1 x = 2 1.115 1.932 180.0 1.895 -248.6 x = 3 1.117 1.882 180.0 1.990 -282.2 x = 4 1.118 1.869 180.0 1.999 -301.5 Cu(I) systems (n = 1)

x = 0 1.121 1.818 180.0 -38.1 x = 1 1.124 1.784 180.0 1.870 -81.8 x = 2 1.129 1.788 180.0 2.012 -99.9 x = 3 1.133 1.787 180.0 2.075 -113.9 x = 4 1.134 1.793 180.0 2.184 -115.7 Cu(0) systems (n = 0)

x = 0 1.152 1.867 140.5 -13.9 x = 1 1.167 1.830 143.2 1.978 -18.4 x = 2 1.171 1.810 150.2 2.122 -22.0 x = 3 1.173 1.831 146.6 2.172 -20.4 x = 4 1.144 1.803 168.2 2.212 -19.8

Energy of reaction: Cu

+ xH

O + CO ! [Cu(H

CO]

;

Energy referenced

to spherically averaged Cu

ion.

the Cu

case, followed by Cu

and lastly Cu

CO has an experimental bond length of 1.128

* A, which is reasonably well reproduced at the LDA level of theory used here (1.131

* A, Table 3.1). CO binds to Cu

in a linear fashion, strongly mixing with and splitting the Cu d orbitals to generate a (d

)

(

\Sigma

) ground state. The calculated C-O bond length decreases by 0.019

* A relative to the free molecule, suggesting that oe donation from CO to Cu

dominates

the Cu

-CO interaction. The Cu

-CO bond energy is calculated to be 96 kcal

mol

\Gamma 1

. While large, this binding energy is considerably less than that found for the

34 Cu

-OH

bond. Further, the calculated Cu

-CO bond length is 0.08

* A greater

than the Cu

-OH

bond length. These results are consistent with a large electrostatic contribution to bonding to Cu

, with the greater polarity of H

O relative to

CO resulting in the stronger Cu

-OH

bond. As we shall see, the preference for

O ligands over CO persists in the larger models incorporating both H

O and CO

ligands.

While CuCO

is strongly bound with respect to fragmentation into Cu

and

CO, it is, in fact, unbound (by 65 kcal mol

\Gamma 1

) with respect to separation into Cu

and CO

. In other words, a bare Cu

ion is capable of oxidizing CO, and CuCO

is not a stable species. Addition of H

O ligands decreases the oxidizing power of

and stabilizes (H

Cu-CO

against loss of CO

. The dissociative behavior

of CuCO

is similar to that of CuNO

, which is discussed in greater detail later.

also prefers polar ligands, although the preference is not as great as in the

case. Cu

has a d

(

S) ground configuration and binds CO in a linear fashion,

yielding a

\Sigma

ground state [174,175]. The C-O bond length decreases relative to free

CO by 0.010

* A at the LDA level, again suggesting that oe donation is more important

than ss back-donation in the bonding interaction. Ab initio calculations including electron correlation predict a similar decrease in C-O bond length [174, 175]. The BP86 Cu

-CO bond energy (38 kcal mol

\Gamma 1

) agrees well both with these ab initio

calculations (33.4 kcal mol

\Gamma 1

including zero-point and relativistic effects) [174, 175]

and with a recent experimental determination (35.5

* A 1.6 kcal mol

\Gamma 1

) [123]. Energy

decomposition analysis indicates that electrostatics dominate the Cu

-CO interaction, but not to the extent found for Cu

. Thus, the Cu

-CO bond is calculated to

be 0.08

* A shorter than the Cu

-OH

bond, and the Cu

-CO and Cu

-OH

bond

energies are nearly equal. Cu

does not discriminate between H

O and CO on the

basis of their relative polarities. Again these same trends persist in the water model calculations.

The binding picture for Cu

is notably different from the above two cases. While

matrix ESR experiments on CuCO have been interpreted in terms of a linear structure [124,125], recent calculations indicate convincingly that the structure is actually bent [169, 170, 172, 173]. The present calculations also find the bent structure to be more stable than the linear one, by 6 kcal mol

\Gamma 1

. One way this bending can be understood is in terms of an orbital mixing and electron density transfer from the singly

35 occupied Cu 4s orbital to the CO 2ss orbital, which is permitted by symmetry only for the bent structure. Thus, addition of CO to Cu

results in a partial oxidation of

the Cu center, and the bonding can be described approximately as [Cu(I)-(C=O\Delta

\Gamma

)].

The molecular orbital analysis (Figure 4.3) is consistent with this characterization: a singly occupied orbital is found several electronvolts higher in energy than the d manifold, containing an admixture of Cu 4s and CO ss=oe orbital character. The transfer of electron density results in an electrostatic attraction between the two partially charged fragments, so that the Cu-CO bond energy is considerably greater than the Cu-OH

bond energy, where no such charge transfer mechanism is available. The bonding energy is calculated to be 14 kcal mol

\Gamma 1

, comparable to the earlier

work [169, 170, 172, 173], but considerably less than in the Cu

and Cu

cases. Finally, because of the transfer of charge into the antibonding 2ss orbital, the C-O bond is considerably lengthened compared to the free molecule.

In summary, then, CO binds to all three bare Cu species studied. For Cu

and

, the binding is understandable in terms of a primarily electrostatic interaction between CO and the Cu ion, with the more highly charged Cu

binding more

strongly and more strongly perturbing the CO. For Cu

, the binding is best understood in terms of a Cu 4s to CO 2ss charge transfer and geometric reorganization of CO to accommodate the additional electron. In general, the binding energies increase with the Cu ion charge, but the preference for binding CO over H

O decreases

with increasing Cu charge. Thus, Cu

shows a strong preference for H

O over CO,

prefers CO over H

O, and Cu

exhibits an approximately equal affinity for CO

and H

O. The CO bond length decreases with increasing Cu charge, suggesting that

the CO vibrational frequencies should increase with increasing Cu charge (see Chapter 6). Such a trend has in fact been found for CO on silica-supported Cu, where distinct absorption peaks for CO bound to all three different oxidation states of Cu have been identified [126].

Cu(H

Molecular and Electronic Structures

With this background, it is simple to understand the interaction of CO with Cu ions bound to framework oxygen in a zeolite. Again, the model we use is that of a Cu ion coordinated to one or more water molecules, but now with the addition of a single CO ligand inserted in the axial position. As in the Cu-H

O clusters

above, symmetry constraints are imposed to provide a more realistic representation

36 of the Cu-zeolite and Cu-CO interactions. Thus, the same caveats discussed above concerning optimization to local, symmetry-constrained energy extrema apply here.

The binding of CO to Cu complexes with one to four waters, i.e., Cu(H

(x = 1-4, n = 0-2), has been investigated. For Cu

and Cu

with x = 2-4 water ligands, C

symmetry is assumed, with CO oriented along the principal axis of rotation

and thus constrained to bind linearly to Cu. Test calculations indicate no tendency for CO to bend on these higher coordinate Cu sites. For x = 1 (i.e., Cu bound to a single water or bridge oxygen) both linear (C

2v;

with a planar H

O ligand) and bent

, with a pyramidal water ligand) structures were considered, with Cu

preferring

the former and Cu

the latter. A bent structure is preferred in all cases for Cu

, as

expected on the basis of the bare Cu results presented above. In our calculations, the CO is constrained to bend in the direction between adjacent water ligands (x ? 1) or between O-H vectors (x = 1), to yield C

complexes. Possible computational difficulties associated with the lower symmetry bent configurations are discussed at length later on in the context of the Cu(H

complexes, which exhibit a greater

tendency for bending. It suffices to mention here that symmetry constraints over and above the point group symmetries mentioned above were imposed in some cases where CO is allowed to bend, in order to expedite geometry optimizations; for instance, in all complexes with one water ligand, the Cu, O (of the water ligand) and H atoms were constrained to be in the same plane, and in all complexes with 2-4 water ligands, all Cu-O bonds were constrained to be equal, as were the O-Cu-C angles and the H-O-Cu-C dihedral angles. Figure 4.1 contains representative sketches of the model geometries used here.

The important structural parameters for the Cu(H

systems are summarized in Table 4.2. Addition of an axially coordinated CO ligand increases the pyramidalization at the Cu center and tends to increase the Cu-OH

bond distances.

For instance, the Cu-O bond distances in Cu(H

and Cu(H

are 1.957 and

1.835

* A, respectively, and these increase to 1.999 and 1.886

* A upon addition of a CO.

Again, these optimal distances are not unreasonable with respect to the dimensions of possible coordination sites within ZSM-5.

The binding of CO to the water-ligated Cu ions is similar to that for the bare ions. Thus, in all the Cu(H

clusters considered, the optimal C-O bond length

is less than that of the free molecule, reflecting the importance of electrostatics and

37 donation in the Cu

-CO interaction. As H

O ligands are added, the Cu

ion

becomes more electron rich and less able to accept electron density from CO, with the result that the C-O bond length increases and the Cu-C bond length decreases.

Similar trends are found in the Cu(H

systems. As the number of coordinated waters increases, the C-O bond length increases gradually, so that in Cu(H

the C-O bond length is slightly greater than that in the free molecule,

suggesting at least some ss back-bonding component to the Cu

-CO bonding interaction. The Cu-C bond length is relatively invariant across the series. The molecular orbital description of the Cu

-CO systems is considerably cleaner than in the Cu

case, because the primarily Cu d orbitals are well separated in energy from both the lower lying CO and H

O orbitals, much as found in Figures 4.2 and 4.3. Thus, these

systems can clearly be characterized as Cu

ions with d levels split by a combination

of interactions with both CO and H

O ligands.

Finally, the results for the Cu(H

clusters considered mirror those found

for CuCO

. The CO ligand binds in a bent fashion, and the C-O bond length is

considerably increased over the free molecule. In the water-ligated clusters, as in CuCO

, the bonding can best be described as a partial oxidation of the Cu atom to

yield approximately a [Cu(I)-CO\Delta

\Gamma

] complex, with the unpaired electron localized in

an essentially CO 2ss orbital. The ability of the CO molecule to oxidize the Cu atom increases as the number of waters increases, as reflected in the increase in charge and decrease in s orbital population on the Cu center and the decrease in Cu-C bond length.

Thus, the geometric and electronic results for the Cu(H

clusters reinforce the conclusions drawn from the CuCO

clusters: CO will bind on Cu

, Cu

and Cu

coordinated to additional water (or bridge oxygen) ligands. The CO bond

lengths are modified by coordination of additional H

O ligands to Cu, but the essential trends of decreasing CO bond length and increasing CO vibrational frequency with increasing Cu oxidation state hold true.

Cu(H

Bond Energies

Table 4.2 also contains the binding energies for the Cu-CO complexes with respect to fragmentation into isolated Cu ions and H

O and CO ligands. As found in the case of

the Cu-H

O complexes, the total binding energy decreases in magnitude from Cu

to Cu

. In all cases the complexes are bound with respect to the fragments.

38 The Cu

results are notable in that the total binding energies are markedly larger

than in the Cu

-H

O cases. The increase in binding results from the partial oxidation

of the Cu

atom by the bound CO and the resultant electrostatic attraction between

the partially cationic Cu and the dipolar H

O and CO ligands.

The third column of Table 4.2 contains the binding energies for dissociation of the Cu(H

clusters into Cu(H

and CO. A number of interesting trends

are apparent from the CO binding energy results. As with the total binding energy, the CO binding energy is largest for Cu

and decreases for Cu

and Cu

. In the

first case, the (H

-CO bond energy is large for small x but falls off rapidly

as x increases. The binding to Cu

is primarily electrostatic in character, and Cu

ion shows a strong preference for binding to the more highly polar H

O ligands than

to CO. As the coordination number of the ion increases and its ability to attract polar ligands decreases, the energetic preference for H

O over CO decreases but is

still present even at the highest coordination numbers considered here. As alluded to above, separation into (H

and CO

fragments also becomes thermodynamically unfavorable as x increases beyond 1. These results suggest that a Cu

ion

will prefer to fill its coordination shell with H

O (or bridge oxygen) ligands rather

than with CO and that CO will not be able to displace a H

O (or bridge oxygen)

ligand from Cu

. The presence of CO should not alter the preference of Cu

ions

for high-coordination sites within a zeolite.

In contrast, Cu

is much less discriminating between H

O and CO in its binding

preferences. For lower coordination numbers, the Cu

-CO and Cu

-OH

binding energies are nearly the same. As the coordination number increases, both binding energies decrease, in particular in a discontinuous jump from two-coordinate Cu(H

-L

to three-coordinate Cu(H

-L. Unlike Cu

, when Cu

is bound to two or more

O ligands, it has a slightly greater affinity for CO than it does for additional H

coordination. The results suggest that Cu

can more readily accommodate both CO

and H

O (or bridge oxygen) ligands in its coordination sphere and that CO should

be able to displace H

O (or bridge oxygen) from a zeolite-coordinated Cu+ ion. This

qualitative difference between Cu

-CO and Cu

-CO binding is in accord with the

common wisdom that Cu

will bind CO while Cu

will not. In fact, the results

show that both Cu

and Cu

do bind CO, but that Cu

binds oxygen-containing

ligands more strongly yet, and that these other ligands block addition of CO to the

39 Cu

coordination sphere.

Finally, the Cu

-CO bond energy is essentially invariant to the number of attached H

O ligands and is consistently greater than the Cu

-OH

bond energies in

the Cu

-H

O complexes. CO does bind to Cu

. While the addition of H

O ligands

does not significantly alter the Cu

-CO bond energy, the presence of the CO ligands

does modify the Cu

-OH

bond energies. The increased binding is a result of the

partial oxidation of Cu

brought about by coordination with CO and the electrostatic

attraction between the partially cationic Cu center and the dipolar H

O ligands that

results. Addition of one or more H

O ligands to Cu(H

CO is energetically unfavorable, however, and if such a system does exist, it will have very low coordination. These results suggest that, while monodispersed Cu

is not likely to be stable within

a zeolite, monodispersed CuCO

may have a weak but favorable binding interaction

with a small number of framework oxygens and may have some stability.

4.3 Interaction of NO with Cu sites Understanding the interaction of NO with Cu sites in Cu-exchanged zeolites is an important step toward understanding their activity for the decomposition and selective catalytic reduction reactions of NO. While the binding of a closed-shell CO ligand to a metal center is well-understood, NO, which differs from CO by the addition of an unpaired electron to the 2ss shell, binds in a more complex fashion [127]. Traditionally, NO has been thought to interact with metal centers in two distinct modes. In the "linear" mode, the bonding is described in terms of a one-electron donation from NO to a metal center to form a formally NO

ligand, which is isoelectronic

with and binds in a fashion analogous to CO. In the "bent" mode, NO accepts an electron from a metal center to form a formally NO

\Gamma

ligand, which is isoelectronic

with and binds in a fashion analogous to O

[128]. The existence of both linear and

bent NO coordination modes is well established [127], but given the prominent covalent character of M-NO bonding, the assignment of formal metal oxidation states to M-NO complexes is now recognized to be ambiguous and potentially misleading [127, 129]. Rather, Enemark and Feltham have proposed a terminology in which the MNO moiety is treated as a whole and characterized by the sum of the number of metal d electrons plus one for each bound NO ligand [129]. Nonetheless, the use of the oxidation state terminology with respect to the Cu-NO interaction in Cu-ZSM-5

40 Table 4.4: Selected geometric parameters [LSDA] and binding energies [BP86] for [Cu(H

(NO)]

complexes. Distances in

* A, angles in degrees, and energies in kcal mol

\Gamma 1

N-O Cu-N Cu-N-O Cu-O BE

Cu(II) systems (n = 2)

x = 0 1.079 1.920 180.0 -158.6 x = 1 1.089 1.756 180.0 1.840 -227.8 x = 2

1.096 1.764 180.0 1.935 -273.4

x = 2

1.092 2.187 121.4 1.870 -283.0

x = 3 1.101 1.754 180.0 1.985 -308.5 x = 4

1.098 1.790 180.0 2.098 -324.4

x = 4

1.104 1.903 121.9 2.080 -331.2

Cu(I) systems (n = 1)

x = 0 1.138 1.851 127.9 -34.8 x = 1 1.150 1.788 133.8 1.880 -74.8 x = 2 1.158 1.782 139.7 1.996 -95.9 x = 3 1.164 1.803 133.9 2.156 -108.5 x = 4 1.168 1.830 130.4 2.172 -111.9 Cu(0) systems (n = 0)

x = 0 1.177 1.865 118.5 -26.7 x = 1 1.217 1.766 134.7 1.920 -38.9 x = 2 1.223 1.785 136.6 2.149 -40.9 x = 3 1.223 1.765 180.0 2.188 -39.1 x = 4 1.234 1.824 131.0 2.314 -39.3

Energy of reaction: Cu

+ xH

O + CO ! [Cu(H

CO]

;

Energy referenced

to spherically averaged Cu

ion.

Linear NO;

Bent NO;

catalysts is widespread, and it is worthwhile to attempt to make a connection with this usage.

Discrete, well-characterized CuNO complexes are quite rare [127, 130], and a theoretical description of the Cu-NO interaction is available for only one model system [130]. We proceed here as in the CO case, by first examining the bonding in simple triatomic CuNO

complexes (n = 0-2) and then proceeding to the inclusion

of H

O ligands as models of coordination to zeolite bridge oxygens.

CuNO

Table 4.4 contains LSDA geometry and BP86 energy results for CuNO

(n = 0,1,2),

and Figure 4.4 contains molecular orbital diagrams for the three. Using the notation of Enemark and Feltham, these systems are described as CuNO

, CuNO

, and

41 Cu2+

N O

1.92

1.08

Cu+

1.84

1.13

128

1.86

1.18

118

5s 1p

dp dp dp

dd ds

ds, dd ds, dd

2p 2p 2p

5s, 1p

1 eV

Figure 4.4: Molecular orbital diagrams for NO on bare Cu atom and ions. For ease of interpretation, the orbitals are shifted vertically so that the tops of the spin-up d orbital manifolds have the same energy.

CuNO

, respectively [129]. These electron counts are unusually large for nitrosyl

complexes, and thus the bonding in the systems is expected to be somewhat unusual.

The LSDA optimized bond length of free NO (1.154

* A) compares favorably with

the experimental value (1.151

* A, Table 3.1). As with CO, NO binds to Cu

in a linear

fashion, with the N-O bond length decreasing to 1.079

* A. CuNO

is isoelectronic

with CuCO

and like the latter has a

\Sigma

ground state. As shown in Figure 4.4,

the electronic structure of CuNO

is characterized by distinct filled NO and Cu d

manifolds, with the latter more than 2 eV lower in energy than the vacant NO 2ss

42 manifold. The d orbitals are split, with the d

orbitals stabilized below the other d

orbitals. Thus, the bonding in CuNO

closely resembles the "linear" bonding model

described above: an electron is transferred from NO to the Cu

) center, yielding

a bonding situation that can be approximately represented as [Cu(I)-(NjO

)]. NO

is a stronger ss acid than CO, and the NO 2ss orbitals mix with and split off the Cu d pair. This same description of the CuNO

system holds when H

O ligands are

added to the model.

The calculated Cu

-NO bond energy (-159 kcal mol

\Gamma 1

) is considerably larger

than that of either Cu

-OH

or Cu

-CO, presumably because of the large covalent

component in the interaction. The strong interaction suggests that Cu

within a

zeolite may have a high affinity for NO. In fact, a relatively high-frequency feature in the infrared spectrum of "oxidized" Cu-ZSM-5 treated with NO has been assigned to NO bound on Cu

[18, 41]; we will have more to say about this in Chapter 6.

However, much like CuCO

, while the Cu

-NO bond is quite stable with respect to

homolytic cleavage, it is unstable with respect to separation into Cu

and NO

fragments, by 106.5 kcal mol

\Gamma 1

at the BP86 level using the LDA geometries. Combined

with the Cu

-NO bond energy, reduction of Cu

by NO is found to be exothermic

by 265 kcal mol

\Gamma 1

in the gas phase, compared with the experimental result (based

on gas-phase heats of formation at 0 K) of 254 kcal mol

\Gamma 1

[131]. While a very small

(!1 kcal mol

\Gamma 1

) barrier to dissociation exists at the LDA level, optimization of the

geometry at the BP86 level yields a barrierless separation into Cu

and NO

fragments. The instability of the Cu

-NO bond to heterolytic cleavage is unsurprising

given the description of the bonding in terms of a charge transfer from NO to Cu

and the expected electrostatic repulsion of the two resultant cationic fragments. This instability is sharply reduced when H

O ligands are added to the model, thus delocalizing the positive charge on the Cu

fragment, and it may disappear completely

in more realistic models of zeolite systems.

CuNO

is isoelectronic with CuCO and, like the latter, adopts a bent geometry with a

ground state [132]. The bending in the

state is severe (

Cu-

N-O = 127.9

ffi

), and the N-O bond length is just 0.02

* A less than that in the free

molecule. A recent ab initio (coupled cluster with a small basis set) investigation of CuNO

finds the same qualitative geometric trends, although all bond lengths are

larger and the bending is smaller [132]. As shown in Figure 4.4, the electronic struc 43 ture of CuNO

is derived from that of CuNO

by the addition of a single electron

into the NO 2ss manifold. As with CuCO, rehybridization of the 2ss orbital with the Cu 4s provides the driving force for bending of CuNO

. The bonding situation can

be conveniently represented as [Cu(I)-

(N=O\Delta )], where the superscript 2 (doublet)

notation is used to emphasize that the unpaired electron is largely localized on NO, in this case in an in-plane hybrid orbital. If CuNO

is imagined as arising from the

interaction of a Cu

cation with NO, the Cu center is neither oxidized nor reduced

by the NO ligand, and the bonding is best described as a simple dative electron pair donation from NO to the Cu center, supplemented by back-donation from Cu to the vacant orbital of NO 2ss origin. This same description has been used for the bonding of an amine-coordinated CuNO

system [130], and as we will show it is also appropriate for the H

O-ligated models. The geometric and electronic structure results

suggest that NO adsorbed on Cu

within a zeolite should have a lower stretch frequency than that found for Cu

. Such a correlation has been observed [41] (Chapter

6).

The Cu

-NO bond energy is 35 kcal mol

\Gamma 1

at the BP86 level, slightly larger than

that found in the earlier ab initio work [132]. This binding energy is much less than that found for Cu

-NO, but unlike CuNO

, CuNO

is stable to separation into

fragments such as Cu and NO

. The Cu

-NO bond energy is also slightly less than

that found for Cu

-OH

and Cu

-CO, but the difference between these three is not

great. Unlike Cu

, Cu

does not strongly discriminate between H

O, CO, and NO,

suggesting that the nature of the interaction between Cu

and the three ligands is

similar.

CuNO

is the only member of the CuNO

series that has been directly observed

experimentally, in an Ar matrix isolation experiment [133]. CuNO

adopts a bent

geometry and has a

ground state, but with a

state only 2.0 kcal mol

\Gamma 1

higher in energy at the BP86 level. Linearly constrained

\Sigma

\Gamma

and

\Pi states are

both approximately 18 kcal mol

\Gamma 1

higher in energy. The bending in the

ground

state (

Cu-N-O = 118.5

ffi

) is even more severe than that in CuNO

, and the N-O

bond length is 0.02

* A greater than in the free molecule. Again, the same general

geometric trends have been found in the ab initio calculations, with only a slightly larger (5.5 kcal mol

\Gamma 1

) singlet-triplet splitting [132]. The bond length variation is also

consistent with the available spectroscopic information [133]. From Figure 4.4, the

44 electronic structure of CuNO

can be qualitatively derived from that of CuNO

by the

addition of a second electron into the NO 2ss derived orbitals, either spin-paired (

)

in an in-plane, N-centered orbital derived from the NO 2ss set or spin-parallel (

) in

the orthogonal in-plane and out-of-plane NO 2ss-derived orbitals. Thus, the bonding situation for CuNO

can be represented approximately as [Cu(I)-

1;3

(N=O

\Gamma

)], with

the unpaired electron density in the triplet case largely localized on NO. If CuNO

imagined as being formed from an isolated Cu atom and an NO ligand, the Cu atom is oxidized by one electron by NO, and the CuNO

bonding resembles the "bent"

model described above. The highest lying orbitals of CuNO are not pure ligand in character, as bending introduces mixing between the NO 2ss and the Cu 4s orbitals, and the one-electron transfer model is of course only an approximate, but useful, description.

The charge transfer bonding model suggests some electrostatic contribution to the bonding in CuNO. The calculated Cu-NO bond energy is 27 kcal mol

\Gamma 1

at the

BP86 level, again somewhat larger than the earlier ab initio work [132]. The bond energy is only 8 kcal mol

\Gamma 1

less than that found for Cu

-NO and is greater by 13

and 25 kcal mol

\Gamma 1

than that found for Cu-CO and Cu-OH

, respectively. Thus,

the Cu-NO bond is predicted to be fairly robust, as the limited experimental results suggest [133].

In summary, then, NO is found to bind to Cu in CuNO

, CuNO

, and CuNO

In each case, the binding is best understood in terms of a Cu(I) species interacting with either NO

, NO radical, or NO

\Gamma

(singlet or triplet), respectively. Thus, definition of a Cu oxidation state in a nitrosyl complex is ambiguous, and it is preferable to identify these as CuNO

, CuNO

, and CuNO

. The N-O bond lengths increase

across the series as electrons are added into the formally NO 2ss antibonding orbital, and the N-O vibrational frequencies are expected to decrease commensurately. All three species are bound with respect to loss of NO, with CuNO

having the largest

binding energy and CuNO

and CuNO

having much less. Further, both Cu

and

have a strong preference for binding NO over H

O or CO, while Cu

shows

almost an equal affinity for CO, NO, and H

O. Finally, while CuNO

is strongly

bound with respect to loss of NO, it is unbound with respect to loss of NO

, and reduction of Cu

by NO is a highly exothermic process. The same qualitative behavior

is found when H

O ligands are included in the model, as we now show.

45 Cu(H

Molecular and Electronic Structures

The models of NO coordination within Cu-exchanged zeolites are analogous to those used above in the CO case: bridge oxygens are modeled by water ligands arranged approximately equatorially about Cu, with the NO ligand added axially. The model systems include Cu(H

(x = 1-4, n = 0-2). In virtually all cases, both linear

, x ? 1) and bent (C

) coordinations of the NO ligand have been examined. The

lower symmetry of the bent systems causes two problems in calculating structures and relative energies that need to be addressed. First, in most of the Cu(H

and

Cu(H

model compounds already discussed, symmetry was used to constrain the system to a "zeolite-like" C

coordination geometry, i.e., pseudoplanar

[Cu(H

] or pseudopyramidal [Cu(H

]. In bent systems, symmetry constraints alone cannot ensure optimization to a pseudopyramidal structure, and care must be taken during the optimization process to locate a local minimum that is a reasonable approximation to the desired model geometry. Second, an unbiased comparison of the energies of optimized linear and bent systems is difficult, because the latter may be artificially stabilized relative to the former by the additional relaxation of the H

O ligands permitted in the reduced symmetry. Thus, in almost all cases

examined for Cu(H

, a bent, lower symmetry structure can be found that

is lower in energy than the linear, higher symmetry counterpart. In particular, NO binds in a linear fashion in [Cu(H

O)NO]

and prefers bent binding in complexes

with 2 and 4 water ligands.

Because of these additional complications, we construct the Cu(H

model systems as follows. For the Cu

and Cu

cases, where the bare Cu results

clearly indicate the tendency for NO to bend, we report results for bent NO coordination on the water models. The geometries chosen for bent NO are the same as those discussed for CO: NO is constrained to bend in the direction "between" the Cu-O bond vectors (for x ? 1) or between the O-H vectors (for x = 1), under the constraint of C

symmetry. For the Cu

case, the choice of model geometries to report is less

clear, and so, both linear and bent structures are reported, whenever possible. Also, just as in the CO binding case discussed above, and in an attempt to handle the two issues raised in the previous paragraph, additional symmetry constraints (over and above the point group symmetries) were imposed in some cases (where NO prefers bent binding); for instance, in all complexes with one water ligand, the Cu, O (of the

46 water ligand) and H atoms were constrained to be in the same plane, and in all other complexes, all Cu-O bonds were constrained to be equal, as were the O-Cu-N angles and the H-O-Cu-N dihedral angles. This scheme has the added benefit of expedient geometry optimizations.

The important structural parameters for the Cu(H

complexes are summarized in Table 4.4. The general features of NO coordination are similar to CO coordination: addition of an NO ligand increases both the pyramidalization angle at the Cu center and the Cu-O bond distances, irrespective of the overall cluster charge. In the Cu

and Cu

complexes, only minor structural relaxation is observed

upon allowing NO to bend. Again, the structural results are not inconsistent with the expected dimensions of coordination sites within zeolites, such as ZSM-5.

The bare CuNO

complexes provide a sound basis for understanding the binding

of NO to oxygen-ligated Cu ions. In all the Cu

-NO (CuNO

) clusters the N-O

bond length is significantly diminished over that of the free molecule. As the number of attached H

O ligands is increased and the Cu center becomes more electron rich,

the N-O bond length increases, but only slightly. The electronic structure of these clusters is complex because of the strong mixing between the energetically similar Cu d levels and the O levels from H

O. The essential features of bare CuNO

are not

lost, however. The NO 5oe and 1ss levels can be identified and are lower in energy and well separated from the Cu d and H

O manifolds, while the vacant NO 2ss orbitals

are 1 eV or more higher in energy than the top of the Cu/H

O manifold. The

characterization of these CuNO

systems is thus the same as in the water-free case:

the Cu center is approximately reduced by one electron by the NO ligand, and the resultant bonding situation can be represented as [(H

Cu(I)-(NjO

)]. The large

contribution of covalence, particularly in the Cu d

-NO

2ss interaction, is confirmed

by a bond energy decomposition analysis.

As in bare CuNO

, the Cu(H

clusters are unstable towards dissociation into Cu(H

and NO

, because of the electrostatic repulsion between the

two fragments. The addition of H

O ligands decreases the dissociation energy at both

the LDA and BP86 levels of calculation. Stronger donor or anionic ligands, such as framework oxygen near Al sites within a zeolite lattice or extralattice OH

\Gamma

, would

likely stabilize these CuNO

systems even further. Thus, we expect the CuNO

systems to be kinetically robust, but to at least have the potential for thermodynamic

47 instability. As noted above, the energy of some of the Cu(H

clusters can

be lowered by allowing the NO ligands to bend.

The Cu(H

results are similarly understood in terms of those for CuNO

Results for bent NO coordination are shown in Table 4.4. The N-O bond lengths in the Cu

-NO (CuNO

) clusters are comparable with that in the free NO molecule.

While rather dramatic bending of the NO ligand is energetically preferred in every case, the difference in energy between linear and bent structures is much less than in bare CuNO

, and the structural relaxation upon bending is also relatively minor.

The one structurally characterized CuNO

complex has a Cu-N-O bond angle of

163

ffi

[130], intermediate between the optimized bent structure reported here and

linear NO. It would appear that in the ligated CuNO

systems the Cu-N-O bending

potential is soft and that the bond angle is likely determined by factors external to the CuNO unit.

In moving from the Cu

-NO clusters to the Cu

-NO ones, an electron is added

to the orbitals derived from the NO 2ss manifold. In the three- and four-H

O cases,

then, the linear NO geometries are of

E symmetry and are Jahn-Teller active, which

likely contributes to the bending of the NO. Upon bending of the NO, the unpaired electron becomes localized in the in-plane orbital derived from the NO 2ss manifold, and the ground states of the bent structures are thus all of

symmetry. Population

analysis confirms that the majority of the spin density resides on the nitrogen center, with the remainder primarily on the NO oxygen. The bonding picture thus described is identical to that obtained for bare CuNO

, and can be represented approximately

as [(H

Cu(I)-2(N=O\Delta )], so that formally the Cu

center is neither oxidized nor

reduced by the addition of NO. Bond energy analysis for Cu(H

-NO indicates

that the interaction is largely covalent, with a particularly large contribution to the bonding derived from the Cu d

-NO ss interaction. The importance of covalence in

CuNO

bonding has also been emphasized in the earlier ab initio work [130].

Unlike the above two cases, the Cu(H

clusters exhibit some important

qualitative differences from bare CuNO

. Like bare CuNO

, the N-O bond lengths

in the Cu

-NO (CuNO

) clusters are considerably longer than that found in the free

NO molecule, and the bond length increases with the addition of H

O ligands, as the

Cu center becomes more electron rich and a better electron donor. Again, both linear and bent NO coordination geometries for Cu(H

have been investigated, and

48 while the Cu-N-O bending is very pronounced in the latter, the energetic difference between linear and bent structures is almost negligibly small, as is the difference in N-O bond length. This indifference to bending is in sharp contrast to bare CuNO

where the bending is strongly preferred, but is similar to the results obtained for the Cu

-NO clusters. Ligation apparently results in a decrease in the Cu-N-O bending

potential for Cu

-NO complexes, and while no structurally characterized CuNO

complexes are known, it is likely that any bending of the NO ligand in such systems will again result from factors external to the CuNO unit. The Cu-N bond lengths are also similar to those found in the Cu

-NO clusters, and as in those clusters, the

Cu-N bond lengths tend to increase with bending of the N-O ligand.

The similarities between the Cu

-NO and Cu

-NO systems are not coincidental.

The Cu

-NO complexes are obtained from the Cu

-NO ones by the addition of a

second electron into the pair of orbitals derived from the NO 2ss set. In the linear case, where the orbitals are degenerate (CuNO, Cu(H

NO, and Cu(H

NO)

or nearly degenerate [Cu(H

O)NO and Cu(H

NO] the electrons combine spinaligned, and triplet ground states are obtained. In bare CuNO

, bending is facilitated

by the mixing between the NO 2ss orbitals and the Cu 4s orbital, leading to a ground state singlet system. Additional H

O ligands are also able to interact with the Cu 4s

orbital, however, making it less available for mixing with the NO 2ss orbitals. The driving force for bending is diminished, as is the driving force for pairing the two electrons upon bending. Thus, unlike bare CuNO

, the ground states of all the bent

-NO clusters are

, with the two unpaired electrons localized in the orthogonal

orbitals derived from the NO 2ss set. Mulliken population analysis confirms that the majority of the spin density resides on the N and O centers. Because the second electron is largely nonbonding with respect to the Cu-N bond and the Cu-N-O bend, one expects and finds the structural results for the Cu

-NO systems to be similar to

those for the Cu

-NO ones.

In summary, then, the Cu(H

structural and electronic results are consistent with three types of Cu-NO linkages within zeolites. As in the bare Cu ion case, these can be characterized as CuNO

, CuNO

, and CuNO

, or perhaps more

descriptively, as [Cu(I)-(NjO

)], [Cu(I)-

(N=O\Delta )], and [Cu(I)-

1;3

(N=O

\Gamma

)], respectively. Again, because of the high degree of covalency in the Cu-NO interaction, formal oxidation states cannot readily be assigned to the Cu centers alone, but rather

49 the CuNO system must be taken as a unit that overall can assume three different "oxidation states". As one moves across the series of increasing electron count, unpaired electron density builds up primarily on the nitrogen center, suggesting that coordination to Cu may enhance the reactivity of NO. Structurally, the N-O bond lengths increase, and vibrational frequencies presumably decrease, as the electron count increases. Both linear and bent coordination geometries have been investigated, and the energetic differences between the two are smaller, so that the coordination geometry will likely differ from system to system with the same overall electron count.

Cu(H

Bond Energies

The last column of Table 4.4 contains the energy for dissociation of the Cu(H

clusters into Cu

, H

O, and NO fragments. The general trends

are not surprising: all the systems studied are stable with respect to dissociation, and the total binding energy decreases with decreasing net positive charge on the systems.

The binding energies from Tables 4.1 and 4.4 are used to calculate the Cu(H

-NO bond energies, which are reported in the last column of Table 4.2.

In the n = 0 and n = 1 cases, where both linear and bent NO coordination modes have been examined, the Cu-NO bond energy is for the lowest energy (most stable) structure found.

NO is strongly bound in all of the Cu

(CuNO

) clusters, although as with the

O and CO binding energies, the NO binding energy falls off rapidly with increasing

coordination number. NO binds to Cu

by donation of its lone 2ss electron, and as

the degree of H

O coordination increases and the ability of Cu

to accept additional

electron density decreases, the Cu

-NO binding energy decreases. NO has a commensurate effect on the (NO)(H

x\Gamma 2

-OH

bond energy, decreasing it with

respect to that of the corresponding (H

x\Gamma 1

-OH

bond energy by approximately 10 kcal mol

\Gamma 1

. Because of the large contribution of covalence, the Cu

-NO

bond energy is greater than the Cu

-CO and Cu

-OH

bond energies in all the

systems considered, i.e., Cu

-NO ? Cu

-OH

? Cu

-CO. On the basis of the

relative bond energies, we argued earlier that CO should not be able to displace a H

O (or presumably bridge oxygen) ligand from the coordination shell of a Cu

ion.

By the same reasoning, because NO binds more strongly to Cu

than does H

NO is able to displace H

O (or bridge oxygen) ligands from the Cu

coordination

50 sphere. The results indicate that oxygen-coordinated Cu

should have a high affinity for NO, consistent with the affinity for NO observed for cupric oxide [134] and for "oxidized" Cu-ZSM-5 [41, 135].

As noted above, all of the CuNO

systems are unstable to separation into Cu

and NO

fragments. From the binding energy results we calculate dissociation to

be exothermic by 77, 72, 50, and 41 kcal mol

\Gamma 1

for the systems with one to four

added H

O ligands, respectively. The instability to dissociation does diminish with

increasing coordination, and in systems in which the overall charge is neutralized by other ligands or framework Al, the instability may disappear altogether. Further investigation of this point is clearly necessary. However, both the electronic structure and energetic results do suggest that NO will both bind to and act as a reductant of Cu

coordinated to oxygen-containing ligands.

NO is much less strongly bound in the Cu

(CuNO

) systems than in the Cu

ones. The same binding energy trend is found for NO as for CO and H

O: the Cu

NO bond energy is essentially the same in the zero and one H

O systems and decreases

by approximately 20 kcal mol

\Gamma 1

in the higher coordinate complexes. The Cu

-OH

bond energy is slightly larger than the Cu

-NO bond energy for low coordination

numbers, but is slightly smaller for higher coordination, while the Cu

-CO bond

energy is slightly larger than either at any level of coordination. In all three cases the binding primarily arises from a dative interaction between the Cu center and the ligands. For low (1 or 2) coordination, the better donor ligands are preferentially bound. For higher coordination (3 or more), the stronger donor ligands become less preferable to the weaker donor, stronger ss-acceptor ligands. The energetic differences are not large, however, and at the level of reliability of the present study we have Cu

-OH

ss Cu

-CO ss Cu

-NO. In zeolites it is likely that Cu

is not able to

discriminate strongly between CO, NO, or H

O (or bridge oxygen) coordination and

that the three should be readily exchanged within the Cu

coordination shell.

NO is bound as or more strongly in the Cu

(CuNO

) complexes than in the

-NO ones. Further, unlike the Cu

and Cu

cases, the Cu-NO bond strength

is actually found to increase slightly as H

O ligands are added and the Cu center

becomes more readily oxidized. A direct comparison of these three is somewhat misleading, however. From the last column of Table 4.4, the total binding energy of the bent Cu(H

NO systems is essentially invariant for x ? 1, indicating that

51 H

O ligands beyond the first are essentially unbound. As with Cu

-CO complexes,

-NO complexes only exist for very low coordination numbers. NO does bind more

strongly to Cu

than does CO or H

O, and in general Cu

-NO ? Cu

-CO ? Cu

. The results suggest that Cu

-NO could exist as a species weakly coordinated

to a zeolite lattice. It is highly unlikely that such a system would form within a zeolite from the combination of a zeolite-coordinated Cu

atom with a free NO

molecule. It is conceivable, however, that a CuNO

structure could exist as an

intermediate, perhaps formed by the reduction of a CuNO

(Cu

-NO) structure,

and then participate in some further chemistry.

4.4 Extension beyond the H

O Model

Clearly, a more realistic cluster model is preferable to one based exclusively on water ligands whenever the location of the extralattice cation of interest is well-established (e.g., a Bro/nsted acid site). However, when such information is not available, as in Cu-ZSM-5, the use of a too detailed--and potentially incorrect--model introduces strong biases into the results that can lead to incorrect conclusions. In such cases, we believe the simple water ligand model is sufficiently reliable to provide important insights at relatively low computational cost.

While the application of the H

O model to a specific zeolite, such as Cu-ZSM-5,

is obviously speculative, we believe that the results obtained here are an encouraging step toward a better fundamental understanding of the catalytic activity of this complex system. The issue of how well the water ligand model reproduces the actual properties of bound Cu ions and Cu-CO and Cu-NO complexes in zeolites has been addressed by some of our coworkers [136]. Legitimate concerns, such as, the adequacy of the cluster sizes considered here and the use of charged clusters, rather than explicit Al countercharges, to vary the Cu oxidation state are addressed in that study. It has, in fact, been shown that the water-ligand models actually provide a remarkably accurate description of local chemical properties at nominal Cu(0) and Cu(I) sites and at nominal Cu(II) sites with a sufficiently realistic (i.e., high) coordination [136]. For these cases, the electronic and geometric structures and the binding energies calculated by the water-ligand model differ by less than a few percent from those calculated with these larger models.

In the present work, we do not report larger model results for otherwise unligated

52 Cu ions in zeolites, and for the interaction of CO and NO to the Cu ion sites; Ref. [136] must be referred to for more details. However, in Chapter 6, we do report vibrational frequency calculations for the simple water-ligand models, as well as for the larger models of Ref. [136]. The vibrational frequency is a more sensitive property, compared to the properties addressed in the present chapter; the performance of the waterligand model will be compared with that of the larger zeolitic ring models in that chapter.

4.5 Summary and Conclusions In an attempt to gain a better understanding of the activity of Cu-ZSM-5 as a catalyst for the NO decomposition and selective catalytic reduction reactions, we have examined the interaction of zeolite-bound Cu ions with NO and CO. Because the actual Cu-ZSM-5 system is very complex on an atomic scale, small molecule models, including Cu(H

, Cu(H

, and Cu(H

(x = 0-4, n = 0-2), have

been used to represent the real system. The essential assumption of this model is that the bridge oxygens that form the anchor points for Cu ions within zeolites can be adequately represented by a set of water ligands. Water ligands obviously do not incorporate the structural and electronic complexities of real zeolites. They do benefit from simplicity, however, and the present results indicate that in most cases they do capture the essential features of the interaction between bridge oxygens and a Cu ion.

First, Cu

and Cu

are both found to interact with H

O ligands (or bridge

oxygens) in an essentially ionic fashion. Cu

shows a strong preference for high

coordination numbers and thus is more likely to bind in 4-fold or higher coordination sites within ZSM-5. In contrast, Cu

prefers, or at least tolerates, lower coordination

numbers and is more likely to bind in 2-fold coordination sites, although no energetic penalty is incurred for choosing higher coordination. Essentially the same results hold when CO or NO is bound to the ions.

Second, CO is found to bind to Cu

, but the bonding interaction is weaker than

that between Cu

and H

O. Thus, CO is not expected to be able to displace H

ligands (or bridge oxygens) from the Cu

coordination sphere, and zeolite-bound

may not always be able to bind CO. In contrast, Cu

has an approximately

equal affinity for CO and H

O ligands, and Cu

within zeolites should be able to

53 readily exchange CO and bridge oxygens in its coordination sphere. Cu

also exhibits

some affinity for CO, but the binding of CuCO

to H

O is very weak, and a CuCO

moiety is unlikely to be stable within a zeolite. The C-O bond length is virtually unchanged from the free molecule when bound on Cu

but is significantly shortened

on Cu

and lengthened on Cu

Third, NO is found to bind to Cu

, Cu

, and Cu

. In the first case, the bonding

is characterized by the transfer of an electron from NO to the Cu

center and

can best be represented as [Cu(I)-(NjO

)]. In the second case, the bonding is

primarily dative, and can best be represented as [Cu(I)-

(N=O\Delta )], with the unpaired

electron localized primarily on NO. In the last case, the bonding is characterized by the transfer of an electron from Cu

to the NO ligand and can be represented

as [Cu(I)-

1;3

(N=O

\Gamma

)], where the singlet and triplet states are close in energy and

arise from parallel or paired alignments of two electrons centered on NO. Use of the Cu oxidation state to describe these three bonding situations is clearly ambiguous, and we prefer to use the nomenclature CuNO

, CuNO

, and CuNO

to describe

the systems that have been modeled by CuNO

, CuNO

, and CuNO

complexes,

respectively. The increased localization of unpaired electron density on the nitrogen centers in the latter two cases suggests that these systems may be activated toward further chemistry, such as interaction with another NO molecule or with an olefin.

Fourth, the binding energy of NO to Cu is sensitive both to the CuNO "oxidation state" and to the coordination number of the metal ion. NO binds more strongly to Cu

than does CO or H

O, and the CuNO

unit should be readily generated

within Cu-exchanged zeolites and should be fairly robust to cleavage to Cu

and NO.

binds NO, CO, and H

O equally well, and the CuNO

unit should be readily

formed (and cleaved) within Cu-exchanged zeolites. Cu

also binds NO reasonably

strongly, and it may be possible to generate a CuNO

unit within zeolites, perhaps

by reduction of the other systems. While the Cu

-NO bond is robust with respect

to fragmentation into Cu

and NO, it is thermodynamically unstable with respect

to fragmentation into Cu

and NO

. As the Cu coordination number increases, the

systems become increasingly kinetically stable, and they may become thermodynamically stable in more realistic coordination environments. However, NO does have the potential to serve as a one electron reductant for Cu

within a zeolite.

54 Chapter 5 Dicarbonyl and dinitrosyl species in Cu exchanged zeolites

One of the intermediates that is believed to be crucial during the catalytic decomposition or the SCR of NO is the Cu-gem-dinitrosyl complex [6, 16-18]. Gem-dinitrosyl species (two NO ligands bound to the same site) have been observed experimentally when the reduced forms of Cu-exchanged zeolites (containing predominantly Cu(I)) are exposed to NO [16-18, 36, 37, 39-41]. This tendency of NO to adsorb in pairs has been observed on many transition metal oxide surfaces and transition metal ion exchanged zeolites as well [139, 140], and has been ascribed to enhanced stability gained by the interaction of the unpaired electron on each of the NO ligands [141]. In this chapter, we attempt to test this hypothesis and characterize various Cu-bound dinitrosyl species that can be found in zeolitic environment.

Before focussing on the Cu-dinitrosyl species, we discuss Cu-bound dicarbonyl species for reasons mentioned earlier in the previous chapter, viz., CO may play a role in the SCR of NO, CO has been employed extensively as a spectroscopic probe, and most importantly, Cu-bound dicarbonyl species are observed in zeolites [17,40]; thus, this study acts as a further test of our model systems. The geometric and electronic structure and binding energies of Cu-dicarbonyl complexes are investigated first. We then explore the same properties for Cu-dinitrosyl complexes. A surprising richness of dinitrosyl binding modes is found; species identified include the gem dinitrosyl species with the NO ligands bound to Cu through the N (N-down), typically referred to in the experimental literature [16-18,36,37,39-41], the closely related O-down gem dinitrosyl species, and Cu-bound hyponitrite-like species. While the N-N bond in all dinitrosyl complexes is long (? 2

* A), that in the hyponitrite-like complexes is much

shorter (1.2-1.3

* A).

We continue to use the water-ligand model in the present investigation as well. The model Cu-dicarbonyl and dinitrosyl complexes are sketched in Fig 55 H O2 OH2

H O2

OH2 OH2 H O2

CuO OC C

Figure 5.1: Schematic of Cu-bound dicarbonyl [Cu(H

(CO)

]

complexes for x = 0, 1, 2 or 4.

Complexes may have overall charge (n = 0, 1 or 2) and are all constrained to C

symmetry except

x = 0, which has a D

ground state.

X YY X

Cu OH2 OH2OH

X YY X

H O2 H O

2H O

H H

Figure 5.2: Schematic structures of Cu-bound dinitrosyl [Cu(H

(NO)

]

(X = N, Y = O) and

[Cu(H

(ON)

]

(X = O, Y = N) complexes for x = 0, 1, 2 or 4.

ures 5.1 and 5.2, respectively. The dicarbonyl complexes are of the general form

56 [Cu(H

(CO)

]

, x = 0,1,2,4, n = 0-2, and the dinitrosyl complexes are of the

general form [Cu(H

(NO)

]

, x = 0,1,2,4, n = 0-2, for N-down binding of the

two nitrosyl ligands to Cu, and [Cu(H

(ON)

]

for O-down binding. All complexes were constrained to C

symmetry (except [Cu(XO)

]

, X = C or N, n = 0-2,

for which the possible D

linear geometry, was also examined) and were assigned a

0, 1+ or 2+ charge. We consider a range of possible coordination of Cu to framework oxygen, both to examine trends that accompany increasing Cu-coordination, and also because of the remaining uncertainties regarding the true Cu environment in zeolites. Cu was coordinated to 0, 1, 2 or 4 water ligands, with the plane of the dicarbonyl and dinitrosyl species between adjacent water ligands (x ? 1) or between O-H vectors (x = 1). For a few selected cases, the C

symmetry constraint was relaxed so

that the two carbonyl (or nitrosyl) ligands become symmetry inequivalent. In such cases, the complexes reverted back to the C

structures, indicating a preference for

this symmetry.

5.1 Cu-dicarbonyl complexes In experimental studies of CO in Cu-exchanged zeolites, CO was found to adsorb at isolated Cu ion sites either singly (as monocarbonyl species) or in pairs (as dicarbonyl species) [17, 38, 40, 108, 109]. In fact, binding of several carbonyl ligands to the same transition metal center is a very common occurence and a widely studied area [142] of inorganic chemistry. Table 5.1 contains the geometric and energy results for [Cu(H

(NO)

]

complexes.

Free CO has a bond length of 1.13

* A. The oe donation from the CO 5oe orbitals to

the vacant metal d orbitals, and ss back-donation from the occupied metal d orbitals to the unoccupied CO 2ss orbitals, have opposite effects on the C-O bond strength and length. The former tends to strengthen and shorten the bond, while the latter tends to weaken and lengthen the bond. Like in the Cu-monocarbonyl complexes discussed in the previous chapter, the former effect dominates in 2+ and 1+ complexes, while the latter dominates in neutral complexes. In each of the three charged cases, increased coordination to water-ligands increases the C-O bond length due to increased electron donating capability of the Cu. The electronic structure of these complexes can be approximately represented as [(H

Cu(II)-(CO)

], [(H

Cu(I)-(CO)

]

and [(H

Cu(II)-(CO)

\Gamma

], in the 2+, 1+ and neutral complexes respectively, with

57 Table 5.1: Selected geometric parameters [LSDA] and binding energies [BP86] for [Cu(H

(CO)

]

complexes. Distances in

* A, angles in degrees and energies in kcal mol

\Gamma 1

C-O Cu-C Cu-O

C-Cu-C Cu-C-O BE

Cu(II) systems (n = 2)

x = 0 1.112 1.966 - 180.0 180.0 -155.6 x = 1 1.114 1.959 1.876 97.1 178.2 -226.5 x = 2 1.116 1.978 1.979 154.2 160.1 -270.4 x = 4 1.121 1.929 2.198 98.6 180.0 -308.8 Cu(I) systems (n = 1)

x = 0 1.120 1.854 - 180.0 180.0 -74.5 x = 1 1.124 1.865 2.019 131.0 176.7 -96.3 x = 2 1.127 1.861 2.068 123.0 177.3 -114.3 x = 4 1.132 1.900 2.346 105.4 180.0 -111.9 Cu(0) systems (n = 0)

x = 0 1.152 1.786 - 180.0 180.0 -37.5 x = 1 1.156 1.791 2.139 152.7 178.2 -42.9 x = 2 1.162 1.827 2.187 140.5 179.7 -43.1 x = 4 1.160 1.820 2.606 127.1 180.0 -31.9

Energy of reaction Cu

+ xH

O + 2CO ! [Cu(H

(CO)

]

;

increased occupation of the CO 2ss level with decreasing cluster charge (Figure 5.3). We, thus, anticipate a lack of coupling between the carbonyl ligands, at least in the 2+ and 1+ charged cases. In agreement with this expectation, we notice that in almost all cases, the dicarbonyl complexes display almost linear Cu-C-O angles. As we will see in the next chapter, the lack of coupling is also reflected in the vibrational analysis; the splitting between the C-O stretch modes is negligible in Cu(II) and Cu(I) complexes and increases significantly in Cu(0) complexes.

Binding energies of Cu-dicarbonyl complexes are listed in Table 5.1. In general, the binding energies increase with the Cu ion charge. Table 5.2 lists the binding energies in a more suggestive format; columns 2 and 3 list the successive binding energies of CO as a function of Cu-coordination to water-ligands. Like in the case of the first CO ligand, the binding energy of the second CO decreases as the Cu

58 9 CO

Cu d's

d (p*)0 d (p*)0

Cu(II)-(CO)Cu(I)-(CO) 2Cu(I)-(CO) 2 2

n = 0 n = 1 n = 2 - d (p*)110 10

Figure 5.3: Molecular orbital diagrams for dicarbonyl binding to bare Cu

(n = 0), Cu

(n = 1)

and Cu

(n = 2). For ease of interpretation, the orbitals are shifted vertically so that the top of

the Cu d orbital manifolds have the same energy. Levels below those indicated by arrows are all occupied, those above are empty.

oxidation state decreases and as the Cu-coordination to water-ligands increases. In Cu

and Cu

complexes, the second CO is slightly less bound than the first CO,

as the electrostatic interaction between CO and Cu which dominates the binding of the first CO is attenuated by the first CO. In the case of Cu

, the second CO is

59 Table 5.2: Successive BP86 binding energies of CO, NO for N-down binding, and relative energies, in kcal mol

\Gamma 1

\Delta E

systems

-96 -60 \Gamma 159 \Gamma 63

Cu(H

-55 -42 \Gamma 99 \Gamma 44

Cu(H

-39 -22 \Gamma 73 \Gamma 29

Cu(H

-5 -7 \Gamma 35 \Gamma 19

systems

-38 -36 \Gamma 35 \Gamma 34 +19 +44

Cu(H

-42 -15 \Gamma 35 \Gamma 25 +17 +33

Cu(H

-19 -14 \Gamma 15 \Gamma 23 +17 +31

Cu(H

-19 -4 \Gamma 16 \Gamma 18 +16 +19

systems

Cu -14 -24 \Gamma 27 \Gamma 33 +6 Cu(H

O) -16 -25 \Gamma 37 \Gamma 31 \Gamma 5

Cu(H

-16 -21 \Gamma 35 \Gamma 35 \Gamma 5

Cu(H

-15 -19 \Gamma 41 \Gamma 37 \Gamma 21

Energy of reaction [Cu(H

]

+ CO ! [Cu(H

CO]

;

Energy of reaction

[Cu(H

(CO]

+ CO ! [Cu(H

(CO)

]

;

Energy of reaction [Cu(H

]

+ NO ! [Cu(H

NO]

;

Energy of reaction [Cu(H

(NO]

+ NO !

[Cu(H

(NO)

]

;

Energy difference between

[Cu(H

(ON)

]

and

[Cu(H

(NO)

]

;

Energy difference between

[Cu(H

]

and

[Cu(H

(NO)

]

bound more strongly than the first, due to the fact that the second CO interacts with a Cu that is already approximately oxidized to Cu(I); thus, the binding energies of the second CO in Cu

complexes are comparable to those of the first CO in Cu

complexes.

60 Table 5.3: Calculated properties [BP86] for the cis- and trans forms of free (NO)

, N

\Gamma

and

2\Gamma

. Bond lengths in

* A, bond angles in degrees and energies in kcal mol

\Gamma 1

cis- trans- cis- trans cis- trans(NO)

(NO)

\Gamma

2\Gamma

2 1

N-N 2.080 2.049 1.986 1.979 1.196 1.228 1.481 1.316 1.310 1.311 N-O 1.165 1.167 1.170 1.167 1.225 1.348 1.271 1.295 1.398 1.414 N-N-O 97.1 108.1 107.5 112.1 146.8 117.3 114.4 121.7 121.7 112.1

E \Gamma 14

\Gamma 19

\Gamma 8

\Gamma 18

\Gamma 11

- +2

Energy of reaction 2NO ! (NO)

;

Energy relative to

trans-N

\Gamma

;

Energy relative

trans-N

2\Gamma

5.2 Cu-dinitrosyl complexes We first review the dimerization of free NO, which provides a useful starting point from which a comparison of the free NO dimers and adsorbed dinitrosyl species can be made.

Free NO dimerization Spontaneous dimerization of NO has been observed experimentally in condensed and gas phases [143-145]; experimental estimates for the dissociation energy of free (NO)

(to two NO molecules) range between 1.5 and 3.7 kcal mol

\Gamma 1

[144,146,147]. The very

weak interaction between the two NO molecules has been notoriously difficult to treat theoretically [148], with results varying significantly with the type of electron correlation treatment [149-151]. Experimental estimates of the geometric parameters vary significantly with the type of experiment [144, 145], and some uncertainty even exists as to whether the ground state of the dimer is a singlet or triplet [148]. In Table 5.3, we list the BP86 geometric parameters and dissociation energies (with respect to the NO (

\Pi ) + NO (

\Pi ) asymptote) for the singlet (

) and the triplet (

) states of

the cis form of (NO)

, as well as for the trans forms identified earlier [148, 152]. The

present study indicates that the cis-triplet state is preferred over the cis-singlet by about 5 kcal mol

\Gamma 1

, and that the former structure is the most stable of all. The

electronic levels of the cis-triplet structure, shown in Figure 5.4 on the left, are derived from those of free NO by forming symmetric and antisymmetric combinations

61 p1 p2p3

1-O N

2a1

NO 5s, 1p

NO 2p

O-O 5sO-O O O

N O

N-N 1p 1b1 1a1

1a21b2

2b13a1

N 1 eV 2b2

3b2 2a2

O Figure 5.4: Schematic molecular orbital diagrams for cis-(NO)

(left), cis-N

\Gamma

(center) and cisN

2\Gamma

(right). Levels below those indicated by arrows are all doubly occupied, and those above

are empty.

of each NO orbital; for instance, the ss

and ss

levels are the symmetric and antisymmetric combinations of the in-plane NO 2ss levels, respectively, and the ss

and

levels are those of the out-of-plane NO 2ss levels. Because of the weak N-N coupling in the dimer through the NO 2ss combinations, most of the structures exhibit very long N-N separations (ss 2

* A). For comparison, typical N-N single, double and

triple bond separations are 1.45

* A (in N

), 1.21

* A (in N

) and 1.09

* A (in N

respectively [102]. The one exception to the long N-N separation is the

trans

structure, whose electronic structure derives from double occupation of one of the out-of-plane NO 2ss combinations. The geometric parameters and the relative ordering and magnitude of energies for the different structures, are in good agreement with earlier density functional studies [148, 152].

Reduction of (NO)

by one or two electrons considerably alters their electronic

and geometric structures. The BP86 optimized geometric parameters and relative

62 energies for the cis and trans forms of N

\Gamma

and N

2\Gamma

are listed in Table 5.3 as well.

To the best of our knowledge, these anions have not been studied previously. The trans form of N

\Gamma

is more stable than the corresponding cis forms, while the opposite

is true for N

2\Gamma

. The N-N bond lengths of N

\Gamma

and N

2\Gamma

are typical of metal

hyponitrites (1.2-1.3

* A) [143, 153], with the exception of cis2

\Gamma

, which has

a somewhat longer N-N bond (ss 1.48

* A). The electronic structure of N

\Gamma

, shown

schematically in the center of Figure 5.4 for the cis2

form, is derived by adding

an electron to the half-filled in-plane ss

orbital of (NO)

; this addition increases the

N-O bond length and destabilizes the 2b

(N-O oe bonding) orbital, so that it lies

close to the HOMO. The decrease in N-N bond length (to ss 1.48

* A) is accompanied

by an increase in N-N ss and oe bonding characters, respectively, of the 2b

and 3a

levels. The electronic structure of the less stable cis2

\Gamma

ion (not shown in

Figure 5.4) can be derived from that of cis2

\Gamma

by the promotion of a single

electron from the 2b

to the 2b

level, so that the 2b

level becomes the singly occupied

HOMO. Accumulation of charge in the 2b

level, which has significant N-N ss charater,

results in an even shorter N-N bond (ss 1.23

* A). In both the cis-N

\Gamma

structures,

the electron density in the 2b

level is mostly localized on the O atoms, and is O

p (in-plane) in character, oriented suitably for interacting with metal d orbitals of like symmetry. In fact, as we will see in subsequent sections, a metal center rich in electrons is particularly conducive to the formation of a short N-N bond in a pair of adsorbed nitrosyl ligands, like that found in cis2

\Gamma

. This singly negatively

charged ion can be understood to be intermediate between the neutral (NO)

dimer

and the hyponitrite ion, depicted below as:

N N

OO N N

O -2 e +2 e

The electronic structure of cis-N

2\Gamma

, shown in Figure 5.4 in the right, is derived

from that of N

\Gamma

(middle panel of Figure 5.4) by the addition of a second electron

to the 2b

level, so that all electrons are now spin paired. Here too, the two electrons

in the 2b

level are localized primarily on the O atoms, typical of hyponitrite species.

63 Table 5.4: Selected geometric parameters, Cu d population [LSDA] and fragmentation energies [BP86] for [Cu(H

(NO)

]

complexes. Bond lengths in

* A, bond angles in degrees and energies

in kcal mol

\Gamma 1

state Cu-N N-N N-O O-O Cu-O

N-Cu-N Cu-N-O d

pop:

systems (n = 2)

x = 0

\Pi

1.855 3.710 1.102 5.914 - 180.0 180.0 9.65 \Gamma 216.4

x = 0

1.959 3.688 1.103 2.866 - 140.6 142.0 9.68 \Gamma 221.4

x = 1

1.968 2.778 1.111 2.698 1.896 89.8 133.0 9.59 \Gamma 271.7

x = 2

1.987 2.713 1.116 2.499 1.954 86.1 131.5 9.55 \Gamma 311.8

x = 4

2.028 2.735 1.121 2.470 2.163 84.8 130.8 9.65 \Gamma 350.7

systems (n = 1)

x = 0

\Sigma

1.731 3.462 1.137 5.736 - 180.0 180.0 9.53 \Gamma 55.6

x = 0

1.947 2.865 1.141 2.274 - 94.8 117.6 9.67 \Gamma 68.2

x = 1

1.926 2.713 1.147 2.223 1.935 89.6 122.9 9.63 \Gamma 99.6

x = 2

1.899 2.642 1.153 2.216 2.032 88.2 125.3 9.58 \Gamma 118.5

x = 4

1.903 2.656 1.158 2.231 2.218 88.5 125.2 9.62 \Gamma 129.9

x = 0

\Sigma

\Gamma

1.732 3.464 1.138 5.740 - 180.0 180.0 9.53 \Gamma 68.4

x = 0

1.871 2.816 1.146 2.626 - 98.5 126.0 9.65 \Gamma 59.6

x = 1

1.861 2.618 1.149 2.492 1.933 89.4 132.2 9.62 \Gamma 94.7

x = 2

1.870 2.619 1.154 2.455 2.046 88.8 131.5 9.60 \Gamma 113.3

x = 4

1.921 2.613 1.159 2.356 2.237 85.7 130.8 9.66 \Gamma 123.0

systems (n = 0)

x = 0

\Pi

1.679 3.358 1.176 5.710 - 180.0 180.0 9.45 \Gamma 58.9

x = 0

1.874 2.904 1.184 2.244 - 101.6 113.0 9.65 \Gamma 59.3

x = 1

1.869 2.730 1.189 2.182 2.011 93.8 119.8 9.65 \Gamma 70.3

x = 2

1.860 2.704 1.194 2.192 2.171 93.3 121.0 9.64 \Gamma 75.9

x = 4

1.887 2.689 1.196 2.237 2.312 90.9 123.7 9.64 \Gamma 76.7

Energy of reaction Cu

+ xH

O + 2NO ! [Cu(H

(NO)

]

;

Energy referenced to spherically

averaged Cu

ion.

N-down structures We now examine the equilibrium geometries, electronic structure and binding energies of Cu-dinitrosyl complexes ([Cu(H

(NO)

]

), where the pair of nitrosyl ligands

are bound to Cu through the N atoms. The important structural parameters for these complexes are summarized in Table 5.4. Table 5.2 contains successive BP86 binding energies of NO to water ligated Cu ions, calculated for the ground state geometries. Because of the high degree of covalency in the Cu-(NO)

interaction, formal oxidation

states cannot be assigned to the Cu centers alone, but rather the fCu(NO)

g system

must be taken as a unit that overall can assume three different `oxidation states'. Using the notation of Enemark and Feltham [129] that was used earlier to characterize

64 mononitrosyl complexes, the dinitrosyl systems with overall charges of 0, 1+ and 2+ can be described as fCu(NO)

, fCu(NO)

and fCu(NO)

, respectively. The

number of electrons indicated by the superscript are distributed among the Cu d levels and the NO 2ss levels. For each nominal oxidation state of Cu, we consider the relatively simpler, otherwise unligated, bare [Cu(NO)

]

complex before discussing

the water ligated complexes. Though minimum energy structures with linear and non-linear N-Cu-N were found for all bare complexes, we confine our attention to the non-linear N-Cu-N structures in the present discussion, as structures with linear N-Cu-N are unlikely to be found in zeolites.

[Cu(H

(N O)

]

. [Cu(NO)

]

with non-linear N-Cu-N (

) is favored over

the corresponding linear structure (

\Pi

) by 5.0 kcal mol

\Gamma 1

. The N-O bond length in

[Cu(NO)

]

(1.10

* A) is significantly shorter than in free NO (1.15

* A). This shortening can be understood by an examination of the molecular orbital diagram for [Cu(NO)

]

, shown in Figure 5.5(a) for the bent

complex. The Cu d levels

are fully filled and the NO 2ss manifold is singly occupied, indicating a transfer of approximately one electron from the antibonding NO 2ss levels (two free NO's have a total of two 2ss electrons) to the Cu d manifold (bare Cu

has a d

ground state),

thereby effectively reducing Cu(II) to Cu(I), as has been seen for a single NO bound to Cu

. The depletion of electronic charge from the NO 2ss levels results in shorter

N-O bond lengths in Cu

-bound dinitrosyl complexes, compared to that in free

NO. The electronic level ordering of the NO-derived levels of [Cu(NO)

]

are identical to that of free (NO)

(cf. Figures 5.5(a) and 5.4); hence, the bonding situation

can approximately be represented as [Cu(I)-(NO)

]. The reduction of Cu

by NO

has an interesting implication for the successive binding energies of two NO ligands. Table 5.2 lists the binding energies of the first NO to Cu

(column 4) and the second NO to [CuNO]

(column 5). Because of a significant difference in electrostatic

contributions, the first binding energy is considerably larger than the second: the first NO interacts with Cu(II), effectively reducing it to Cu(I), while the second NO interacts with an already reduced Cu(I). NO binding to Cu(II) has been shown to be stronger than to Cu(I) [14, 136].

Results for complexes with additional Cu coordination are similar to those for bare [Cu(NO)

]

. The N-O bond length increases slightly as the Cu-coordination

to O increases (as the Cu center becomes a better electron donor), but in all cases

65 1

[Cu(NO) ]1+2

(b) 3a24b2

1 eV NO 5s, 1p

1a1 1a2 2a12b2

1b1 1b2

[Cu(NO) ] 2b13a1 2a24a1 3b2

2+ 2

(a)

NO 5s, 1p

[Cu(NO) ] 02

NO 2p

2 p3p4 3b1 pNO 2p

Figure 5.5: Molecular orbital diagrams for N-down dinitrosyl binding to bare Cu

(a), Cu

(b)

and Cu

(c). For ease of interpretation, the orbitals are shifted vertically so that the top of the Cu

d orbital manifolds have the same energy. Levels below those indicated by arrows are all doubly occupied, those above are empty, and those with a dominant Cu d component are indicated by bold lines.

is lower than in free NO. The electronic structure of the water-ligated complexes is more complicated than that of [Cu(NO)

]

because of the strong mixing between the

energetically similar Cu d levels and the O levels of H

O, but the essential features

observed for bare [Cu(NO)

]

are not lost. For instance, the NO 5oe and 1ss levels

can be identified and are lower in energy and well separated from the Cu d and H

derived levels, while the singly occupied NO 2ss levels are more than 1.5 eV higher in energy than the top of the Cu/H

O manifold. The Cu d populations listed in Table 5.4

are high, indicating an effective Cu(I) oxidation state. The characterization of these fCu(NO)

systems is thus the same as in the bare [Cu(NO)

]

case: the Cu

66 center is approximately reduced by one electron by the NO ligands, and the resultant bonding situation can be represented as [(H

Cu(I)-(NO)

]. The first NO binds

quite strongly to [Cu(H

]

(Table 5.2), but as in the case of bare [Cu(NO)

]

the second NO binds much less strongly.

[Cu(H

(N O)

]

. [Cu(NO)

]

prefers a geometry with linear N-Cu-N when

in a triplet state (

\Sigma

\Gamma

), and one with a bent N-Cu-N structure when in a singlet

state (

), with a negligible difference in energy between these two minimum energy

structures (Table 5.4). The N-O bond length in

[Cu(NO)

]

(1.141

* A) is close

to that in free NO (1.15

* A) and also in [CuNO]

(1.137

* A) (Table 4.4). Figure 5.5(b)

shows the molecular orbital diagram for bent [Cu(NO)

]

(

). Evidently, the

electronic structure of [Cu(NO)

]

is derived from [Cu(NO)

]

by the addition of

an electron to the singly occupied NO 2ss manifold of [Cu(NO)

]

in a spin-paired

(resulting in the singlet state shown in Figure 5.5) or in a spin-aligned fashion. Here again, the electronic level ordering of the NO-derived levels are identical to that of the free NO dimer. The bonding situation in [Cu(NO)

]

can be approximately described

as [Cu(I)-

1;3

(NO)

], as there is no net electron transfer between the Cu

ion and the

pair of nitrosyl ligands. Table 5.2 indicates that the binding energy of a single NO radical to a Cu

ion is \Gamma 35 kcal mol

\Gamma 1

, with an almost identical binding energy for a

second NO to [CuNO]

(\Gamma 34 kcal mol

\Gamma 1

). The interaction of the first NO with Cu

leaves the oxidation state of Cu unchanged (effectively Cu(I)), so that the second NO interacts with an effective Cu(I) as well; thus, both the first and the second NO interact with a similarly charged Cu ion. Though the second NO, in general, might be expected to have a lower binding energy because of the higher coordination of the Cu

to which it binds [14], the favorable interaction between the pair of nitrosyl

ligands offsets this effect, resulting in almost identical binding energies for the first and second NO.

The water-ligated complex results are similarly understood in terms of those for bare [Cu(NO)

]

. Results for singlet and triplet states are listed in Table 5.4,

with the singlet state being preferred over the triplet state by about 5 kcal mol

\Gamma 1

(at the BP86 level) in all water ligated complexes. As the coordination of Cu increases, the N-O bond length increases slightly, as does the Cu-OH

bond length;

other structural parameters do not change significantly. The bonding picture is identical to that obtained for bare [Cu(NO)

]

, and can be represented approximately

67 as [(H

Cu(I)-

1;3

(NO)

], so that formally the Cu center is neither oxidized nor

reduced by the addition of a pair of nitrosyl ligands. The relatively high Cu d population further reflects the effective Cu(I) oxidation state for Cu. The binding energies of the first and second NO's are more or less comparable, with slight differences arising due to particular preferences in geometries (for instance, Cu

prefers a tetrahedral

coordination environment, so pseudo-tetrahedral [Cu(H

(NO)

]

is preferred over

[Cu(H

NO]

[Cu(H

(N O)

]. Isolated neutral Cu atoms are not anticipated to be found

in zeolites. For completeness, however, we consider dinitrosyl binding to bare and water ligated Cu(0). Linear N-Cu-N (

\Pi

) and bent N-Cu-N (

) [Cu(NO)

]

geometries are very close in energy, with the bent complex being preferred very slightly (ss 0.4 kcal mol

\Gamma 1

at the BP86 level) over the linear one. The N-O bond

length in the bent structure (1.184

* A) is higher than in free NO (1.15

* A). As before,

the increase in N-O bond length can be explained in terms of the electronic structure of [Cu(NO)

], shown in Figure 5.5(c) for the bent C

structure. The molecular

orbital diagram for [Cu(NO)

] is derived by the further addition of an electron to

the NO 2ss manifold of [Cu(NO)

]

, resulting in fully filled Cu d and triply occupied

antibonding NO 2ss manifolds. This implies an effective transfer of electronic charge from Cu to the NO 2ss levels, thereby weakening and lengthening the N-O bond compared to free NO. The bonding situation can thus be approximately represented as [Cu(I)-(NO)

\Gamma

]. Increasing the coordination of Cu to O leaves the electronic and

geometric structure essentially unchanged. Table 5.2 contains the successive binding energies of the first and second nitrosyl ligands to bare and water ligated Cu(0). The second NO binds more strongly to [CuNO] than the first NO does to Cu, as the interaction of the first NO with Cu(0) is weaker than that of the second NO with the already oxidized (by the first NO) Cu(I). The Cu-NO and ONCu-NO bond strengths increase slightly as the coordination of Cu increases, i.e., as the Cu center becomes a better electron donor.

Comparison to experiments: Two peaks observed in the infrared spectrum of Cu-exchanged zeolites exposed to NO have been assigned to the symmetric and antisymmetric NO stretch modes of Cu

-bound dinitrosyl species [16-18, 36, 37, 39-41];

our study of the vibrational spectra of dinitrosyl species adsorbed to various Cu ion sites (to be discussed in the next chapter) reinforce this assignment [19]. Curiously,

68 infrared frequency measurements show no evidence of Cu

-bound dinitrosyl species,

even when the oxidized forms of Cu-exchanged zeolites (containing predominantly Cu

sites) are exposed to NO. This could be due to a combination of two factors.

Firstly, Table 5.2 shows that the second NO binds almost as strongly as the first NO in Cu

systems, but much less strongly than the first NO in Cu

systems. Thus,

free NO shows no particular preference between Cu

with or without a bound NO

ligand, whereas it preferentially binds to Cu

with no previously bound NO ligand.

(A preference of NO for Cu in one oxidation state over the other is more difficult to discern because of the tendencies of Cu

and Cu

toward low and high coordination, respectively.) Secondly, Cu-bound extra-lattice O

\Gamma

and/or OH

\Gamma

species (not

included in our models) may impose additional geometric or energetic constraints on the system that inhibit the adsorption of a second nitrosyl ligand to Cu

sites. Such

extra-lattice species are believed to partly charge compensate Cu

sites, especially

in over-exchanged zeolites [6, 30].

Estimates of the N-Cu-N angle based on infrared frequency measurements of the symmetric and antisymmetric frequencies of Cu

-bound dinitrosyl species in

zeolites yield a value of 104

ffi

if the integrated intensities are used, and 90

ffi

if the

peak intensities are used [41]. Our calculations yield a value of about 90

ffi

in all Cu

bound dinitrosyl complexes with at least one water ligand, in agreement with the latter experimental estimate. Other calculated geometric parameters of the Cu-bound dinitrosyl species are, however, quite different from what others have anticipated. For instance, complexes considered here always preferred C

symmetry with the two

symmetry equivalent nitrosyl ligands bent towards each other (the O-O separations being much less than the N-N separations, corresponding to Cu-N-O angles of 110- 140

ffi

), rather than the geometry suggested by Moser [180] and those found for early

transition metal dinitrosyl species [128, 154, 155] where one of the nitrosyl ligands binds linearly and the other binds in a bent fashion. Also, the N-N bond lengths in all the complexes considered in this section are considerably and consistently larger than the already large value in free (NO)

. A discussion of the preference for long

N-N bonds and the tendency of the two NO ligands to bend towards each other is deferred to Chapter 7.

69 O-down structures A pair of nitrosyl ligands bound through the N atoms to a Cu site in zeolites (examined above) are what have been traditionally called `dinitrosyl' species [16-18, 36, 37, 39-41]. Although it is expected that O-down binding of the pair of nitrosyl ligands to Cu is less favorable, it is important to consider this possibility, as such species may be intermediaries in the disproportionation of NO. O-down bidendate chelating and bridging hyponitrite complexes involving transition metal atoms are known to exist [156]. Copper hyponitrites, although identified [157, 158], have not been characterized; platinum hyponitrites, on the other hand, which also have a high d electron filling, have been shown experimentally to exist in an O-down bidendate structure with a relatively short N-N bond (ss 1.21

* A) [153].

Our calculations for [Cu(H

(ON)

]

complexes indicate that O-down binding

to zeolite-bound Cu can occur, with the bound (ON)

fragment resembling either the

dinitrosyl species encountered earlier, or a hyponitrite ion. In the latter cases, the N- N bond is considerably shorter than in complexes considered in the previous section. In the following, we discuss only the Cu

and Cu

O-down dinitrosyl complexes, as

the Cu

complexes are in all cases unstable to dissociation.

[Cu(H

(ON )

]

. Two types of stable geometries (singlet and triplet states

for each type) are observed for these complexes: one in which the N-N bond length is ss 1.9-2.0

* A, and another in which it is ss 1.2

* A. We continue to denote the former

type of complexes as [Cu(H

(ON)

]

, but denote the latter as [Cu(H

]

The important structural parameters, Cu d populations and BP86 binding energies are summarized for all the above types of complexes in Table 5.5. Singlet [Cu(H

(ON)

]

have different electronic configurations (though the same states)

than singlet [Cu(H

]

. The former complexes are indicated as

, and the

latter as

\Lambda

in Table 5.5 to highlight this difference.

The electronic structure of [Cu(H

(ON)

]

, shown in Figure 5.6(a) for bare

[Cu(ON)

]

(

), is very similar to that of [Cu(H

(NO)

]

(Figure 5.5(b)) discussed in the previous section; the level ordering of the NO-derived levels is preserved, and as in the N-down case, is identical to that of free (NO)

. The bonding situation

in these complexes can be approximately represented as [(H

Cu(I)-(ON)

], with

the Cu center neither oxidized nor reduced, and the (ON)

fragment remaining more

or less neutral. The Cu d populations listed in Table 5.5 reinforce this view; in fact,

70 Table 5.5: Selected geometric parameters, Cu d population [LSDA] and fragmentation energies [BP86] for [Cu(H

(ON)

]

and [Cu(H

]

complexes. Bond lengths in

* A, bond angles

in degrees and energies in kcal mol

\Gamma 1

state Cu-O

N-O N-N Cu-O

O-Cu-O Cu-O-N d

pop:

[Cu(H

(ON)

]

x = 0

2.060 1.153 2.010 - 80.4 123.5 9.83 \Gamma 49.4

x = 1

2.043 1.159 1.965 1.907 77.0 127.0 9.75 \Gamma 83.1

x = 2

2.034 1.168 1.902 2.009 75.5 127.6 9.71 \Gamma 101.9

x = 4

2.093 1.170 1.916 2.166 72.4 130.1 9.78 \Gamma 114.3

x = 0

2.056 1.160 1.964 - 80.9 121.9 9.87 \Gamma 42.2

x = 1

1.986 1.164 1.962 1.986 80.0 125.6 9.78 \Gamma 76.7

x = 2

2.169 1.176 1.778 1.924 74.4 121.8 9.72 \Gamma 100.7

x = 4

2.254 1.179 1.755 2.126 71.0 124.8 9.78 \Gamma 113.8

[Cu(H

]

x = 0

\Lambda

1.927 1.270 1.161 - 82.5 105.9 9.57 \Gamma 18.4

x = 1

\Lambda

1.875 1.286 1.170 1.882 80.1 109.9 9.45 \Gamma 62.7

x = 2

\Lambda

1.900 1.285 1.170 2.063 80.6 109.6 9.49 \Gamma 78.4

x = 4

\Lambda

1.894 1.308 1.182 2.161 80.9 110.4 9.46 \Gamma 108.7

x = 0

1.953 1.255 1.259 - 79.1 100.3 9.61 \Gamma 24.4

x = 1

1.924 1.263 1.266 1.896 78.3 113.4 9.51 \Gamma 66.5

x = 2

1.928 1.276 1.242 2.011 78.3 113.0 9.48 \Gamma 87.9

x = 4

1.940 1.284 1.261 2.167 76.5 114.3 9.49 \Gamma 110.7

[Cu(H

]

x = 0

1.883 1.319 1.215 - 85.8 106.4 9.65 \Gamma 53.5

x = 1

1.871 1.329 1.216 1.938 83.3 109.8 9.58 \Gamma 74.8

x = 2

1.886 1.333 1.218 2.146 83.3 109.5 9.62 \Gamma 81.1

x = 4

1.958 1.348 1.221 2.247 79.5 111.9 9.61 \Gamma 97.5

Energy of reaction Cu

+ xH

O + 2NO ! [Cu(H

(ON)

]

or [Cu(H

]

the d populations in this case are even higher than in [Cu(H

(NO)

]

, listed in

Table 5.4. Hence, these complexes should be characterized as dinitrosyl complexes, and not as hyponitrites, or even hyponitrite-like. The N-O bond length in these O-down dinitrosyl complexes is consonant with this view of bonding and are also very similar to the N-O bond length in [Cu(H

(NO)

]

. As before, increasing

Cu coordination has the usual effect of decreasing the N-O bond length. Table 5.2 lists the differences in energies between the most stable N-down (

) and the most

stable O-down (

) dinitrosyl complexes in column 6. The N-down structures are

16-19 kcal mol

\Gamma 1

more stable than the O-down structures; the latter may thus not be

sufficiently long-lived to be observed experimentally, although it is conceivable that

71 1 eV p1

1a1 1b1 1a2

2a1 1b2

2 2b2

3b1 3a2

4b2

5a1 3b1

3b2

1a1 1b1 2a1

1b2 1a2

(a) (b)

4a13b22b1,3a1,2a2

2b1,3a1,2b22a2

4a1

NO 2p

NO 5s, 1p

2N O Os, Np,

[Cu(ON) ] 1+2

3b13b2 3a2 4b2

5a1

1a1 2a11b1

1a2 1b2

2b13a1,2b2 2a24a1

(c)

[CuO N ]0 5a1

p3 p4

[CuO N ]1+2 2 2

Figure 5.6: Molecular orbital diagrams for O-down dinitrosyl binding to bare Cu

(a), hyponitritelike binding to bare Cu

(b) and hyponitrite-like binding to bare Cu

(c). For ease of interpretation,

the orbitals are shifted vertically so that the top of the Cu d orbital manifolds have the same energy. Levels below those indicated by arrows are all doubly occupied, those above are empty, and those with a dominant Cu d component are indicated by bold lines.

they play a role in catalytic processes on Cu sites at elevated temperatures.

The nature of bonding in [Cu(H

]

is qualitatively different from that

in all other complexes considered so far, as exemplified by the electronic structure of these complexes, shown in Figure 5.6(b) for bare [CuO

]

(

). No clear separation between the NO derived and Cu d levels is seen, and so assignment of a formal oxidation state for Cu becomes more difficult. Though Figure 5.6(b) suggests a d

configuration for Cu, the Cu d populations (Table 5.5) and the decomposition

of the molecular orbitals shown in Figure 5.6(b) indicate an oxidation state of Cu closer to Cu(II) than to Cu(I). For instance, the 2b

and 3b

levels, although predominantly Cu d and O p in character, respectively, have significant contributions

72 from both orbitals; since the former is fully occupied and the latter is not, the Cu d levels are not fully filled. Comparison of the electronic structures (and level ordering) shown in Figure 5.4 with that of [Cu(H

]

indicates that the O

fragment in the latter complex most resembles N

\Gamma

; a fragment molecular orbital

analysis of [CuO

]

(

), in which Cu

and N

\Gamma

are treated as interacting

fragments, shows significant mixing between the b

Cu d level and the 1b

and 2b

levels (Figure 5.4) of N

\Gamma

, as anticipated earlier in Section III, with all other Cu and

\Gamma

-derived levels remaining almost `pure'. Not surprisingly, analysis of the spin

densities in [Cu(H

]

indicates that the unpaired spins are mostly shared

by Cu and the O atoms. The bonding situation in [Cu(H

]

is thus perhaps

best represented formally as [(H

Cu(II)-(O

)

\Gamma

]. The charge transfer suggested

by this model is reflected in the other geometric parameters of the complexes, including decreases in Cu-O

and Cu-O

bond lengths, and marked increases in N-O

bond lengths.

The most stable O-down dinitrosyl complexes (

) are more stable than the most

stable hyponitrite-like complexes (

) by 25, 16, 14 and 3 kcal mol

\Gamma 1

(difference

between columns 6 and 7 of Table 5.2) when Cu

is 0-, 1-, 2- and 4-fold coordinated,

respectively, to O. Thus, increasing the degree of coordination of the Cu, which increases its electron donating ability, enhances the propensity of formation of the short N-N bond, hyponitrite-like structures. More realistic models of zeolites, which explicitly take into account Al counter-charges, will result in even higher electron density at the Cu center [136], and may reverse the relative stability of these two structures.

[Cu(H

(ON )

]. Only one type of structure is found for the neutral complexes,

which have a N-N bond length of about 1.2

* A. No long N-N bond structures are

observed, as the higher electron density on the nominal Cu(0) increases the preference for the formation of the hyponitrite-like structures; in fact, in all cases except the bare, water unligated case, the neutral O-down hyponitrite-like structures are even more stable than the neutral N-down dinitrosyl complexes (last column of Table 5.2). We denote the O-down complexes as [Cu(H

]. Consistent with this description,

the electronic structure of these complexes, shown in Figure 5.6(c) for bare [CuO

]

(

), is derived by the addition of an electron to the singly occupied 3b

level of

[CuO

]

(Figure 5.6(b)). While this may imply that Cu remains in an oxidation

73 state close to Cu(II), with the extra electron adding another negative charge to the N

\Gamma

fragment of [Cu(H

]

, the Cu d populations listed in Table 5.5

(cf. Table 5.4) and slight changes in the composition of the b

levels suggest an

oxidation state closer to Cu(I). Selected geometric parameters of the neutral O-down complexes are listed in Table 5.5. All structural parameters in [Cu(H

] are

similar to those in typical metal hyponitrites [143]. Unlike the neutral dinitrosyl complexes examined in Section III.B, the neutral hyponitrite-like complexes display significant binding to water molecules (last column in Table 5.5), typical of metal hyponitrites [157, 158].

5.3 Summary and Conclusions In this chapter, we have examined the nature of Cu-bound dicarbonyl and dinitrosyl complexes in zeolites by studying simple cluster models that incorporate the dominant interactions within these complexes in real zeolites. Our main conclusions can be summarized as follows:

1. Stable 2+, 1+ and neutral Cu-dicarbonyl complexes were found. Linear Cu-C-

O angles were found in general, with very little coupling between the carbonyl ligands in the 2+ and 1+ charged cases, due to negligible occupancy of the CO 2ss antibonding orbital.

2. N-down binding is the most stable binding mode for a pair of nitrosyl ligands

to Cu

and Cu

. In such complexes, the N-N bond is long (ss 2.8

* A) and Cu

has a strong tendency to remain in a nominal Cu(I) oxidation state, irrespective of its pre-adsorbed state and degree of coordination. N-down dinitrosyl binding to Cu

and Cu

can hence be approximately represented as [Cu(I)-

(NO)

] and [Cu(I)-(NO)

], respectively, with net electron counts of 11 and 12

on fCu(NO)

g units.

3. Two different metastable O-down binding modes are also observed in Cu

systems. The first resembles the dinitrosyl binding of N-down complexes (N-N bond length ss 2

* A), while the second resembles a hyponitrite bound to a metal

atom (N-N bond length ss 1.2

* A). The former is more stable than the latter (with the difference in energies between the two decreasing with increasing

74 coordination of Cu). The formal oxidation states in these two cases are best represented as [Cu(I)-(ON)

] and [Cu(II)-O

\Gamma

], respectively. Hyponitrite-like

species are also observed on Cu

, but no stable O-down binding is observed on

75 Chapter 6 Vibrational spectra of adsorbed CO and NO in Cu-exchanged zeolites

In order to gain insight into the mechanisms of catalytic NO decomposition, and to characterize various species present under reaction conditions, several researchers have used infrared spectroscopy to probe the adsorption of NO on oxidized and reduced forms of various Cu-exchanged zeolites (such as ZSM-5, UHSY, mordenite, erionite and Y) [16-18, 36, 37, 39-44]. The vibrational spectrum of NO adsorbed on the oxidized form of the catalyst (which contains predominantly Cu

ions) displays

two bands at 1895 cm

\Gamma 1

and 1912 cm

\Gamma 1

, which have been assigned to the stretching

modes of NO coordinated to a Cu

ion near one and two framework Al atoms,

respectively [17,39]. The vibrational spectrum of NO adsorbed on the reduced form of the catalyst (containing predominantly Cu

ions) includes a band at 1810-1812 cm

\Gamma 1

assigned to a single NO on Cu

[16-18, 36, 37, 39-41] and bands at 1824-1827 cm

\Gamma 1

and 1729-1735 cm

\Gamma 1

, assigned to the symmetric and anti-symmetric NO stretch of

gem dinitrosyl species coordinated to Cu

, respectively [16-18, 36, 37, 39-41].

In this chapter, we extend our density functional theory cluster approach to study the vibrational spectra of CO and NO species adsorbed at exchanged Cu sites. This work complements the growing number of theoretical studies of adsorbate vibrations in zeolites that focus on Bro/nsted acid sites [71-77], and at least two prior calculations at the Hartree Fock level for NO bound to Cu sites [79, 80]. We begin by examining the vibrational spectrum of Cu-bound CO in complexes including [Cu(H

CO]

x = 0,1,2,4, n = 0-2 (water ligand models) and larger, more realistic models [136] (described in the next section), and the corresponding gem dicarbonyl complexes [Cu(H

(CO)

]

. Next, we examine the analogous NO containing complexes,

including [Cu(H

NO]

, x = 0,1,2,4, n = 0-2 (water ligand models) and larger

models [136], and the corresponding gem dinitrosyl complexes [Cu(H

(NO)

]

Throughout this chapter, we attempt to address the following specific questions:

76 (a) are the vibrational frequencies calculated using our models consistent with experimentally observed frequencies? (b) do our results confirm or contradict earlier assignments of observed frequencies? (c) do modifications of the water ligand model, such as considering larger cluster models, have a significant effect on calculated frequencies? (d) what general factors affect CO and NO frequencies?

6.1 Computational details Larger models of nominal Cu(I) and Cu(II) sites in zeolites that explicitly include framework Si and Al atoms were obtained from Ref. [136]. The finer integration mesh used here required a re-optimization of the ground state geometries found in Ref. [136]. Thus, these models were re-optimized using the criteria of the present study together with the symmetry and other geometric constraints imposed previously [136]; for the most part, this re-optimization produced only minor changes. Two extreme cases of Cu coordination were considered for nominal Cu(I) sites: Cu bonded to one framework oxygen atom, [Cu(T

)YO], X = H, OH, Y = C or N, shown in

Figure 6.1(a), and Cu bonded to four framework oxygen atoms, [Cu(T

)YO],

shown in Figure 6.1(b). Only the relevant high coordination case (Figure 6.1(b)) was considered for nominal Cu(II) systems [136]. For purely siliceous clusters, in which all the T sites are occupied by Si atoms, net charges of 1+ and 2+ were imposed to represent nominal Cu(I) and Cu(II), respectively. Neutral cluster models for nominal Cu(I) were constructed by replacing a Si atom by an Al atom or a pair of Si atoms by a pair of hybrid J atoms; neutral nominal Cu(II) models are constructed by replacing two Si atoms by 2 Al atoms. Each J atom has an atomic number of 13.5 and each pair of J atoms allows a single negative framework charge to be represented without reducing the cluster symmetry. The J atom basis set is constructed by averaging Si and Al basis sets. In Tables 6.1 and 6.2, we list selected geometric parameters of the re-optimized larger model complexes.

In addition to monocarbonyl and mononitrosyl complexes, vibrational frequency calculations were also performed for the dicarbonyl ([Cu(H

(CO)

]

) and dinitrosyl ([Cu(H

(NO)

]

) complexes within the framework of the water ligand

model considered earlier (Figures 5.1 and 5.2).

Vibrational frequencies were evaluated using LSDA potential energy surfaces at the LSDA ground state equilibrium geometries. Harmonic frequencies were calculated

77 Cu

X O

Y O

T T X

X X

H2 H2

OO O

T T

O T

T O

(a) (b) Figure 6.1: Basic geometries assumed for (a) 1-coordinated Cu and (b) 4-coordinated Cu, for larger cluster models of YO (Y = C or N) ligated Cu(I) and Cu(II) sites in zeolites. Tetrahedral sites (T) may be occupied by Si, Al or J atoms. Terminating X species in 1-coordinated Cu complexes may be H or OH.

in all cases using an approximate `energy-factored force field' (EFFF) method [161, 162] and in many cases from a full normal mode analysis as well. The EFFF method assumes that the CO and NO stretch frequencies are decoupled from all the other vibrational modes of the complex [163]; this assumption is justified because the CO and NO frequencies are well separated from the high frequency O-H, Si-H, Al-H and J-H modes and the low frequency Cu-C, Cu-N, Al-O, Si-O, J-O and Cu-O modes. EFFF calculations for CO and NO stretch modes thus require just two singlepoint force evaluations in the case of monocarbonyl and mononitrosyl complexes and two single-point force evaluations followed by the (trivial) diagonalization of a 2 \Theta 2 matrix in the case of dicarbonyl and dinitrosyl complexes. The single-point forces were calculated for geometries in which the NO and CO bond lengths were stepped from their equilibrium values by \Sigma 0.01

* A. Full normal mode frequencies were

calculated in the usual manner within ADF by numerical differentiation of analytic gradients. Some of the full normal mode calculations yield imaginary frequencies for modes that break the imposed symmetry constraints by rotation or twisting of the water molecules. These modes are not points of concern as we are not interested

78 Table 6.1: Selected geometric parameters and scaled EFFF CO stretch frequencies for larger model carbonyl complexes. Distances in

* A and frequencies in cm

\Gamma 1

C-O Cu-C Cu-O *

Cu(I) systems

Larger models for 1-coordinated Cu:

[Cu(Si

)CO]

1.124 1.786 1.896 2169

[Cu(Si

O(OH)

)CO]

1.126 1.784 1.921 2155

[Cu(J

)CO] 1.133 1.754 1.836 2101

[Cu(J

O(OH)

)CO] 1.134 1.755 1.852 2097

[Cu(SiAlOH

)CO] 1.135 1.754 1.839 2078

[Cu(SiAlO(OH)

)CO] 1.134 1.752 1.851 2086

Larger models for 4-coordinated Cu:

[Cu(Si

)CO]

1.134 1.802 2.234 2097

[Cu(Si

)CO] 1.138 1.794 2.209 2063

[Cu(Si

AlO

)CO]

1.141 1.765 2.677 2051

2.002 Cu(II) systems

Larger models for 4-coordinated Cu:

[Cu(Si

)CO]

1.125 1.843 2.172 2156

[Cu(Si

)CO] 1.135 1.812 2.145 2076

symmetry imposed; Optimized Cu-C-O = 180

ffi

in the global minima of complexes but rather in complexes that provide realistic approximations to the local environments of Cu ions in zeolites.

Comparisons of frequencies calculated by both methods for all monocarbonyl and mononitrosyl complexes and a few dicarbonyl and dinitrosyl complexes (Tables 6.3, 6.4, 6.5 and 6.6, respectively) indicate generally good agreement between EFFF and normal mode frequencies. The EFFF frequencies can be either higher or lower depending on a competition between: (a) the coupling to the lower frequency Cu-Y (Y = C, N) modes, which shifts the Y-O normal mode frequencies upwards, and (b) the off-diagonal interaction between Y-O and Cu-Y bonds, which is largely determined by the degree of covalency in these bonds, and which shifts the Y-O

79 Table 6.2: Selected geometric parameters and scaled EFFF NO stretch frequencies for larger model nitrosyl complexes. Distances in

* A, angles in degrees, and frequencies in cm

\Gamma 1

N-O Cu-N Cu-N-O Cu-O *

Cu(I) systems

Larger models for 1-coordinated Cu:

[Cu(Si

)N O]

1.150 1.789 133.8 1.901 1848

[Cu(Si

O(OH)

)N O]

1.153 1.788 132.8 1.928 1838

[Cu(J

)N O] 1.164 1.749 138.0 1.839 1781

[Cu(J

O(OH)

)N O] 1.164 1.754 137.0 1.856 1782

[Cu(SiAlOH

)N O] 1.174 1.761 136.1 1.850 1715

[Cu(SiAlO(OH)

)N O] 1.175 1.767 134.3 1.868 1708

Larger models for 4-coordinated Cu:

[Cu(Si

)N O]

1.167 1.846 123.7 2.304 1774

2.169 [Cu(Si

)N O] 1.173 1.842 123.2 2.269 1742

2.141 [Cu(Si

AlO

)N O] 1.173 1.772 136.1 2.690 1736

1.988 Cu(II) systems

Larger models for 4-coordinated Cu:

[Cu(Si

)N O]

2+ a

1.109 1.767 180.0 2.152 2017

[Cu(Si

)N O]

2+ b

1.119 1.860 127.4 2.134 1944

2.131 [Cu(Si

)N O] 1.135 1.831 127.2 2.128 1844

2.087

Linear NO;

Bent NO.

normal mode frequencies downwards [164]; a FG matrix formalism for decoupling frequencies and the effects due to such a decoupling are outlined in Appendix A. In Cu-YO complexes, normal mode frequencies are generally higher than EFFF results for Y = C (Table 6.3), but for Y = N, the discrepancies are less systematic (Table 6.4), probably reflecting greater covalency of the Cu-NO bond. For both ligands, errors in the approximate EFFF frequencies are at most 20-30 cm

\Gamma 1

(ss 1%). In Cu-(YO)

complexes, the errors are typically somewhat larger (up to 53 cm

\Gamma 1

), with CO and

NO normal mode frequencies uniformly higher and lower, respectively, than EFFF frequencies (Tables 6.5 and 6.6). For the sake of consistency, most of the discussion in this paper focuses on EFFF results, which are the only frequencies we have calculated for our larger zeolite models because of their significantly lower cost compared

80 Table 6.3: C-O bond length and scaled EFFF and full normal mode (in parenthesis) CO vibrational stretch frequencies for [Cu(H

(CO)]

complexes. Distances in

* A and frequencies in cm

\Gamma 1

C-O *

Cu(II) systems (n = 2)

x = 0 1.112 2252 (2276) x = 1 1.112 2257 (2289) x = 2 1.115 2238 (2256) x = 4 1.118 2207 (2214) expt. 2180

Cu(I) systems (n = 1)

x = 0 1.121 2197 (2219) x = 1 1.124 2173 (2198) x = 2 1.129 2130 (2153) x = 4 1.134 2109 (2124) expt. 2150-2160

Cu(0) systems (n = 0)

x = 0 1.152 1966 (1955) x = 1 1.167 1876 (1876) x = 2 1.171 1849 (1857) x = 4 1.144 1985 (2014) expt. 2108

Cu-ZSM-5 [109];

Cu-ZSM-5 [17, 38, 40, 108, 109];

Cu-ZSM-5 [108].

to full normal mode calculations for these systems. Normal mode results are used only when comparing bare [Cu(YO)

]

results, x = 1,2, n = 0-2, to experiments or

to earlier calculations.

Harmonic frequencies calculated by conventional quantum chemistry techniques (ab initio and density functional based) tend to overestimate or underestimate the observed frequencies in a systematic manner [89, 165, 166] due to the neglect of anharmonicity and incomplete treatment of electron correlation. Introduction of either an overall scaling factor, or a set of scaling factors for different types of modes, can greatly improve agreement between calculated and experimental frequencies [89,165].

81 Table 6.4: N-O bond length and scaled EFFF and full normal mode (in parenthesis) NO vibrational stretch frequencies for [Cu(H

(NO)]

complexes. Distances in

* A and frequencies in cm

\Gamma 1

N-O *

Cu(II) systems (n = 2)

x = 0 1.079 2234 (2223) x = 1 1.089 2171 (2181) x = 2

1.096 2129 (2137)

x = 2

1.092 2137 (2121)

x = 4

1.098 2107 (2115)

x = 4

1.104 2077 (2057)

expt. 1895, 1909-1912

1900, 1950

1900

1895-1958

1895-1946

Cu(I) systems (n = 1)

x = 0 1.138 1872 (1854) x = 1 1.150 1853 (1843) x = 2 1.158 1816 (1810) x = 4 1.168 1773 (1760) expt. 1810-1812

1815

1810

Cu(0) systems (n = 0)

x = 0 1.177 1671 (1648) x = 1 1.217 1522 (1525) x = 2 1.223 1497 (1499) x = 4 1.234 1447 (1427)

Linear NO;

Bent NO;

Cu-ZSM-5 [16-18, 36, 37, 39-41];

Cu-UHSY [16];

Cumordenite [16];

Cu-erionite [39];

Cu-Y [18, 39].

82 Table 6.5: C-O bond length and scaled EFFF and full normal mode (in parenthesis) antisymmetric and symmetric CO vibrational stretch frequencies for [Cu(H

(CO)

]

complexes. Distances

* A and frequencies in cm

\Gamma 1

C-O *

anti

sym

Cu(II) systems (n = 2)

x = 0 1.112 2261 (2287) 2262 (2292) x = 1 1.114 2240 (2259) 2245 (2267) x = 2 1.116 2228 2232 x = 4 1.121 2185 2190 Cu(I) systems (n = 1)

x = 0 1.120 2199 (2205) 2209 (2242) x = 1 1.124 2162 (2167) 2177 (2199) x = 2 1.127 2128 2147 x = 4 1.132 2093 2111 Cu(0) systems (n = 0)

x = 0 1.152 1929 (1962) 2001 (2054) x = 1 1.156 1914 (1945) 1981 (2028) x = 2 1.162 1861 1942 x = 4 1.160 1880 1941 expt.

2150-2151 2177-2178

Cu-ZSM-5 [17, 40]

Selective scale factors that are specific to the type of system under consideration have also been used [71]. These scale factors are obtained by comparison of calculated frequencies to a small set of robustly assigned observed frequencies. In the present study, we make use of such selective scale factors. Table 6.7 lists the calculated and experimental vibrational frequencies for CO, CO

, NO, NO

and NO

\Gamma

. Calculated vibrational frequencies are consistently higher than experimental frequencies by about 3% in nitrosyl species and by about 2% in carbonyl species. In Tables 6.1- 6.6 and in all subsequent figures, we have therefore scaled the calculated NO stretch frequencies by 0.97 and the CO stretch frequencies by 0.98. Unless otherwise stated, we compare our scaled frequencies with experimentally determined frequencies, but

83 Table 6.6: N-O bond length and scaled EFFF and full normal mode (in parenthesis) antisymmetric and symmetric NO vibrational stretch frequencies for [Cu(H

(NO)

]

complexes. Bond lengths

* A and frequencies in cm

\Gamma 1

N-O *

anti

sym

systems (n = 2)

x = 0 (

) 1.103 2029 (2010) 2112 (2105)

x = 1 (

) 1.111 1969 (1940) 2068 (2056)

x = 2 (

) 1.116 1930 2043

x = 4 (

) 1.121 1892 1999

systems (n = 1)

x = 0 (

) 1.141 1828 (1798) 1890 (1869)

x = 1 (

) 1.147 1773 (1735) 1881 (1859)

x = 2 (

) 1.153 1748 1857

x = 4 (

) 1.158 1721 1831

systems (n = 0)

x = 0 (

) 1.184 1583 (1539) 1698 (1699)

x = 1 (

) 1.189 1564 (1527) 1690 (1665)

x = 2 (

) 1.194 1538 1670

x = 4 (

) 1.196 1519 1664

expt. 1729-1735

1824-1827

1729

1825

Cu-ZSM-5 [16-18, 36, 37, 39-41];

Cu-Y [18, 39]

compare our unscaled frequencies with other theoretical calculations. 6.2 Cu

-bound monocarbonyl complexes

Vibrational frequency calculations were performed for a set of water ligand model complexes in which CO is bonded to Cu in each of its three nominal oxidation states: Cu(0), Cu(I) and Cu(II), and for larger model Cu(I) and Cu(II) monocarbonyl complexes. Tables 6.3 and 6.1 list CO stretch frequencies for these cases, as well as experimentally observed frequencies that have been assigned to carbonyl ligands adsorbed at Cu(0), Cu(I) and Cu(II) sites in ZSM-5 [17, 38, 40, 108, 109].

84 Table 6.7: Calculated equilibrium bond lengths and calculated and experimental vibrational frequencies of diatomic molecules in the gas phase. Bond lengths in

* A and frequencies in cm

\Gamma 1

Bond length *

theory

expt

theory

Bare CO 1.131 2170 2143

0.988

Bare CO

1.114 2277 2214

0.972

scale factor for carbonyl frequencies 0.98 Bare NO 1.154 1930 1876

0.972

Bare NO

1.063 2426 2345

0.967

Bare NO

\Gamma

1.286 1398 1353

0.968

scale factor for nitrosyl frequencies 0.97

Reference [102]

Reference [101]

Reference [143]

Experimental and computational results are available for the triatomics CuCO and CuCO

, comparison with which provides some measure of the expected accuracy of our calculated vibrational frequencies. Our scaled value for CuCO (1955 cm

\Gamma 1

) is approximately 60 cm

\Gamma 1

lower than experimental cryogenic

matrix values (2014 cm

\Gamma 1

[167] and 2010 cm

\Gamma 1

[168]), a difference that can in part

be attributed to the perturbing influence of the matrix. A variety of density functional [169, 170], ab initio [171, 172] and hybrid [173] calculations of the CO stretch frequency in CuCO have been reported, which yield unscaled harmonic frequencies from 20 cm

\Gamma 1

less (gradient-corrected DFT [169, 170]) to more than 70 cm

\Gamma 1

greater

(second order Mo/ller-Plesset, modified coupled-pair functional methods [171, 172]) than our unscaled result (1995 cm

\Gamma 1

). Our result is consistent with those calculations of comparable quality. [CuCO]

has been examined previously with ab initio Hartree-Fock [174, 175] and coupled-cluster [174] methods; again, our unscaled normal mode result (2264 cm

\Gamma 1

) is within 30 cm

\Gamma 1

of the more accurate coupledcluster determination. These comparisons indicate that our overall computational approach--and, in fact, any computational approach tractable for systems of the size considered here--has at best an accuracy of tens of wavenumbers, even neglecting the uncertainties associated with the models we employ.

The increase in monocarbonyl frequencies with increasing Cu oxidation state for the [CuCO]

complexes can be understood in terms of charge transfer and orbital

85 mixing considerations. In CuCO, partial charge transfer from the singly occupied Cu 4s orbital to the CO 2ss antibonding orbital (which is symmetry-allowed only if CuCO is bent) results in a longer CO bond and a decreased CO stretch frequency compared to gaseous CO. In the singly and doubly charged complexes, net electronic charge transfer from the occupied 5oe antibonding orbital of CO to Cu results in a shorter CO bond and increased CO stretch frequency compared to free CO.

These trends are modified in understandable ways as the Cu coordination is varied. As the coordination to O is increased, the Cu center becomes a better electron donor and poorer electron acceptor and the CO bond tends to lengthen and the CO stretch frequency tends to decrease. The CO stretch frequencies for the 1+ and 2+ complexes (Table 6.3) lie in almost overlapping, fairly narrow ranges (! 90 cm

\Gamma 1

for 1+ complexes and ! 50 cm

\Gamma 1

for 2+ complexes). The neutral [Cu(H

CO]

complexes exhibit a less regular behavior, associated with the unusually weak carbonyl bonding in these systems; while the C-O bond length and frequency exhibit the expected correlation, they do not vary in a regular fashion with coordination number.

EFFF results for the larger cluster models are tabulated in Table 6.1 as well. Of all the models listed, the purely siliceous ones are most comparable to the corresponding water ligand models with like coordination and charge. The agreement between the water ligand and the purely siliceous models is excellent in the case of Cu(I) complexes, and reasonable in the case of Cu(II) complexes, for binding energies [136], and equilibrium geometries and vibrational frequencies (Tables 6.3 and 6.1). The 51 cm

\Gamma 1

difference in CO stretch frequencies between

[Cu(H

CO]

and [Cu(Si

)CO]

likely reflects the weaker electron accepting ability of Cu in the larger model. In Cu(I) complexes, inclusion of Al atoms or, to a somewhat lesser extent, pairs of hybrid J atoms in the larger models further decreases the electron accepting ability of Cu and thus increases the C-O bond length and decreases the CO stretch frequency. For instance, neutral 1-coordinated and 4-coordinated Cu(I) complexes display CO stretch frequencies 60-90 cm

\Gamma 1

and 35-

50 cm

\Gamma 1

lower, respectively, than those displayed by the corresponding charged Cu(I)

complexes. A similar trend is found in Cu(II) systems; neutral [Cu(Si

)CO]

yields a frequency that is 80 cm

\Gamma 1

lower than [Cu(Si

)CO]

Clear trends in CO stretch frequencies emerge from these models: a decrease in

86 1.100 1.120 1.140 1.160C-O bondlength (A*)1800.0 1900.0 2000.0 2100.0 2200.0 2300.0

CO stretch frequency (cm -1)

Cu(II) systems (water-ligand model) Cu(II) systems (larger model) Cu(I) systems (water-ligand model) Cu(I) systems (larger model) Cu(0) systems (water-ligand model)

expt: Cu(II)CO expt: Cu(I)CO

n = -7077.72 + 10121.67r

CO (gas)

Figure 6.2: Calculated CO frequencies (*, from EFFF method, scaled by 0.98) vs. C-O bond lengths (r) for monocarbonyl complexes. Linear fit to data and ranges of experimental values (from Table 6.3) are also shown.

the Cu oxidation state, an increase in the Cu coordination, and a greater proximity to strong Lewis base sites (like the Al or J atoms of the present study), all tend to shift the CO frequency downward. The same factors determine the C-O bond lengths and, in fact, a linear correlation exists between the calculated bond lengths and stretch frequencies. Figure 6.2 shows a plot of these quantities for all the water ligand and larger models considered along with the best fit straight line (correlation coefficient 0.9935). Interestingly, the data point corresponding to gas phase CO,

87 which was not used in the fitting procedure, also lies on this best fit line. A similar linear correlation between CO frequency and bond length, based on available experimental data, has been proposed earlier [176] for CO adsorbed on various surfaces of several different metals. However, no definitive relationship between frequency and bond length could be obtained from that study, as the errors in the experimentally determined C-O bond lengths (ss 0.1

* A) were of the same order as the correlation

that was sought. While bond lengths are more difficult to measure experimentally than frequencies, the latter are more expensive to obtain computationally. In light of these considerations, a certain predictive power can be attributed to the plot in Figure 6.2, in that, given either the frequency or the bond length, a rough estimate of the other can be readily obtained. Further, shifts in frequencies can be associated with the factors described above.

The ranges of experimental IR absorption frequencies that have previously been assigned to CO adsorbed on Cu(I) and Cu(II) sites in Cu-ZSM-5 are also indicated in Figure 6.2 and Table 6.3. As is clearly seen, the two ranges are narrow and separated by only ss 20 cm

\Gamma 1

and both fall within the corresponding--but, much broader--

ranges of calculated frequencies for Cu(I) and Cu(II) carbonyl complexes. The calculated ranges overlap significantly, with the Cu(II) results covering a wider range and extending to higher frequency. The small differences between CO frequencies on Cu(I) and Cu(II) reflect a similarity in CO bonding; the slightly higher frequencies for Cu(II) are due to a slightly larger de-population of the antibonding CO 5oe orbital. The better agreement of the water ligand model results with experiments for Cu(I) and Cu(II) is most likely fortuitous. Errors introduced by particular models may be offset to some extent in the present work by uncertainties associated with the assumed transferability of frequency scale factors from gas phase molecules to adsorbates on Cu. Given this situation, and the considerable sensitivity of the calculated CO frequencies to the details of a particular model, it is clearly impossible to make absolute comparisons between calculated and experimental frequencies. Rather, the present results serve to confirm the changes in CO frequency that accompany variations in Cu oxidation state, and to indicate the expected shifts in frequency associated with variations in local coordination environment. Our calculated frequencies for CO on isolated Cu(0) lie significantly below the experimental value of 2108 cm

\Gamma 1

that had

tentatively been assigned to this species in Cu-ZSM-5. This discrepancy most likely

88 reflects a clustering of Cu(0) in the sample studied, as 2108 cm

\Gamma 1

is much closer to

observed frequencies for CO on Cu metal surfaces [177].

6.3 Cu

-bound dicarbonyl [Cu(H

(CO)

]

complexes

In studies of CO in Cu-exchanged zeolites, vibrational bands observed at 2150- 2151 cm

\Gamma 1

and 2177-2178 cm

\Gamma 1

have been assigned to the antisymmetric and symmetric CO stretch modes, respectively, in dicarbonyl complexes adsorbed at isolated Cu

sites [17,40]. While dicarbonyl species are unlikely to play a role in the catalytic

reduction of NO, they do provide an additional test of our water ligand models. In Table 6.5, we list the calculated antisymmetric and symmetric CO stretch frequencies in [Cu(H

(CO)

]

complexes. The IR spectrum of [Cu

(CO)

] has been

measured in an argon matrix [168]; bands at 1876 cm

\Gamma 1

and 1891 cm

\Gamma 1

have been

assigned to the antisymmetric and symmetric CO stretch modes, respectively. Our calculated normal mode frequencies for [Cu(CO)

] are more than 100 cm

\Gamma 1

greater,

which likely reflects a difference in Cu stoichiometry in the experiments [168] and calculations. Our unscaled normal mode results for the antisymmetric and symmetric CO stretch modes in [Cu(CO)

] (2002 cm

\Gamma 1

and 2096 cm

\Gamma 1

, respectively)

do compare well with Barone's [178] hybrid density functional values of 1998 cm

\Gamma 1

and 2114 cm

\Gamma 1

. Hartree-Fock calculations for [Cu(CO)

]

[175] yield CO stretch

frequencies more than 150 cm

\Gamma 1

greater than our (unscaled) normal mode results

for this system, reflecting the known systematic overestimation at the Hartree-Fock level [174].

Figure 6.3 shows a plot of the EFFF CO (symmetric and antisymmetric) stretch frequencies vs. the C-O bond length for dicarbonyl species adsorbed on Cu in each of its three nominal oxidation states. A higher cluster charge (i.e., a higher nominal Cu oxidation state) results in higher stretch frequencies and shorter bond lengths. Also, as in monocarbonyl complexes discussed earlier, a higher degree of coordination makes the Cu center a better electron donor and poorer electron acceptor resulting in longer CO bonds and lower CO stretch frequencies. The line in Figure 6.3 is taken directly from the fit to monocarbonyl results in Figure 6.2. The average of the symmetric and antisymmetric frequencies of the dicarbonyl species has very nearly the same linear dependence on the C-O bond length, regardless of the Cu oxidation state. The splitting between the two CO stretch modes on the other hand increases significantly

89 1.100 1.120 1.140 1.160C-O bondlength (A*)1800.0 1900.0 2000.0 2100.0 2200.0 2300.0

CO stretch frequency (cm -1)

Cu(II) systems (sym) Cu(II) systems (anti) Cu(I) systems (sym) Cu(I) systems (anti) Cu(0) systems (sym) Cu(0) systems (anti)expt: sym

expt: anti

Figure 6.3: Calculated symmetric and antisymmetric CO stretch frequencies (from EFFF method, scaled by 0.98) vs. C-O bond lengths for dicarbonyl [Cu(H

(CO)

]

complexes. Linear fit to

monocarbonyl results (from Figure 4) and ranges of experimental values (Table 6.5) are also shown.

from Cu(II) to Cu(I) to Cu(0) complexes. The increased coupling with decreasing oxidation state likely reflects the increasing occupation of the CO 2ss orbitals, which interact strongly with each other. Figure 6.3 also shows experimentally observed frequencies [17, 40] that have been assigned to dicarbonyl species adsorbed on Cu(I) sites in ZSM-5. The present results reinforce this assignment.

90 6.4 Cu

-bound mononitrosyl complexes

Tables 6.4 and 6.2 list NO stretch frequencies for the water ligand and larger model complexes, respectively, along with the experimentally observed frequencies [16-18, 36,37,39-41] assigned to NO bound to the Cu(I) and Cu(II) sites in Cu-exchanged zeolites. For comparison, previous unrestricted Hartree-Fock calculations for NO bound to nominal Cu(I) sites in cluster models of zeolites yielded NO stretch frequencies of 2231 cm

\Gamma 1

[80] and 1776 cm

\Gamma 1

[79]. Hartree-Fock vibrational frequencies typically overestimate experimental measurements by about 11% [89]. Application of a standard Hartree-Fock scale factor [89] somewhat improves the former computational result, but further increases the descrepancy in the latter.

As discussed previously, in all mononitrosyl complexes, Cu has a strong tendency to exist in an effective Cu(I) oxidation state, i.e., the bonding between NO and Cu

and Cu

can be approximately represented as [Cu(I)-NO

\Gamma

], [Cu(I)-NO] and

[Cu(I)-NO

], respectively. Thus, NO adsorption tends to oxidize Cu

and reduce

. In CuNO, a partial electron transfer from the Cu 4s level to the antibonding

NO 2ss level lengthens the NO bond and decreases the NO stretch frequency compared to gas phase NO. We calculate the normal mode NO stretch frequency in CuNO to be 1648 cm

\Gamma 1

, which is in reasonable agreement with the experimental Ar matrix

isolation result (1611 cm

\Gamma 1

) [133]. In [CuNO]

, formally no charge transfer occurs

and the N-O bond length and stretch frequency (Table 6.4) are very close to their gas phase values of 1.15

* A and 1876 cm

\Gamma 1

, respectively. The NO 2ss orbital is populated

in both CuNO and [CuNO]

; as with CuCO, rehybridization of the 2ss orbital with

the Cu 4s orbital provides the driving force for the bending of NO in these two cases. In [CuNO]

, a partial charge transfer from the NO 2ss level to the incompletely

filled Cu d level results in a shorter NO bond and higher NO stretch frequency than those of gas phase NO. [CuNO]

is isoelectronic with [CuCO]

, and like the latter,

is linear.

In water ligand models, the nominal Cu oxidation state is again the most important influence on the calculated NO stretch frequency, with a higher oxidation state resulting in a higher frequency. Additional coordination has a secondary, but significant, effect comparable to that found for the carbonyl complexes. Regardless of the oxidation state, as coordination increases and the Cu center becomes more electron rich, the NO bond lengthens and the NO stretch frequency decreases. Bending also

91 affects the NO bond length and frequency. We expect and find NO to bend in all the nominal Cu(0) and Cu(I) complexes, but surprisingly, as the Cu-coordination increases, bending becomes favorable for the Cu(II) complexes as well. Bent and linear results for NO on Cu(II) are listed in Table 6.4. NO bending results in an increased occupation of the antibonding NO 2ss level and thus an increase in NO bond length and decrease in NO stretch frequency (by up to 70 cm

\Gamma 1

The nominal Cu(I) water ligand models and comparable purely siliceous models yield similar geometries and vibrational frequencies (Tables 6.4 and 6.2). As with the carbonyl systems, reducing the overall cluster charge and increasing the electron donation to Cu by introducing either Al or hybrid J atoms into the larger models results in a systematic decrease in calculated frequencies. The coordination and cluster charge effects are comparable in magnitude and difficult to separate in the Cu(I) models. In fact, for the larger ring models of Cu(I), the symmetry reduction accompanying bending allows the Cu center to move closer to two oxygen atoms, so that the framework coordination is ill-defined but certainly less than four. This effect is particularly pronounced in the nominally 4-coordinated [Cu(Si

AlO

)NO]

complex, in which the Cu ion clearly moves to a 2-coordinate location over the Al T-site, and illustrates the influence of the Al location on Cu coordination.

The coordination number and the nature of the model coordination environment have distinctive influences on the NO stretch frequencies in Cu(II) systems. The NO frequencies for linear and bent [Cu(Si

)NO]

(nominally Cu(II)) are more

than 90 cm

\Gamma 1

less than those of [Cu(H

NO]

. Introducing two Al atoms in the

larger Cu(II) model reduces the NO vibrational frequency even further, so that the 1- to 4-coordinated Cu(II)-NO water ligand models and the larger charged and neutral Cu(II)-NO models span separate regions of the vibrational spectrum.

Figure 6.4 shows a plot of the EFFF NO stretch frequency vs. the N-O bond length for both water ligand and larger model complexes. Unlike the monocarbonyl complexes, three distinct frequency regimes are observed corresponding to nominal Cu(0), Cu(I) or Cu(II) (i.e., effectively [Cu(I)-NO

\Gamma

], [Cu(I)-NO] or [Cu(I)-NO

respectively). An almost linear correlation, independent of the cluster charge, binding mode of NO (linear or bent) and details of the local coordination environment of Cu, is observed with an overall fit quality of 0.9910. Here again, the data point corresponding to gas phase NO, which was not used in the fitting procedure, lies

92 1.05 1.10 1.15 1.20N-O bondlength (A*)1400.0 1600.0 1800.0 2000.0 2200.0 2400.0

NO stretch frequency (cm -1)

Cu(II) systems (water-ligand model) Cu(II) systems (larger model) Cu(I) systems (water-ligand model) Cu(I) systems (larger model) Cu(0) systems (water-ligand model)

expt: Cu(I)NO expt: Cu(II)NO NO (gas)

n = -4914.34 + 7494.84r Figure 6.4: Calculated NO frequencies (*, from EFFF method, scaled by 0.97) vs. N-O bond lengths (r) for mononitrosyl complexes. Linear fit to data and ranges of experimental values (from Table 6.4) are also shown.

close to the best fit line. Comments that were made earlier about the predictive nature of a similar plot for carbonyl complexes apply here as well. The N-O bond lengths and frequencies span a much greater range and are thus much more sensitive to model choice than was the case with carbonyl complexes. This greater sensitivity is consistent with the increased charge transfer and greater covalency in the Cu-NO bond than in the Cu-CO bond.

In Figure 6.4, we also show frequency ranges corresponding to absorptions that

93 have been assigned to NO adsorbed on Cu(I) and Cu(II) sites in zeolites [16-18,36,37, 39-41]. The two ranges are separated by 100 cm

\Gamma 1

, with the higher one assigned to

NO on Cu(II) and the lower one to NO on Cu(I). These assignments are consistent with our model results. For Cu(I), both water ligand and larger models produce frequencies in the range of the experimental results; both are reasonable models of Cu(I) sites in Cu-exchanged zeolites. Again, given the uncertainties associated with the overall computational method and models, we cannot unequivocally associate the experimental frequencies with any one coordination model considered here. For Cu(II), the larger models clearly produce frequencies that are most consistent with the experimental results, while the water ligand models produce frequencies that are consistently too large. As noted earlier, bands at 1895 cm

\Gamma 1

and 1912 cm

\Gamma 1

have been

assigned to the stretching modes of NO bound to Cu

near one and two framework

Al, respectively [17, 39]. The trends we observe in frequency vs. local coordination environment suggest the opposite assignment. However, an additional factor that may be important in these and all Cu(II) vibrational frequency assignments is the presence of extra-lattice O

\Gamma

and/or OH

\Gamma

. Extra-lattice oxygen is thought to be important in

charge compensating Cu(II), particularly in over-exchanged zeolites [6, 30]. While we have not explored the effects of extra-lattice oxygen in detail, we have found that inclusion of an OH

\Gamma

ligand in the Cu coordination sphere can shift CO and

NO stretch frequencies downward in the same way that Al or hybrid J atoms do. For this and the reasons listed above, we hesitate to associate one particular Cu(II) coordination model with Cu(II) in ZSM-5.

6.5 Cu

-bound dinitrosyl [Cu(H

(NO)

]

complexes

Dinitrosyl species have been observed experimentally when the reduced forms of CuZSM-5 or Cu-Y (containing predominantly Cu(I)) are exposed to NO [16-18, 36, 37, 39-41]. Also, dinitrosyl species have been suggested to play a role in the mechanism of NO decomposition [6, 18, 40, 41]. We describe here the results that we obtained from vibrational frequency calculations on dinitrosyl complexes within the framework of our water ligand model. The calculated symmetric and antisymmetric dinitrosyl stretch frequencies for these complexes, along with experimentally observed frequencies in Cu-exchanged zeolites [16-18, 36, 37, 39-41], are collected in Table 6.6. For Cu(I) complexes, frequency calculations were performed only for singlet (

) states,

94 which were the ground states. Hartree-Fock calculations [79] for nominal Cu(I)- bound dinitrosyl species yield symmetric and antisymmetric NO stretch frequencies of 1646 cm

\Gamma 1

and 1578 cm

\Gamma 1

, respectively. These values significantly underestimate

the observed dinitrosyl frequencies in Cu-exchanged zeolites (by over 150 cm

\Gamma 1

even without allowing for a further reduction by a typical Hartree-Fock scaling factor (ss 0.89 [89]).

Cu in the dinitrosyl complexes, as in mononitrosyl complexes, has a strong propensity to remain in an effective Cu(I) oxidation state, irrespective of the overall charge and degree of coordination. As described in Chapter 5, dinitrosyl binding to Cu

, Cu

and Cu

can be approximately represented as [Cu(I)-(NO)

\Gamma

], [Cu(I)-

(NO)

] and [Cu(I)-(NO)

], respectively, so that across the series, electrons are removed from orbitals of NO 2ss origin. The N-O bond lengths and vibrational frequencies of the dinitrosyl species are consonant with this view of charge transfer. In the case of [Cu(NO)

]

, with effectively neutral (NO)

, the calculated scaled symmetric

and antisymmetric normal mode NO stretch frequencies (1869 cm

\Gamma 1

and 1798 cm

\Gamma 1

respectively) and bond length (1.14

* A) are even in surprisingly good agreement with

the observed gas phase bare NO dimer frequencies of 1860-1870 cm

\Gamma 1

and 1760-

1788 cm

\Gamma 1

[143, 144] and bond length of 1.16

* A. In the more reduced Cu(NO)

systems, the N-O bond lengths are increased and vibrational frequencies decreased,

while for the more oxidized [Cu(NO)

]

systems, the opposite trend is observed. As

before, higher Cu coordination has the effect of decreasing frequencies and increasing bond lengths. Regular correlations are again observed (Figure 6.5) between the N-O bond lengths and EFFF NO frequencies for Cu-bound dinitrosyl complexes. As in dicarbonyl systems, the averages of the symmetric and antisymmetric NO stretch frequencies lie reasonably close to the straight line taken from the fit to the corresponding mononitrosyl results in Figure 6.4. The splitting between the two stretch modes again decreases with increasing Cu oxidation state, but by a much smaller amount than in dicarbonyl complexes, presumably because the bonding combination of 2ss orbitals is always at least singly occupied in dinitrosyl complexes.

Experimentally observed frequencies [16-18, 36, 37, 39-41] that have been previously assigned to symmetric and antisymmetric modes of dinitrosyl species adsorbed at Cu(I) sites in Cu-ZSM-5 and Cu-Y zeolites are also indicated in Figure 6.5. The present calculations reinforce this interpretation, as only the calculated frequencies

95 1.05 1.10 1.15 1.20N-O bondlength (A*)1400.0 1600.0 1800.0 2000.0 2200.0

NO stretch frequency (cm -1)

Cu(II) systems (sym) Cu(II) systems (anti) Cu(I) systems (sym) Cu(I) systems (anti) Cu(0) systems (sym) Cu(0) systems (anti)

expt: sym expt: anti

Figure 6.5: Calculated symmetric and antisymmetric NO stretch frequencies (from EFFF method, scaled by 0.97) vs. N-O bond lengths for dinitrosyl [Cu(H

(NO)

]

complexes. Linear fit to

mononitrosyl results (from Figure 6.4) and ranges of experimental values (Table 6.6) are also shown.

for Cu(I) complexes are in reasonable agreement with the experimentally observed frequencies. The above experience with monocarbonyl and mononitrosyl species suggests that this assessment would persist even if the simple water ligand models considered in this section were supplemented with results for larger clusters. The present Cu(I) results are also consistent with the frequency ranges of 1810-1940 cm

\Gamma 1

and

1685-1815 cm

\Gamma 1

, that have been assigned to symmetric and antisymmetric NO stretch

frequencies, respectively, for dinitrosyl species adsorbed on other transition metal ion

96 exchanged zeolites and on supported and unsupported transition metal oxides [139]. This indicates that the mode of dinitrosyl binding found here for Cu

complexes,

viz., [Cu(I)-(NO)

], (with the dinitrosyl remaining more or less neutral) is probably

the preferred mode in most other systems as well.

6.6 Summary and Conclusions In this chapter, we have presented a set of CO and NO vibrational frequency calculations for Cu-bound mono- and dicarbonyl and mono- and dinitrosyl complexes. We have shown that the results of these calculations can be combined with available IR experimental measurements both to assess the reliability of our models and to help interpret experimental observations. In general, our models yield CO and NO stretch frequencies in ranges that are quite consistent with IR measurements. In all cases, our calculations reinforce previous assignment of the observed frequencies.

We have identified several factors that affect the CO and NO stretch frequencies:

1. In general, a lower nominal Cu oxidation state results in lower CO and NO

frequencies. Because mono- and dinitrosyl species interacting with Cu(0), Cu(I) and Cu(II) can be approximately described as [Cu(I)-(NO)

\Gamma

], [Cu(I)-(NO)

]

and [Cu(I)-(NO)

], x = 1,2, respectively, three distinct frequency regimes are

observed for nitrosyl complexes, one for each charged state of the adsorbed (NO)

species. The dependence on oxidation state is less dramatic in the case of

carbonyl complexes; Cu(I) and Cu(II) complexes display CO stretch frequencies in overlapping ranges (due to similar extent of charge transfer between CO and Cu in these two cases).

2. A higher degree of Cu coordination has the secondary, but significant, effect of

lowering the CO and NO frequencies. The Cu center becomes a better electron donor and poorer electron acceptor as its coordination number increases, resulting in a greater charge transfer to CO and NO, an increase in the C-O and N-O bond lengths, and a decrease in stretch frequencies.

3. More sophisticated zeolite models generally result in lower CO and NO stretch

frequencies. The frequency trends can be summarized by:

water ligand

CO;NO

* *

larger (siliceous)

CO;NO

? *

larger (with Al or J)

CO;NO

97 where the equal sign is for Cu(I) systems. The overall frequency range is much broader for Cu(II) than for Cu(I) systems, with a much greater disparity between water ligand and larger models in the former case. The water ligand models may provide a reasonable description of Cu(I) sites in zeolites, but more sophisticated models may be required to study the Cu(II) sites.

4. In the mononitrosyl complexes, NO bending lowers the NO stretch frequency.

Despite the large variations in NO and CO stretch frequencies that occur in our models, we find very strong linear correlations between calculated frequencies and bond lengths for each class of adsorbates considered. These correlations and the above trends should prove useful in future studies of Cu-exchanged zeolites.

98 Chapter 7 Orbital symmetry analysis of Cu-dinitrosyl complexes

The field of chemistry deals not just with total energies of systems of atoms and molecules, but largely with how these systems evolve in phase space (chemical reactions). It was mentioned in Chapter 3 that the potential energy hypersurface of a system of atoms and molecules is multidimensional, and chemical reactions are paths on this hypersurface. Each electronic state (determined from the occupations and symmetries of the one-electron orbitals, OE

) of the system is characterized by its own

hypersurface. Usually, we are concerned only with the lowest surface, corresponding to the ground state.

In principle, a reacting system must conform to the dictates of quantum mechanics at every stage of the reaction, i.e., at every point on the energy hypersurface; but, in general, the explicit analysis of a reacting system (i.e., obtaining detailed information about the potential energy hypersurface in the vicinity of the reaction path) is forbiddingly complex. There are, however, select cases when symmetry considerations enter in a relatively straight-forward manner, and by proper analysis, very powerful and general conclusions about the feasibility of reactions can be drawn. The most comprehensive study in this area has been performed by Woodward and Hoffmann [20-22].

The Woodward-Hoffmann rules are symmetry-based selection rules for the feasibility of chemical reactions, relying mainly on the conservation of orbital symmetry along the reaction coordinate.

Reactions can thus be classified as forbidden or allowed by a systematic application of these rules. For these symmetry rules to be

Symmetry-based conservation principles are not new in the physical sciences: for instance, the

conservation of momentum, angular momentum and energy follow from the translational, rotational and time-translational invariance, respectively, of the physical laws.

99 applicable, the following two conditions need to be fulfilled: (i) the reaction should be a concerted process; a reaction is said to be concerted or synchronous if the reactants come together and are transformed into products in one continuous, progressive manner, such that the bond-breaking and bond-forming steps occur simultaneously, and (ii) during the entire course of the concerted reaction, one or more symmetry elements of the reacting system must be preserved. Orbitals of the reactants must then continuously evolve along the reaction coordinate, implying that a reactant orbital of a certain symmetry cannot become a product orbital of a different symmetry.

Group theory, the mathematical tool that helps simplify problems and analyse results in physical systems that have an inherent symmetry, is used to classify the orbitals, OE

, based on their symmetries. That OE

's can be classified this way at all

follows from Wigner's theorem, which states that the solutions of the Schr"odinger-- or, in the present context, the Kohn-Sham--equation belong to one of the symmetry species of the point group of the molecular system. Once the reactant and product orbitals are classified, orbitals of like symmetry are correlated in what are referred to as correlation or "Walsh" diagrams, which are used to predict the feasibility of reactions.

It is well known that NO is thermodynamically unstable to decomposition to N

and O

[179, 180]. However, free NO has an unusual kinetic stability [179, 180] due

to a rather high activation barrier (ss 70 kcal mol

\Gamma 1

) to the decomposition reaction,

2N O ! N

+ O

: (7.1)

The high activation barrier is, in part, due to the symmetry forbidden nature of the symmetric, concerted reaction passing through a cyclic transition state [180, 181]; under extreme conditions, reaction 7.1 instead occurs via a sequence of high-energy atom exchange reactions [182].

In this chapter, by using an orbital symmetry analysis, we show that the singlestep decomposition of all Cu-bound dinitrosyl (N-down, O-down) and hyponitrite species discussed in the Chapter 5 is symmetry forbidden as well. We also attempt to explain the basic features of the equilibrium geometries of the Cu-bound dinitrosyl species and draw a formal connection, using orbital overlap considerations, between the free NO dimer (which also has a long N-N bond length) and the adsorbed dinitrosyl species. We first review the symmetry forbidden nature of reaction 7.1 in the gas phase, passing through a cyclic transition state.

100 1b1 2a12b2

3a12b1

1b21a2

3b22a2 4a14b2

1a1

3a1

O N

NO 6s NO 2p

NO 5s NO 1p

O 6s N 2p

p pp

1 2 3

O O

N N N

O N

2b2 3b2

2a2

N 5s O 2p

2b1 4a1

1a21b2

1a1 2a1 1b1

N 1p O 5s O 1p

Figure 7.1: Orbital correlation (`Walsh') diagram for levels of the same C

symmetry associated

with two isolated NO molecules (left), the cis-symmetric dimer (NO)

(center) and decoupled N

and O

(right). Levels below those indicated by arrows are all doubly occupied, and those above are

empty. Levels involved in forbidden crossings are connected by solid lines, and the levels themselves are darkened and pictured. The majority spin level crossing is indicated by a circle.

7.1 Free NO decomposition The decomposition reaction 7.1 is exothermic by about 44 kcal mol

\Gamma 1

at the BP86

level of theory, in good agreement with the value of 43 kcal mol

\Gamma 1

, determined using

the experimental atomization energies of NO, N

and O

[89, 102]. Figure 7.1 shows

a schematic of the orbital correlation diagram [20-22] along such a pathway, with C

symmetry maintained throughout. The diagram depicts the 1ss, 5oe, 2ss and 6oe

derived levels of two isolated NO molecules (left), cis-(NO)

(middle), and N

and

(right). The ground state of each of the three sets of molecules is triplet; the

unpaired electrons are indicated by arrows in Figure 7.1 and C

symmetry labels are

used to label the molecular orbitals. Orbitals of like symmetry in the three parts of Figure 7.1 are connected by lines (while adhering to the non-crossing rule for levels of the same symmetry [20-22]) to indicate the continuous evolution of levels along a

101 13 13 *B

B13

B13 13 *B

13 *B O

O O O N N N N O

Figure 7.2: State correlation diagram for states of the same C

symmetry associated with two

isolated NO molecules (left), the cis-symmetric dimer (NO)

(center) and decoupled N

and O

(right).

suitable reaction coordinate. All occupied and unoccupied levels of the two isolated NO molecules correlate with the occupied and unoccupied levels, respectively, of (NO)

. The dimerization of NO is, thus, symmetry allowed. In going further to the

decomposition products N

and O

, however, an initially occupied b

level and an

initially unoccupied a

level, which correlates with the N

5oe orbital, cross (circled in

Figure 7.1) among majority spin (") levels; among minority spin levels, there are two more crossings of levels in addition to the circled crossing, as the initially occupied a

and b

levels and unoccupied a

and b

levels (which correlate with the N

1ss

orbitals) cross. It follows that a major reorganization of charge density is necessary in (NO)

for its decomposition to N

and O

. The decomposition reaction is thus

multiply symmetry forbidden, as the formation of both the oe and ss bonds of N

lead

to energy level crossings [20].

An alternative argument can be made based on state correlations (Figure 7.2). The ground state of two isolated NO molecules and (NO)

\Theta b

) resulting

102 from the same electronic configuration (Figure 7.2), and so, NO dimerization is symmetry allowed. The ground state of the decomposition products N

and O

is also

\Theta b

), but correlates to a quadruply excited state for the two isolated NO

molecules (and (NO)

)

, indicated as

\Lambda

in Figure 7.2. Since excited state wavefunctions of the same symmetry as the ground state can mix with the ground state wavefunctions during the course of the reaction (configuration interaction), thereby permitting the reaction to occur in the ground-state potential energy surface throughout, the intended crossing implied at the orbital level is avoided. Nevertheless, the fact that it was intended and the fact that the excited state involved is considerably higher in energy (as it is a quadruply excited state), lead to a large barrier [20]. Such reactions, which are allowed by state symmetry and disallowed by orbital symmetry considerations, are termed forbidden by orbital symmetry [20].

7.2 Free NO dimers vs. Cu-bound dinitrosyl species A surprising structural feature of the N-down dinitrosyl complexes discussed in Chapter 5 is the `tilting in' of the NO ligands, such that the O-O separations are considerably less than the N-N separations (Table 5.4). This tilting in suggests some electronic interaction between the nitrosyl ligands, but mediated through the O atoms rather than through the N atoms, contrary to what is normally supposed for metal dinitrosyl complexes [128,183,184]. In the O-down complexes, a similar, although less surprising, effect is seen in which the terminal N atoms are closer to each other than are the O atoms. It is interesting to consider the interaction between two nitrosyl ligands on a single Cu site, to gain insight into these geometric features and into the nature of the ligand-ligand interactions.

A useful starting point for this discussion is the interaction of a gas-phase NO dimer with an isolated Cu ion. We choose the case of [Cu(NO)

]

, as here a minimal

amount of charge transfer between the two fragments occurs. Figure 7.3 shows a schematic interaction diagram for the formation of [Cu(NO)

]

(center) from (NO)

That it is a quadruply excited state can be seen by rearranging the electrons in the left (and

middle) of Figure 3 (thereby creating an excited state), so that levels of the same symmetry remain occupied in going to the right.

103 d 2p

3a12b1

2a23b2

2b25s

CuNN 1+

N O

1+ O

3a1 2a2 4a1

2b1

5a1

2b2 3b2

3b1

s 1 eV

3a2 4b2

Figure 7.3: Schematic interaction diagram for the formation of [Cu(NO)

]

from Cu

and free

(NO)

. The [Cu(NO)

]

orbitals are shown in the center (labels as in Figure 5.5(b)), and those

of the free (NO)

(labels as in Figure 7.1) and Cu

fragments are shown in the left and right,

respectively.

(left, with orbital labels as in Figure 5.4) and Cu

(right). The primary metalligand bonding interaction occurs between the out-of-phase combination of NO 5oe orbitals and a Cu d

orbital, with the orbitals of NO 2ss origin further interacting

104 with and splitting the Cu d manifold. The NO 2ss manifold is doubly occupied, with singlet and triplet states obviously close in energy. The oe-bonding (2b

) interaction

dominates the metal-ligand bonding and is maximized at an N-Cu-N angle of 90

ffi

favoring an increased separation of the N centers, while the inter-ligand interactions are mediated through the 5a

and 3b

orbitals and favor a decrease in ligand separation. Figure 7.4(a) shows the evolution of these orbitals as the N-N separation is varied and the remaining geometric parameters relaxed, while Figure 7.4(b) shows the variation in total (BP86) energy along the same geometric coordinate. As the N-N separation is increased beyond the 2.0

* A displayed in Figure 7.3, the oe-bonding

orbital drops in energy and the total energies of both the singlet and triplet states decrease until a separation of approximately 3.0

* A is reached, corresponding to an

N-Cu-N angle of ss 90

ffi

. Thus, the N centers of the coordinated (NO)

are forced

apart by the drive to maximize the metal-ligand oe-bonding.

The increased separation of N centers does not lead to any qualitative changes in the [Cu(NO)

]

electronic structure, which retains a similarity to a combination of

and (NO)

fragments. In particular, the orbitals of NO 2ss origin are essentially

unchanged in energy along the N-N separation coordinate (Figure 7.4(a)). The slight stabilization of the 5a

level is due to a monotonic decrease of the Cu-N-O angle

as the N-N bond length increases (shown in Figure 7.4(c)), which maximizes the favorable overlap interaction between the two NO 2ss orbitals through the O atoms. The decrease of the Cu-N-O angle is such that the O-O separation at the equilibrium geometry is 0.5

* A less than in free (NO)

. This bending clearly reflects some coupling

between the two NO ligands, mediated through the O atoms rather than the N atoms. Figure 7.5 shows the change in orbital and total energies for fixed (equilibrium) N-N separation and N-Cu-N angle, for a range of values of the Cu-N-O angle. Bending inward of the NO ligands is accompanied by a stabilization of the bonding combinations of the NO 2ss levels, and decreases the total energy by approximately 20 kcal mol

\Gamma 1

(Figure 7.4(b)). A further 10 kcal mol

\Gamma 1

stabilization arises due to

relaxation from the triplet state favored for large values of the Cu-N-O angle to the singlet state preferred for smaller values of the angle (Figure 7.4(b)). Thus, the ability of the Cu ion to tie-up the NO oe orbitals and to force apart the N atoms results in the longer N-N and shorter O-O separations found in [Cu(NO)

]

, relative

to those in free (NO)

105 Orb ital En

erg y

Tot al E

ner gy

N-N Bond Length (A*) 1.5 2.0 2.5 3.0 Cu -NO ( deg

ree s)

120 180 240

1A1

3B1

(a) (b) (c)

3b1

5a1

3b2 NO 2pp

Cu d

NO 5ss 40 kcal/mol

4 eV

O O N N

3a2

4b2

Figure 7.4: Evolution of BP86 energy levels (a), BP86 total energy (b) and optimal Cu-N-O angle (c) of [Cu(NO)

]

along a N-N separation coordinate. All geometric parameters are optimized at

each N-N bond length.The square indicates the forbidden crossing of levels of unlike symmetry during N-N bond formation.

Additional coordination of the Cu center does not alter this general picture of its interaction with (NO)

. Similarly, oxidation or reduction of the system by one

electron does not change the qualitative orbital picture, but only alters the occupation of orbitals of NO 2ss origin which control the O atom coupling. Thus, the O atom coupling and physical separation are diminished in [Cu(NO)

]

and increased in

[Cu(NO)

] relative to those in [Cu(NO)

]

106 Orb ital En

erg y

Cu-N-O (degrees) 100 120 140 160 180

Tot al E

ner gy

(a)

(b)

NO 2pp

Cu d

20 kcal/mol

2 eV 4b2 3a2 3b1

5a1

Figure 7.5: Evolution of BP86 energy levels (a) and BP86 total energy (b) of [Cu(NO)

]

as a

function of the Cu-N-O angle. The Cu-N bond length, N-Cu-N angle and N-Cu-N-O dihedral angle are fixed at 1.95

* A, 95

ffi

and 0

ffi

, respectively (corresponding to a N-N bond length of 2.87

* A),

and the N-O bond length is optimized for a range of Cu-N-O angles.

As we have seen, an O-down dinitrosyl structure is also accessible on Cu

which we have designated as [Cu(H

(ON)

]

. As seen from a comparison of

Figures 5.6(a) and 5.5(b), the electronic structure of this O-down state is not sub 107 stantially different from the corresponding N-down one. Again this structure is well described in terms of separate Cu

and (NO)

fragments, with the O-O separation determined primarily by the requirements of coordination to Cu, and the N-N coupling, and tendency for pairing of the highest lying electrons, enhanced by the presense of Cu.

The geometries and electronic structures of all the Cu dinitrosyl complexes can thus be readily described in terms of the interaction of Cu ions with (NO)

. In fact,

the results suggest that it may be most appropriate in these complexes to consider (NO)

as a single, bidentate ligand, and it may even be possible that within the

confined channels of a zeolite, (NO)

may adsorb directly onto a Cu site in either the

N-down or O-down orientation. Evidence does exist for the enhanced dimerization of NO within zeolite nanopores [185]. The presence of the Cu ion does increase the coupling within the bound (NO)

, but the primary coupling occurs through the atoms

not directly coordinated to Cu. We have found no evidence of other types of binding of two NO ligands on Cu, for instance structures analogous to those found in earlier transition metal dinitrosyl complexes, in which one of the nitrosyl ligands is linear and the other bent [128, 154, 155, 180].

As an aside, we mention that CO does not dimerize in the gas phase, and shows no tendency to couple when bound to a Cu site in geminal form. We found previously in Chapter 5 that dicarbonyl species bound to Cu ions in zeolitic environments exhibit only linear Cu-C-O bonds, as do monocarbonyl species [19]. Furthermore, these dicarbonyl species display negligible splitting between symmetric and antisymmetric CO vibrational frequencies, which reflects weak coupling between the two CO ligands [19]. In contrast, Cu-bound dinitrosyl species display a relatively large splitting between the corresponding NO frequencies [19].

7.3 NO decomposition and N-N bond formation on zeolite

bound Cu ions

Finally, we examine if the concerted, symmetric reaction of the dinitrosyl structures just discussed, either to form a short N-N bond structure or free N

and O

, is

feasible. We address the former issue by focussing on the evolution of total and orbital energies as the N-N bond length is gradually decreased from its equilibrium value for the specific case of [Cu(NO)

]

. The discussion naturally carries over to

108 complexes with higher Cu-coordination, as well as to other charged cases.

Earlier studies of the formation of a short N-N bond in N-down transition metal dinitrosyl complexes focussed on systems with lower metal d electron counts: 4 in ReCl

(NO)

\Gamma

[186] and 6 in FeCl

(NO)

[187]. The former study [186] used

empirical methods to calculate orbital and total energies, and no geometry optimization of the complexes were performed; the latter study [187] used ab initio (GVB-CI) methods, but reported only restricted optimization of reaction end-point geometries. Neither considered the possible decomposition of the bound dinitrosyl species to N

and O

. Formation of a N-down hyponitrite structure, with a short N-N bond, from

adsorbed dinitrosyl species has also been suggested to occur on Rh surfaces [181].

[Cu(N O)

]

. As discussed in the previous section, the NO-derived levels in Cubound dinitrosyl complexes are essentially unchanged from those shown in Figure 7.1 for two isolated NO molecules or free (NO)

. The Cu d levels in [Cu(H

(NO)

]

(shown in Figure 7.3 for [Cu(NO)

]

), lie between the NO 5oe/1ss and the NO 2ss

derived levels, and the occupancy of the NO 2ss derived levels is determined by the nominal oxidation state of the Cu. Hence, introduction of Cu in any of its three nominal oxidation states preserves the level ordering of (NO)

. The concerted,

symmetric decomposition of a pair of nitrosyl ligands bound to Cu ion sites in zeolites to free N

and O

is thus still multiply forbidden by orbital symmetry.

The possibility of formation of a stable short N-N bond structure in the N-down dinitrosyl species is examined in Figure 7.4, which includes the evolution of orbitals and variation in (BP86) total energy of [Cu(NO)

]

with a decrease in N-N separation below that found in free (NO)

(i.e., 2.0

* A). The total energy is found to

increase monotonically with the decrease in N-N separation, by a total of almost 70 kcal mol

\Gamma 1

above the equilibrium structure at the shortest distances considered.

Along this pathway, an initially occupied 2b

level and an initially unoccupied 3b

level cross (denoted by a square in Figure 7.4(a)), reflecting an approximate oneelectron oxidation of the Cu center. The resultant electronic state is reminiscent of the `hyponitrite-like' O-down structures discussed earlier, but no minimum energy structure is found for the N-down orientation in the short N-N separation limit. Similar conclusions are reached for [Cu(NO)

] and [Cu(NO)

]

, and we conclude

that strong N-N coupling in N-down dinitrosyl complexes of Cu does not occur. Figure 7.4(a) suggests that for even lower electron counts, N-N coupling of the

109 nitrosyl ligands would become symmetry allowed and possibly energetically favorable

. Kersting and Hoffmann [186] previously concluded that N-N bond formation

on ReCl

(NO)

(with a fRe(NO)

core) is symmetry-allowed but thermodynamically unfavorable, and Casewit and Rapp'e [187] found that N-N bond-formation in FeCl

(NO)

(fFe(NO)

) is symmetry-allowed as well as thermodynamically

feasible.

The cross-over point in Figure 7.4(a) corresponds to a switch of the dinitrosyl species to a N-down hyponitrite-like structure. The O-down hyponitrite-like complex is about 40 kcal mol

\Gamma 1

lower in energy than the [Cu(NO)

]

structure with a

N-N bond length of 1.1

* A. At such short N-N distances, the O atoms are well separated from each other and little geometric distortion is necessary for its conversion to [CuO

]

. Thus, the conversion of N-down bound dinitrosyl complexes to the

corresponding O-down structure is symmetry allowed, and thermodynamically and geometrically accessible, provided that the symmetry forbidden and thermodynamically unfavorable initial N-N coupling step occurs.

[Cu(ON )

]

and [CuO

]

. The electronic structure of [Cu(ON)

]

is very

similar to that of [Cu(NO)

]

, both of which have electronic level ordering identical

to that of free (NO)

. Thus, the disproportionation of bound (ON)

to free N

and

remains multiply forbidden by orbital symmetry. As in dinitrosyl complexes, the

electronic structures of the hyponitrite-like complexes ([CuO

]

and [CuO

]) are

also different from those of N

and O

(right panel of Figure 7.1). Hence, the disproportionation of the hyponitrite-like complexes to N

and O

is symmetry forbidden

as well.

In Cu

systems, although stable, short N-N bond, O-down structures exist, their

formation from their long N-N bond counterparts is disallowed by orbital and state symmetry (cf. Figures 5.6(a) and 5.6(b)). Such a symmetry disallowedness is unimportant when the short N-N bond structure has a comparable or higher stability than the long N-N bond structure. As mentioned earlier, the stability of the former structure increases with increasing electron density at the Cu center (for instance,

The relative positions of the metal d and NO levels may depend strongly on the d electron

count, so that the orbital diagram appropriate for systems with lower d electron counts may be different from that in the present case.

110 either when the Cu is highly coordinated or in proximity of strong Lewis base sites like framework Al).

All these considerations indicate that a simple, single-step disproportionation of Cu-bound dinitrosyl or hyponitrite-like species to free N

and O

by a symmetric,

concerted process is symmetry forbidden. For a single Cu site to be active for NO decomposition, the decomposition products, viz. N

and O

, must instead be formed

in a multi-step process, for instance, by the formation of a N

O intermediate, as

has been suggested earlier [16-18, 41]. The formation of a N-N bond necessary for the production of such an intermediate seems unlikely in all dinitrosyl (N-down and O-down) complexes studied; however, the hyponitrite-like complexes identified here hold considerable promise as precursors for such a multi-step decomposition process.

7.4 Summary and Conclusions We have examined the possibility of N-N bond formation in Cu-bound dinitrosyl and hyponitrite species by studying simple cluster models that incorporate the dominant interactions within these complexes in real zeolites. Our main conclusions can be summarized as follows:

1. The presence of the Cu ion does enhance the coupling between the pair of

bound nitrosyl ligands, but the primary coupling occurs through the atoms not directly coordinated to Cu.

2. The ground state electronic level ordering of dinitrosyl as well as hyponitrite-like

complexes indicate that the simple single-step, symmetric, concerted decomposition reaction of these Cu-bound species to N

and O

remains as kinetically

unfavorable as the gas phase NO decomposition. The short N-N bond lengths in Cu-hyponitrite-like complexes, on the other hand, suggest that such complexes may be intermediates in a more complex multi-step decomposition over Cu-zeolites. This last possibility will be addressed in the next chapter.

111 Chapter 8 The mechanism of catalytic decomposition of NO by Cu-exchanged zeolites

The main tactical problem in modeling the course of chemical reactions, be

they ozone depletion or a pericyclic reaction under new conditions, is to find a reasonable balance between completeness of description of an object or

phenomenon under study, and the simplicity of the models applied.

--Roald Hoffmann

The results of the last chapter have clearly indicated that a single-step decomposition of a Cu bound dinitrosyl (or hyponitrite) species remains symmetry forbidden and electronically disallowed, and hence, is as unlikely to occur as the free NO decomposition. However, as NO decomposition in the presence of Cu-exchanged zeolites is observed, it must occur by a more complex multi-step process. In fact, controlled experiments show a selectivity of the reduced Cu-exchanged zeolite catalysts (containing predominantly Cu

) for the formation of N

O at low temperatures; it is only

at higher temperatures (? 600 K) that N

formation is observed at all [17]. Based

on these observations, Aylor et al [17] propose that N

O is formed from (N-down)

-dinitrosyl species in an initial step, followed by the activation of N

O and its

conversion to N

at a higher temperature. However, it is not clear how the N-down

-dinitrosyl complex rearranges to result in N

O. In fact, our analysis of the geometric and electronic structures of N-down dinitrosyl species (Chapter 7) shows that this mechanism is unlikely.

In this chapter, we examine the possibility of a more novel multi-step NO decomposition process that differs from all previous mechanistic speculations. The O-down hyponitrite species encountered in Chapter 6 displays a short N-N bond, and could well be the reactive intermediate resulting in the formation of N

O following the

scission of one of the two O-N bonds. The decomposition process proposed here is initiated by the formation of the Cu

-bound O-down hyponitrite or isonitrosyl inter 112 mediate, and yields sequentially N

O and Cu-bound O followed by N

and Cu-bound

. Decomposition of Cu-bound hyponitrites to CuO and N

O in non-zeolitic environments have been observed earlier [157, 158]. We identify transition states for each of the reactions considered, and find that the catalytic cycle is energetically as well as electronically feasible (i.e., allowed by orbital symmetry). Thus, we find evidence for a pathway involving two succesive O-atom transfers to an isolated zeolite-bound Cu

center. Since the reactive O-down intermediate is found only at Cu

sites, we conclude that isolated Cu

sites in zeolites are inactive, at least for the decomposition

initiation process.

The complete characterization of a chemical reaction entails a knowledge of the full potential energy hypersurface of the reacting system. In practice, this requirement is reduced to determining the hypersurface in the vicinity of the reactants, the products, the transition state, and the minimum energy pathway connecting the three. While the first two quantities are routinely calculated these days, determination of the third can be somewhat tricky (Appendix B), and determination of the fourth depends, in practice, on a knowledge of the transition state. The minimum energy pathway is usually determined by following the two steepest descent paths from the transition state, one leading to the reactants and the other to the products. When mass weighted coordinates are used, the minimum energy path becomes the intrinsic reaction coordinate (IRC), proposed earlier by Fukui [159]. Reaction pathways can be found by this method for most simple chemical reactions, although exceptions exist due to the so-called "chemical hysteresis" which manifest for reactions with more than one saddle-point (transition state) along the reaction coordinate [160]. Fortunately, all chemical reactions examined in the present study were amenable to the IRC treatment.

8.1 Computational details All calculations reported in this chapter were performed using three models of Cu

sites in zeolites (Figure 8.1), which we generically represent as ZCu

, Z = none,

2(H

O), Al(OH)

\Gamma

, so that Cu is in a 1+ oxidation state formally; we refer to these

three models as the bare, the water ligand and the T-site models, respectively. The choice of these models is motivated by the preference of Cu

ions in zeolites for 2-

fold coordination environments. When a ligand L is bound to the Cu, we represent

113 ZCu1

N5 O2

(d)

ZCu1 O2

(f)

N4 1+

N5 ZCu1

(e)

N4 N3

O5 O2

Cu1

H9O6

H14

(c)(b)(a) Cu1 Cu1

H11H9

1+ 1+

H8H10 O6 O7

Al10

O12O11 H13

Figure 8.1: Schematic sketches of the bare (a), the water-ligand (b) and the T-site (c) models of zeolitic Cu

sites, and the transition state structures ZCuO

(d), ZCuONNO

(e) and

ZCuOONN

(f). Dotted lines indicate bonds that are being cleaved. Atom indices are used to

define natural internal coordinates in Appendix B.

the complex as ZCuL

; the oxidation state of Cu in this case is determined by the

nature of the ligand. One of the implications of the results of Chapter 7 is that the decomposition reaction is unlikely to occur in the higher symmetry C

energy surface, either in free form or in the presence of zeolitic Cu sites. Hence, all complexes here are constrained to the lower C

symmetry, the highest symmetry permitted by

the reactions considered.

As mentioned in Chapter 2, transition state and IRC searches were performed by optimization of natural internal coordinates [104, 105]; natural internal coordinates, as described in Appendix B, are suitable (symmetry-adapted) linear or non-linear combinations of internal coordinates. The reason for not preferring ordinary internal coordinates is that these coordinates are, in general, strongly coupled, leading to large off-diagonal Hessian (second energy derivative) matrix elements, which results in slow or no convergence during transition state geometry optimizations. Natural internal coordinates make the Hessian diagonally dominant, and so expedite the convergence

114 process. As the option of using natural internal coordinates was not available in ADF, the optimizer in GAMESS [106] (which had this utility built-in) was used. ADF was used to calculate the initial Hessian, and energies and gradients at each optimization step [107]. As in equilibrium geometry determinations, transition state geometries were determined within the LSDA, and energies were calculated at the BP86 level of theory at the LSDA optimized geometries. For the simplest (bare) models, transition state geometries and IRCs were determined both at the LSDA and BP86 levels. Harmonic vibrational frequencies were calculated at the LSDA optimized transition states. In general more than one imaginary frequency was found. All the imaginary a

frequencies correspond to vibrational modes breaking the C

symmetry imposed,

and all but the largest a

mode involve O-H stretches and are not points of concern in

the present study. In all cases, the largest imaginary frequency always corresponded to the mode along the reaction coordinate.

8.2 Results Free NO decomposition The gas phase interaction of two NO molecules provides important clues for possible Cu-zeolite catalyzed decomposition mechanisms of NO. It was shown earlier in Chapter 7 that the symmetric, concerted, single-step reaction of two NO molecules to produce N

and O

(reaction (7.1)) is forbidden by orbital symmetry; hence, it has

a high activation barrier and is unlikely to occur. Instead, at high temperatures, the free decomposition reaction proceeds by a multi-step process [182], beginning with the formation of N

O and O:

ON + N O ! O(

P ) + N

O (8.1)

Transition state calculations for the above reaction followed by IRC searches indicate that it occurs along a coordinate in which the two NO approach through the N ends. The geometry at the transition state is listed in Table 8.1. A correlation diagram for reaction (8.1), under C

symmetry, is depicted in Figure 8.2; the energy levels of the

reactants (2NO) are shown in the left panel and those of the products (O(

P ) + N

are shown in the middle panel. Unlike in Figure 7.1, Figure 8.2 demonstrates the smooth evolution of occupied and virtual orbitals characteristic of an electronically allowed reaction pathway; thus, the lowest energy

potential surface yields ground

state products. Reaction (8.1) was found to have a large barrier (38 kcal mol

\Gamma 1

), due

115 Table 8.1: Geometries, frequencies and total energies for the transition state complexes involved in the NO decomposition reactions. Atom indices are consistent with those in Figure 8.1. BP86/LSDA stands for LSDA geometries and single-point BP86 energies at LSDA geometries. Values in parenthesis are LSDA energies. All bond lengths in

* A, bond and dihedral angles in degrees, frequencies

in cm

\Gamma 1

and energies in kcal mol

\Gamma 1

ONNO

-N

: 1.183 N

-N

: 1.163 N

-O

: 1.695 O

-N

: 165.1 N

-N

-O

: 109.2

E -516.3 NNOO

-N

: 1.145 N

-O

: 1.292 O

-O

: 1.593 N

-N

-O

: 145.7 N

-O

: 116.0

E -501.8

Z = none Z = 2H

O Z = Al(OH)

\Gamma

4 BP86/LSDA BP86 BP86/LSDA BP86/LSDA

ZCuO

2 Cu1-O2 2.979 2.845 2.526 2.542

Cu1-O3 1.770 1.834 1.765 1.747

O2-N4 1.181 1.202 1.196 1.201

N4-N5 1.173 1.192 1.158 1.162 N5-O3 1.651 1.653 1.761 1.775 Cu1-O6 - - 1.991 1.932 O2-Cu1-O3 73.9 75.6 82.7 83.0

N4-N5-O3 156.1 151.2 152.6 150.8 O6-Cu1-O7 - - 90.4 78.1 O6-Cu1-O2-O7 - - 166.2 160.6 imag. freq. a

: 473i 627i 537i; 120i 517i; 23i

: 291i; 80i 134i

E -376.1 -378.3 -1087.0 -1741.5

(-439.8) - (-1207.8) (-1902.7) ZCuONNO

Cu1-O2 1.773 1.831 1.762 1.756

O2-N3 1.604 1.616 1.624 1.642

N3-N4 1.183 1.203 1.179 1.173 N4-O5 1.173 1.190 1.182 1.196 Cu1-O6 - - 1.988 1.930 Cu1-O2-N3 110.8 110.0 107.9 103.6

O2-N3-N4 109.5 108.8 109.1 110.5 N3-N4-O5 158.2 153.3 155.4 154.0 O6-Cu1-O7 - - 91.5 78.4 O6-Cu1-O2-O7 - - 166.7 175.3 imag. freq. a

: 617i 644i 583i; 145i 530i; 64i

: 273i 256i; 112i; 32i

E -380.2 -381.4 -1091.5 -1738.9

(-444.8) - (-1209.1) (-1900.7) ZCuOONN

Cu1-O2 1.778 1.826 1.767 1.758

O2-O3 1.552 1.645 1.551 1.553

O3-N4 1.397 1.460 1.375 1.343

N4-N5 1.132 1.128 1.141 1.154 Cu1-O6 - - 1.987 1.930 Cu1-O2-O3 109.7 103.7 107.9 108.0

O2-O3-N4 117.0 121.3 114.6 111.9

O3-N4-N5 138.4 142.9 135.6 133.8 O6-Cu1-O7 - - 93.2 78.5 O6-Cu1-O2-O7 - - 177.3 168.5 imag. freq. a

: 1001i 1028i 889i 690i; 16i

: 328i 144i

E -364.0 -365.7 -1072.7 -1722.5

(-420.6) - (-1186.0) (-1879.1)

116 N O2

N O2 N O2

O2 O2 N2 N2 N O2

O2 N2

N O2 N2 O2 NO 5s

NO 2p

O 2p

1p 5s

7s 2p

5s 1p

2p 2p

NO 1p

2NO + O +Reaction 8.1 Reaction 8.2 Figure 8.2: Schematic orbital correlation diagram for reactions (8.1) and (8.2) along a planar reaction coordinate. Arrows indicate filling of highest occupied molecular orbitals, and solid and dashed lines indicate symmetric (a

) and antisymmetric (a

) orbitals, respectively. The diagram demonstrates

smooth evolution of occupied and virtual orbitals, characteristic of an electronically allowed reaction pathway.

almost wholly to its net endothermicity (36 kcal mol

\Gamma 1

). At high temperatures the

above reaction initiates a series of Zeldovich substitution reactions [182], but in the present context it is more useful to consider a simpler process in which the products of reaction (8.1) recombine through the O centers on the same

potential energy

surface to produce ground state products:

O + O(

P ) ! N

+ O

(8.2)

Figure 8.2 shows the orbital correlation diagram for reaction (8.2), indicating the electronic feasibility of the second step as well. Calculations indicate that this step is both highly exothermic (81 kcal mol

\Gamma 1

) and has a modest barrier (16 kcal mol

\Gamma 1

);

the geometry at the transition state is listed in Table 8.1. Reactions (8.1) and (8.2) suggest that a catalytic site that can behave as a reservoir for O atoms, by accepting and stabilizing it in the first step, and by releasing it in the second to produce the final products, may serve as a suitable candidate for the thermodynamically efficient decomposition of NO. Below, we demonstrate the plausibility of Cu-exchanged zeolite

117 aided NO decomposition akin to the above process in the gas phase, and identify a microscopic route by which such successive atom transfers can occur.

The first step: N

O formation from Cu-bound O-down hyponitrite

We now consider the feasibility of reactions (8.1) and (8.2) in an environment similar to what might be found in a Cu-exchanged zeolite, with the bare (Cu

), the

water-ligand ((H

) and the T-site (Cu(AlO

)) models. Selected geometric

parameters and energies of equilibrium and transition state structures of all relevant complexes are listed in Tables 8.2 and 8.1, respectively.

An isolated Cu

ion in a zeolite is a likely candidate to serve as an O(

P ) atom

reservoir. ZCuO

has been postulated to be formed during the NO decomposition

process, but has not been definitively identified experimentally [17, 47]. Calculations indicate that, irrespective of the choice of the model, ZCuO

is stable with a

ground state. The extra-lattice O atom partially oxidizes the Cu center, yielding an electronic structure intermediate between ZCu

-O and ZCu

-O

\Gamma

, with the unpaired

electron density distributed over both the Cu and O centers. While orbital and charge analyses give greater weight to the latter, the former resonance structure makes explicit the connection to ground state ZCu

and O(

P ). The binding energy

of O(

P ) to ZCu

is 51, 43 and 79 kcal mol

\Gamma 1

within the bare, water-ligand and

T-site models, respectively (Table 8.3). The products of reaction (8.1) can thus be considerably stabilized.

Next, we search for possible reactants that could result in ZCuO

and N

O. We

anticipate finding some form of N-N coupling in such reactants. Clearly, the N-down structures discussed in Chapter 6 fail to qualify, due to the pronounced absence of such a coupling, and are likely spectator species and not intermediates in this reaction. The Cu

-bound O-down species, particularly the hyponitrite species, on the other

hand have an electronic configuration (

ground state) and geometric structure

(short N-N bond, partially cleaved N-O bonds) that are suggestive of the first step in an NO decomposition process. A search for a transition state of the following reaction:

ZCuO

! ZCuO

+ N

O; (8.3)

resulted in the structures listed in Table 8.1 for the three models.

Geometric Structure and Frequencies of ZCuO

. A schematic of ZCuO

shown in Figure 8.1. We first focus on the bare model results before dealing with the

118 Table 8.2: Geometries and total energies for reactant and product complexes involved in the NO decomposition reactions. O

refers to framework O. Atom indices for ZCuONNO

are consistent

with those in Figure 8.1. BP86/LSDA stands for LSDA geometries and single-point BP86 energies at LSDA geometries. Values in parenthesis are LSDA energies. All bond lengths in

* A, bond and

dihedral angles in degrees and energies in kcal mol

\Gamma 1

Z = none Z = 2H

O Z = Al(OH)

\Gamma

BP86/LSDA BP86 BP86/LSDA BP86/LSDA

ZCu

)

Cu-O

- - 1.861 1.938

-Cu-O

- - 176.2 85.9

E +187.4 - -538.3 -1159.3

(+191.4) - (-592.1) (-1252.4)

ZCu(ON)

)

Cu-O 2.056 2.204 2.169 2.038

O-N 1.160 1.167 1.176 1.205

N-N 1.964 2.111 1.778 1.548 Cu-O

- - 1.924 1.937

O-Cu-O 80.9 80.1 74.4 74.5

Cu-O-N 121.9 121.8 121.8 104.9 O

-Cu-O

- - 93.3 79.1

E -409.5 -411.4 -1112.8 -1744.2

(-471.8) - (-1232.3) (-1908.1)

ZCuO

)

Cu-O 1.953 2.002 1.928 1.895

O-N 1.255 1.275 1.276 1.297

N-N 1.259 1.278 1.242 1.245 Cu-O

- - 2.011 1.930

O-Cu-O 79.1 78.5 78.3 79.8

Cu-O-N 100.3 111.3 113.0 112.9 O

-Cu-O

- - 93.3 77.1

E -391.7 -392.8 -1099.9 -1754.0

(-464.2) - (-1227.2) (-1923.4) ZCuONNO

)

Cu1-O2 1.878 1.970 2.130 1.819

O2-N3 1.203 1.211 1.190 1.207

N3-N4 1.949 2.100 1.904 1.742 N4-O5 1.126 1.132 1.141 1.161 Cu1-O6 - - 1.901 1.938 Cu1-O2-N3 121.0 119.5 113.9 128.5

O2-N3-N4 106.9 109.1 107.0 108.8 N3-N4-O5 110.6 112.0 109.1 112.3 O6-Cu1-O7 - - 162.7 78.2 O6-Cu1-O2-O7 - - 174.4 169.8

E -411.1 -412.6 -1113.5 -1746.8

(-469.1) - (-1227.2) (-1904.7) ZCuO

)

Cu-O 1.736 1.786 1.717 1.699 Cu-O

- - 2.007 1.925

-Cu-O

- - 88.4 76.1

-Cu-O-O

- - 180.0 180.0

E +100.8 +100.6 -617.7 -1274.1

(+96.9) - (-676.8) (-1376.7)

ZCuO

)

Cu-O 1.861 1.950 1.990 1.793

O-O 1.231 1.250 1.243 1.264 Cu-O

- - 1.924 1.936

Cu-O-O 117.3 115.5 111.4 119.0 O

-Cu-O

- - 148.6 78.4

-Cu-O-O

- - 178.8 170.6

E -50.5 -50.7 -762.1 -1400.3

(-75.0) - (-841.3) (-1525.9)

continued. . .

119 Table 8.2 (continued.) Free molecules

P ): E = -36.0; N

: E = -378.7 r

N\Gamma N

= 1.098; O

: E = -221.2 r

O\Gamma O

= 1.218

NO: E = -277.4 r

N\Gamma O

= 1.154; N

O: E = -483.0 r

N\Gamma N

= 1.130, r

N\Gamma O

= 1.181

water-ligand and T-site models. The geometric parameters at the transition state for the bare model were determined both at the LSDA and at the BP86 levels of theory; the difference between the two results are only a few percent (Table 8.1). Reaction (8.3) has a late transition state (almost fully formed N-N and N-O bonds in the N

O fragment) and a structure consistent with the simultaneous cleavage of

one of the Cu-O bonds and that of the O-N bonds involving the other O; it also has an imaginary frequency of 473i cm

\Gamma 1

(LSDA) and 627i (BP86) for the mode

corresponding to the cleavage of these same bonds. BP86 thus predicts a steeper potential energy surface in the vicinity of the transition state.

Table 8.1 also contains the (LSDA) transition state structural parameters for the water-ligand model. Within this model, all bond lengths and bond angles that do not involve the long Cu-ON

bond are in agreement with those of the bare model (LSDA)

to within a few percent. The Cu-ON

bond, on the other hand, is almost 25% shorter

Table 8.3: Reaction and activation energies (in kcal mol

\Gamma 1

) for various reactions.

Z = none Z = 2H

O Z = Al(OH)

\Gamma

BP86/LSDA BP86 BP86/LSDA BP86/LSDA

Reaction energies:

ZCu

+ O(

P ) ! ZCuO

-51 -51 -43 -79

ZCu

+ 2N O ! ZCuO

-24 -27 -7 -40

ZCuO

! ZCuO

+ N

O +10 +12 -1 -3

ZCu

+ 2N O ! ZCuON N O

-44 -47 -20 -34

ZCu

+ (N O)

! ZCuON N O

-26 -27 -2 -15

ZCuON N O

! ZCuO

+ N

O +29 +30 +13 -10

ZCuO

+ N

O ! ZCuO

+ N

-47 -47 -40 -22

ZCuO

! ZCu

+ O

+17 +17 +3 +20

Activation energies:

ZCuO

! ZCuO

+ N

O +16 +16 +13 +13

ZCuON N O

! ZCuO

+ N

O +31 +31 +22 +8

ZCuO

+ N

O ! ZCuO

+ N

+18 +17 +28 +35

120 in the water-ligand model, due to the higher electron donating capacity of Cu. The transition state has an imaginary a

LSDA frequency of 537i cm

\Gamma 1

, corresponding to

the cleavage of the Cu-ON

and CuO-N

O bonds. Other a

imaginary frequencies,

smaller in magnitude, correspond to modes that break the imposed C

symmetry

constraints by rotating or twisting of the water molecules.

The transition state structure in the T-site model, especially the OCuON

fragment, is very similar to that in the water-ligand model. The only differences arise in the zeolitic (Z) fragment, almost entirely due to the fact that in the water-ligand model, the "zeolitic" O atoms are free to relax (within the constraint of the C

symmetry), but in the T-site model, they are constrained by the presence of the Al atom. This is reflected in large differences in the O

-Cu-O

angle in these two models. The

Cu-O

bond, however, is only 3% shorter in the T-site model, compared to that in the

water-ligand model. Again, as in the water-ligand model discussed above, more than one imaginary frequency is found at the transition state. The largest (517i cm

\Gamma 1

)

mode corresponds to the cleavage of the Cu-ON

and CuO-N

O bonds.

Energetics of Reaction (8.3). The energy profiles, determined both at the LSDA and at the BP86 levels of theory, along the IRC are shown in Figure 8.3 for the bare model. Let us first focus on the reactant side of the profile, viz., to the left of the activation barrier in Figure 8.3(a) of reaction (8.3). The steepest descent from the transition state towards the reactants goes past a small "bump" in the potential energy surface (indicated by the arrow in Figure 8.3) before finally reaching the minimum corresponding to the O-down dinitrosyl structure (Cu(ON)

). The bump

coincides with the transition from the O-down hyponitrite to the O-down dinitrosyl structure. While under the constraint of C

point-group symmetry the two structures

are in different states (

and

, respectively), under the C

symmetry relevant to

the present discussion, they are in the same state (

), making the transition from

one structure to another allowed by state symmetry. While in the bare model, the Odown dinitrosyl structure is lower in energy than the O-down hyponitrite structure, the opposite is true in the T-site model, and so, in the latter case, the steepest descent from the transition state would naturally lead to the minimum corresponding to the hyponitrite structure. Thus, for the sake of consistency, we consider the hyponitrite as the reactant of reaction (8.3) in all models. Under that assumption, the activation energy of reaction (8.3) is predicted to be 16 kcal mol

\Gamma 1

at the BP86 level, both at

121 -480.0 -460.0 -440.0 -420.0 -400.0

Energy, kcal/mol

Reaction Coordinate

LSDA (a) (b) Cu+ + 2NO

CuO+ + N2O

Cu+ + O2

+ N2

-440.0 -430.0 -420.0 -410.0 -400.0 -390.0 -380.0 -370.0 -360.0

Energy, kcal/mol

Reaction Coordinate

BP86 (a) (b) Cu+ + 2NO

CuO+

Cu+ + O2

+ N2

+ N2O

Figure 8.3: LSDA and BP86 energy profiles along the IRC for (a) reactions (8.3) (open diamonds) and (8.5) (solid diamonds), (b) and reaction (8.6) (b) for the bare model. Arrows indicate transition from a long to short N-N bond length. Also shown are energies of reactants and products.

122 the LSDA and BP86 geometries.

We now turn to the DFT description of the potential energy surface in the product side of reaction (8.3). Both the LSDA and BP86 predict a product state corresponding to N

O physisorbed to CuO

, with rather long CuO-N

O and Cu-ON

bonds

(ss 2.2 and 3.7

* A, respectively). This may well be a real effect due to a van der

Waals or ion-dipole type of interaction between the CuO

and N

O, or it could be an

artifact of approximate DFT, which has been known to strongly disfavor bond breaking. Similar observations at the LDA and GGA levels have been made earlier [99]. Frequency calculations indicate that the physisorbed structure has low frequencies of 38 and 34 cm

\Gamma 1

(LSDA and BP86, respectively) for the mode corresponding to

the reaction coordinate, reflecting the flatness of the potential energy surface in this region. Also indicated in Figure 8.3 is the total energy of the products (CuO

O). The energy of desorption of N

O is predicted to be 17 and 9 kcal mol

\Gamma 1

at the

LSDA and BP86 levels, respectively. The BP86 description of the potential energy surface is markedly different, in that the disfavor to bond cleavage is mitigated at this level of theory. Under the assumption that the reactant of reaction (8.3) is CuO

the net endothermicity of the reaction is 11 kcal mol

\Gamma 1

(BP86).

Figure 8.4 shows the stationary points of reaction (8.3) for the water-ligand and T-site models. Although IRC searches were not performed for the larger models, a search for the possible physisorbed product state, found in the bare model was performed. The stabilization of the physisorbed products disappears at the higher (BP86) level of theory for the larger models (although it continues to remain at the LSDA level). Thus, the stabilization effect is a function of both the level of theory as well as the model used; for the smaller bare model, which has a more inhomogeneous electron density, even the higher level BP86 potential predicts a physisorbed product state. More work is needed to gain better insight into this observation. The activation energy for reaction (8.3) is the same in both the water-ligand and T-site models (13 kcal mol

\Gamma 1

, BP86), and not too different from the bare model result. Reaction

(8.3) is exothermic by 1 and 3 kcal mol

\Gamma 1

(BP86) in the water-ligand and the T-site

models, respectively.

The net thermodynamics of reaction (8.3) depends on that of reaction (8.1) and the extent to which the reactants and products of the latter reaction are stabilized by interaction with ZCu

(Table 8.3). The extent of stabilization of the prod 123 20 kcal/mol (b)

(a)

(i)

(viii)

(vii) (vi) (v)

(iii) (ii)

(iv)

(ix) (i)

(ix) (viii)

(vii) (vi) (v)(iv) (iii)

(ii)

Figure 8.4: Relative energies of reactants, transition states and products involved in reactions (8.3)-(8.7) within the water-ligand (a) and T-site (b) models: (i) ZCu

+ 2NO, (ii) ZCuO

, (iii)

ZCuONNO

, (iv) ZCuO

, (v) ZCuONNO

, (vi) ZCuO

+ N

O, (vii) ZCuOONN

, (viii)

ZCuO

+ N

and (ix) ZCu

+ O

+ N

ucts (O(

P )) relative to that of the reactants increases along the the series: Cu

, (AlO

)Cu, and so, the endothermicity of reaction (8.3) decreases along

the same series. In more realistic models of the zeolite with even higher electron density at the Cu center, the reaction may become highly exothermic.

O formation from Cu-bound isonitrosyl species

While it is possible that the hyponitrite is itself an intermediate in the catalytic decomposition of NO, it is more likely that the same favorable electronic and geometric effects are achieved without the second NO ever interacting directly with the Cu. N

O can be formed either by the interaction of a gas phase NO with a O-down

isonitrosyl intermediate (ZCuON

) through an Eley-RidealfootnoteAn Eley-Rideal

124 process is described as one in which one of the reactants, bound to a catalytic site, reacts with a second reactant in the gas phase process, or via the formation of a weakly bound adduct. We do find evidence for a (meta)stable ZCuONNO

species with only

one of the nitrosyl ligands bound to Cu through its O, and the other nitrosyl ligand bound to the Cu-bound nitrosyl ligand via a N-N bond:

ZCu

+ 2N O ! ZCuON

+ N O ! ZCuON N O

(8.4)

ZCuON N O

! ZCuON N O

! ZCuO

+ N

O (8.5)

Alternatively, ZCuONNO

could also be formed by the interaction of a dimerized

(NO)

with Cu

. Enhanced dimerization of NO within the confines of the zeolite

pores has been observed earlier [185]. This process may be unlikely at the elevated temperatures at which the decomposition reaction takes place.

The electronic structure of the ZCuONNO

species is very similar to that of the

Cu-bound dinitrosyl species (N-down or O-down), discussed earlier in Chapter 5. Thus, like the dinitrosyl species, the ZCuONNO

too can be represented as [Cu(I)-

ONNO], with effectively no charge transfer between the Cu(I) site and the cis-(NO)

species, in all three models considered here. Mulliken population and MO decomposition analyses are consistent with the above representation of the ZCuONNO

complex.

Selected geometric parameters and binding energies of ZCuONNO

are listed in

Table 8.2. Unlike in cases discussed earlier, the structural parameters vary considerably from model to model. For instance, the LSDA Cu-O bond lengths are 1.878, 2.130 and 1.819

* A for the bare, water-ligand and T-site models, respectively. Another

striking feature is that the CuO-N bond is already considerably elongated (1.2

* A)

compared to the N-O bond length either in free NO or in the free (NO)

dimer,

whereas the N-O bond length in ZCuONNO

of the nitrosyl not directly bound to

Cu is equal to or shorter than the same bond in free (NO)

. The N-N bond length

is 1.9

* A in the bare and water-ligand models, but is shorter by 0.2

* A in the larger

T-site model.

From an energetic point of view, ZCuONNO

is more stable than the hyponitrite

by 19 and 14 kcal mol

\Gamma 1

in the bare and water-ligand models, respectively, but less

stable than the hyponitrite by 13 kcal mol

\Gamma 1

in the T-site model. Reaction (8.4) is

exothermic by 47, 20 and 34 kcal mol

\Gamma 1

in the three models.

125 Geometric Structure and Frequencies of ZCuONNO

. We now consider the activated complex ZCuONNO

(Figure 8.1), the transition state of reaction (8.5). As

before, we first focus on the bare model results before dealing with the water-ligand and T-site models. The LSDA and BP86 geometries at the transition state are only a few percent different from each other (Table 8.1). The transition state structure has an almost fully formed N-N bond and a partially cleaved CuO-N

O bond; it

has imaginary LSDA and BP86 frequencies of 617i cm

\Gamma 1

and 644i cm

\Gamma 1

for the mode

corresponding to the cleavage of the CuO-N

O bond. Again, BP86 predicts a sharper

saddle-point than LSDA.

Moving on to the water-ligand model, the stuctural quantities at the transition state change by less than a percent. The transition state has a few imaginary frequencies, the highest (583i cm

\Gamma 1

) corresponding to the CuO-N

O bond breaking

mode.

The T-site model, too, yields geometric results very similar to the bare and waterligand models, differing from them by about a percent. Again, due to the constraint on the "zeolitic" O atoms in the T-site model, the O

-Cu-O

angle in this model

differs significantly from that of the water-ligand model, where it was free to relax to a larger value. The CuO-N

O bond breaking mode has an imaginary frequency of

530i cm

\Gamma 1

Energetics of Reaction (8.5). LSDA and BP86 energy profiles along the IRC are shown in Figure 8.3. As in reaction (8.3), a small bump in the potential energy surface can be seen in the reactants side (indicated by the arrows in Figure 8.3). Inspection of the geometries in the vicinity of the bump indicates that the bump coincides with the formation of the N-N bond. The presence of this bump explains the almost fully formed N-N bond in CuONNO

. The activation energy of reaction (8.5) is

predicted to be 24 kcal mol

\Gamma 1

at the LSDA level and 31 kcal mol

\Gamma 1

at the BP86

level. The activation energy calculated from single-point BP86 energy evaluations at the LSDA equilibrium and transition state geometries also turns out to be 31 kcal mol

\Gamma 1

. As before, both the LSDA and BP86 predict a product state corresponding

to physisorbed N

O, with the energy of desorption of N

O from CuO

being 24 and

17 kcal mol

\Gamma 1

, respectively, at the two levels of theory. Once again, BP86 gives a

slightly different description of the potential energy surface in the region of phase space where the CuO-N

O bond cleaves. The net endothermicity of reaction (8.5)

126 is 29 kcal mol

\Gamma 1

(BP86), higher than that of the decomposition reaction beginning

with the hyponitrite.

The activation barrier of reaction (8.5) (Figure 8.4, Table 8.3) is calculated to be 22 and 8 kcal mol

\Gamma 1

for the water-ligand and T-site models, slightly higher and lower,

respectively, than the calculated values for the N

O formation step beginning with

the hyponitrite. A product state corresponding to physisorbed N

O was found only

at the LSDA level. Reaction (8.5) is endothermic by 13 kcal mol

\Gamma 1

in the water-ligand

model and exothermic by 10 kcal mol

\Gamma 1

in the T-site model.

The variation of the net thermodynamics of reaction (8.5) with model is more than that for reaction (8.3) (Table 8.3). This is due to the higher stability of ZCuONNO

than the hyponitrite in the bare and water model (by 20 and 13 kcal mol

\Gamma 1

, respectively) and a slight lower stability of the former in the T-site model (Table 8.3).

The second step: N

formation

From the analogy with gas-phase NO chemistry drawn above, a possible next step in a catalytic NO decomposition cycle is recombination of N

O and O(

P ) to produce N

and O

. As will be shown below, the O

thus generated would remain coordinated to

the Cu center. Selected geometric parameters and energies of all relevant complexes are collected in Tables 8.2 and 8.1.

We now consider a Eley-Rideal process in which a gas-phase N

O reacts with

ZCuO

+ N

O ! [ZCuOON N ]

! ZCuO

+ N

(8.6)

Again, a molecularly detailed pathway can be traced out on the

energy surface

for this reaction, involving the interaction of the two species through their O centers and direct formation of the transition state [ZCuOONN]

Geometric Structure and Frequencies of [ZCuOONN]

. Figure 8.1 shows a

schematic of the structure of [ZCuOONN]

. Bare model calculations yield very

similar LSDA and BP86 geometries for the transition state (Table 8.1). The reaction has an early transition state, with the N

-O bond lengthened by just about 0.2

* A and

the O-O bond only partially formed, and with imaginary LSDA and BP86 frequencies of 1001i and 1028i cm

\Gamma 1

, respectively. Both LSDA and BP86 thus predict a much

sharper saddle-point for the second reaction than for the N

O formation reaction.

The water-ligand model, too, predicts an early transition state for reaction (8.6), with geometric parameters within a percent of the bare model results at the LSDA

127 level of theory. An imaginary LSDA frequency of 889i cm

\Gamma 1

is predicted for the O-N

bond breaking and O-O bond formation mode.

The T-site model results for the geometry of the transition state are similar to the above two cases. Within this model, reaction (8.6) has a slightly earlier transition state than the above two cases. The frequency of the mode corresponding to the O-N bond breaking and O-O bond formation is predicted to be 690i cm

\Gamma 1

at the LSDA

level of theory.

Energetics of Reaction (8.6). LSDA and BP86 energy profiles along the IRC are shown in Figure 8.3. The steepest descent from the transition state towards the reactants leads to a structure with a long CuO-ON

bond (ss 3

* A), with the energy

of desorption of N

O from CuO

being 23 and 17 kcal mol

\Gamma 1

, respectively, at the

two levels of theory, similar to the desorption energies of the N

O adduct oriented

so that there is a long CuO-N

O bond, encountered earlier. The activation energy

of reaction (8.6), relative to isolated CuO

and N

O, is predicted to be 10 kcal

mol

\Gamma 1

at the LSDA level and 17 kcal mol

\Gamma 1

at the BP86 level, roughly the same

as the activation barrier in the gas phase. The activation energy calculated from single-point BP86 energy evaluations at the LSDA equilibrium and transition state geometries is 18 kcal mol

\Gamma 1

. On the products side of the potential energy surface,

the steepest descent leads smoothly to Cu-bound O

and free N

. Reaction (8.6) is

exothermic by 47 kcal mol

\Gamma 1

(BP86).

Like in earlier cases, the physisorbed reactant state disappears at the BP86 level of theory for both the water-ligand and T-site models. The activation energy is predicted to be 28 and 35 kcal mol

\Gamma 1

in the water-ligand and T-site models, respectively

(Figure 8.4, Table 8.3), more than 10 kcal mol

\Gamma 1

larger than in the bare model.

Higher activation energies for the formation of N

than for the formation of N

is consistent with the selectivity for N

O formation at low temperatures observed

experimentally [17]. Reaction (8.6) is predicted to be exothermic by 40 and 20 kcal mol

\Gamma 1

by the two models.

The lower exothermicity of reaction (8.6) compared to reaction (8.2) is due to the higher binding energy of O(

P ) to ZCu

than of O

to ZCu

(see below). The

ZCu

-O

binding energy relative to the ZCu

-O binding energy decreases along the

series: Cu

, (H

, (AlO

)Cu, and so does the exothermicity of reaction

(8.6).

128 We consider ZCuO

, one of the products of reaction (8.6), an intermediate that

has been postulated earlier but not observed directly in Cu-zeolite chemistry [17, 47]. Our calculations predict that, irrespective of the choice of Z, ZCuO

has an end-on,

bent "superoxo" structure, with an O-O bond length increased by 0.03-0.05

* A relative to free O

(Table 8.2). The electronic structure of ZCuO

can be described as

a mix between Z-Cu

-O

and Z-Cu

-O

\Gamma

; while Mulliken charge analyses indicate

a roughly equal mix between the two, MO decomposition analyses indicates a mix dominated by the former. Thus, Cu is in an intermediate state of oxidation between ZCu

and ZCuO

. As the qualitative description suggests, ZCuO

has a

ground

state, with spin density distributed between the Cu and the two O centers.

The decomposition cycle is completed by the desorption of triplet O

to regenerate

the reduced Cu site:

ZCuO

$ ZCu

+ O

(8.7)

The O

BP86 desorption energy is calculated to be 17, 2 and 20 kcal mol

\Gamma 1

in the

bare, water-ligand and T-site models, respectively, comparable to the binding energy of a pair of nitrosyl ligands to Cu (in ZCuONNO

or ZCuO

8.3 Discussion Shown in Figure 8.5 is the correlation diagram for reactions (8.5) and (8.6) in the bare model. The energy levels of CuONNO

are shown in the left panel, those of

CuO

and N

O in the middle and those of CuO

and N

in the right. The smooth

evolution of occupied and virtual orbitals characteristic of an electronically allowed reaction pathway can be seen. Except for the presence of Cu d-derived levels, Figure 8.5 is similar to Figure 8.2. Figures 8.3 and 8.4 also demonstrate the kinetic plausibility of the decomposition mechanism proposed here, with modest activation barriers--comparable to the adsorption energies of reactant molecules--for each step. Thus, reactions (8.4)-(8.7) consitute an electronically, thermodynamically and kinetically plausible pathway for the conversion of NO to N

and O

on isolated Cu sites.

A distinguishing feature of this mechanism is the successive transfer of two O atoms to the mononuclear active site, the first transfer oxidizing the active site, the second transfer partially rereducing it and the desorption of O

restoring the active site.

This redox behavior of the zeolitic Cu is delineated in Figure 8.6. The ability to act as a template for O

production without irreversible formation of more highly

129 Cu

O N

N O

O N

a'' a'

a'a' a''

a''a' a'a'' a'

a' a''

a'a'' a' a'a''

a' a'a'' a'a''

a'a'' a'

a'' a'

a' a' a'

a''

a'' a''

a''

a'a'' a'a''

a' (NO)2

1p,5s

N2O s, 1p

N2O 3p N2O 2p N 5s

N 1p

O 2p

O 5s O 1p

N 2p 2p

O py

O pz Cu d

Cu d Cu d

(NO)2

Cu dz2

O px

Reaction 8.7Reaction 8.6 [Cu(I)-(NO) ] [Cu(II)-O ] + N O [Cu(I)-O ] + N2

2 2 2

a''a' a'a' Cu s

Cu s Cu s

Figure 8.5: Schematic orbital correlation diagram for reactions (8.5) and (8.6) along a planar reaction coordinate. Arrows indicate filling of highest occupied molecular orbitals. The diagram demonstrates smooth evolution of occupied and virtual orbitals, characteristic of an electronically allowed reaction pathway. All qualitative features are similar to those in Figure 8.2 except for the presence of the Cu d levels.

oxidized species may in part account for the high activity of Cu-exchanged zeolites for NO decomposition, and suggests a criterion by which to evaluate other exchanged metal ions for this activity. Clearly, ZCuO

is a crucial intermediate in establishing the balance between reactions (8.5) and (8.6): environments (or Z models) that stabilize ZCuO

will promote the N

O formation step but inhibit subsequent N

130 N O2N O2

ZCu O

ZCuO

2ZCuONNO +

NO Figure 8.6: The redox catalytic cycle for NO decomposition with Cu-exchanged zeolites.

formation, while environments that destabilize ZCuO

may be inactive for the first,

and hence the overall, decomposition process. Table 8.3 indicates that, along the series: Cu

, (H

and (Al(OH)

)Cu, reaction 8.5 becomes more exothermic, and

reaction 8.6 becomes less exothermic, resulting in a balance between the formation and destruction of ZCuO

. The ability to balance the two may well be an important

criterion for a catalytic system.

A variety of more complicated NO decomposition mechanisms for Cu-exchanged zeolites have been proposed (Chapter 2), postulating for instance the intermediacy of Cu ion dimers [37] or the spontaneous decomposition of ill-defined Cu-N

aggregates [18]. Although we have not assessed the relative importance of these other mechanisms, we have demonstrated that the simple mechanism proposed here can explain the fundamental observation of stoichiometric NO decomposition over Cuexchanged zeolite catalysts, and is consistent with other aspects of the observed chemistry. For instance, inhibition of the catalytic activity by excess O

has been

observed [188]. Present results are consistent with this observation, as excess O

shifts the equilibrium of reaction (8.7) to the left, depleting the catalytically active

131 Cu

sites. Another important experimental observation is the production of N

O at

lower temperatures [17, 55] than required for the formation of N

. Again, our model

calculations are consistent with the observation, as the calculated activation barrier for the formation of N

(equation (8.6)) is higher than that for the formation of N

(equation (8.5)).

8.4 Conclusions Using three simple models of zeolitic Cu

sites, viz., Cu

, (H

, and

(AlO

)Cu, the essential features of a new, plausible mechanism of catalytic NO

decomposition are outlined. The decomposition process proposed here is initiated by the formation of the Cu

-bound hyponitrite or isonitrosyl intermediate, and yielding

sequentially N

O and Cu-bound O (whence Cu

gets oxidized to Cu

), followed by

the formation of N

and Cu-bound O

. O

then desorbs regenerating the catalytically

active Cu

site. The redox nature of zeolite bound Cu is crucial to the proposed mechanism. Transition states and intrinsic reaction coordinates have been determined for the various mechanistic steps. This is the first reaction pathway for NO decomposition with Cu-exchanged zeolites that has been shown to be energetically, kinetically (i.e., with modest activation barriers) as well as electronically feasible (i.e., allowed by orbital and state symmetry).

132 Chapter 9 Summary

The mechanism of a chemical reaction is a logical construction based on a perforce limited set of experimental facts, which are then interpreted by human beings in the

framework of current, fashionable and ephemeral theoretical models.

--Roald Hoffmann

We have presented a first-principles analysis of some of the elementary steps in a heterogeneous catalytic cycle for the decomposition of NO by Cu-exchanged zeolites like ZSM-5. Our results suggest a likely pathway for this widely studied reaction that differs from all previous mechanistic speculations [6, 16-18, 41, 44, 52], and that involves a number of unusual and unanticipated intermediates. These new insights into the decomposition chemistry of NO may have broad implications, given the known environmental [9, 179] and biological [9, 192] significance of this molecule.

Our calculations have proceeded systematically, beginning with the development of a tractable model of the catalytically active Cu ion sites in zeolites, and then to study the interaction of the zeolite bound Cu with relevant adsorbates, including binding energies, vibrational frequencies and especially chemical reactions [14, 15, 19, 23].

Cu in zeolites We found that Cu

shows a strong preference for high coordination numbers and

thus is more likely to bind to 4-fold or higher coordination sites within ZSM-5. In contrast, Cu

prefers, or at least tolerates, lower coordination numbers and is more

likely to prefer 2-fold coordination sites. These results are consistent with EXAFS and XANES experiments [48-50].

Binding of CO and NO at Cu sites Cu-bound monocarbonyl, mononitrosyl, C-down gem-dicarbonyl (two CO ligands bound to the same site) and N-down gem-dinitrosyl species are all observed ex 133 perimentally by their vibrational signatures [16-18, 35-39, 41, 44], and are predicted here to be quite stable species as well. The binding of a single NO to Cu

, Cu

and Cu

can be best represented as [Cu(I)-(NjO

)], [Cu(I)-

(N=O\Delta )] and [Cu(I)-

1;3

(N=O

\Gamma

)], respectively, and that of a N-down dinitrosyl species by [Cu(I)-(NO)

[Cu(I)-(NO)

] and [Cu(I)-(NO)

\Gamma

], respectively [14, 15].

Binding modes of gem-dinitrosyl complexes The N-down Cu-gem-dinitrosyl complex (two NO ligands bound to the same Cu site) was believed to be the crucial intermediate for the catalytic decomposition or the SCR of NO [6, 16-18] through coupling between the two N atoms. However, present calculations indicate that there is negligible coupling between the N atoms in N-down gem-dinitrosyl species [15]; irrespective of the degree of coordination or oxidation state of Cu, the N-N bond in the dinitrosyl was consistently longer than 2.8

* A. In addition to the N-down binding mode of the dinitrosyl species (the only

one observed experimentally), two diferent O-down binding modes to Cu

were also

found in the present study: the first resembles the dinitrosyl binding of N-down complexes although with much shorter N-N bond lengths (ss 2

* A), while the second

resembles a hyponitrite bound to a metal atom (N-N bond length ss 1.2

* A). The

formal oxidation states in these two cases are best represented as [Cu(I)-(ON)

] and

[Cu(II)-O

\Gamma

], respectively. Neither of these two modes is found in the case of Cu

and only the latter is found in the case of Cu

[15]. All the above qualitative features

are independent of the type of zeolitic model used and should persist in any realistic study of Cu-exchanged zeolites.

Vibrational frequencies of adsorbates Vibrational frequency calculations were also performed on mono- and dicarbonyl, and mono- and dinitrosyl complexes to determine the adsorbate stretch frequencies, and have identified several factors that contribute to the shift of the adsorbate frequencies from their gas phase values [19]. These calculations have helped assess the reliability of our models and method, with predicted frequencies within a few percent of the observed ones. The calculations have also helped reinforce various experimental frequency assignments.

134 Mechanism of NO decomposition with Cu-exchanged zeolites Gem-dinitrosyl species were believed to either decompose directly in a single-step [6, 52] or by a multi-step process beginning with the formation of N

O in the first

step [16, 17]. By using an orbital symmetry analysis based on the WoodwardHoffmann selection rules, we have shown that, like the concerted, symmetric, singlestep decomposition of free NO, the single-step decomposition of all Cu-bound dinitrosyl (N-down, O-down) and hyponitrite species is symmetry forbidden [15]. Thus, the decomposition process has to proceed by a multi-step process in a lower symmetry environment. However, our analysis of the geometric and electronic structures of N-down dinitrosyl species indicates that such species are unlikely to form N

O as

well. Further, we have been unable to identify a molecular pathway leading indirectly from the N-down mononitrosyl plus a second gas-phase NO to N

O formation.

In the present study, we propose a novel decomposition mechanism beginning with the Cu

-bound hyponitrite or ZCuONNO

, none of which have been observed

experimentally to date. Using transition state searching and intrinsic reaction coordinate following, we have mapped out a multi-step reaction pathway, in which the O-down species mentioned above disproportionates to yield Cu-bound O (Cu

oxidized to Cu

) and N

O in the first step, and Cu-bound O

and N

in the second

step. O

then desorbs regenerating the catalytically active Cu

site. The redox nature of zeolite bound Cu is crucial to the proposed pathway. This simple mechanism is consistent with experimental observations like inhibition of the catalytic activity by excess O

[188] and the selectivity of N

O at low temperatures.

Aspects of this generic mechanism may also play a role in non-zeolitic NO chemistry: e.g., in the gas-phase disproportionation of NO to N

O and NO

at high

pressures [189], where an additional NO molecule may play the O atom accepting role outlined here for Cu, and in other inorganic [5, 191] and enzymatic [9, 192] NO decomposition reactions, where N

O is a known intermediate.

Future directions The zeolitic models used in the present study were not designed to mimic any particular zeolite, but just zeolite-like environments. Thus, the varying activities shown by different zeolites (of which ZSM-5 shows the highest activity) has not been addressed here. The necessary conditions for a zeolite to be active could be: (i) large pore sizes required to stabilize the transition state structures (all zeolites that show

135 high activity have channel intersections with diameters of 10

* A or larger, and typical

transition state structures identified here span more than 6

* A), and (ii) ability to

stabilize ZCuO

--the pivotal intermediate--just the right amount. Clearly, more

elaborate calculations are necessary to identify the crucial role ZSM-5 plays in the catalytic activity of exchanged Cu ions.

The present study has focussed on the role of isolated Cu ion sites in zeolites in the decomposition of NO, in the absence of any other reductants. Issues pertaining to the role of "oxocations" (-[Cu

-O

2\Gamma

-Cu

]

-) [37], and those pertaining to

the more industrially relevant selective catalytic reduction (SCR) [6, 9], where other reductants like CO, NH

, or hydrocarbons play an important role in the NO decomposition mechanism are not addressed here. The importance and significance of other species, like NO

, NO

, and other higher oxides of nitrogen, present during the direct

decomposition reaction conditions are also not assessed.

136 Appendix A Errors in decoupled EFFF frequencies

For the specific case of a linear triatomic complex CuYO (Y = C, N), we demonstrate the effects of decoupling the Y-O stretch mode from the Cu-Y stretch mode. Neglect of the doubly degenerate Cu-Y-O bending modes do not affect the stretch frequencies in this case as the bend and stretch modes are of unlike symmetry.

Let r and r

be the Y-O and Cu-Y bond distances, respectively. The secular

equation for the vibrational modes and frequencies is

jFG \Gamma E*j = 0 (A.1) F is the force constant matrix in terms of the internals r and r

F =

0 @

1 A

(A.2)

with f

= @

E=@r

, f

= f

= @

E=@r@r

, and so on. The G matrix is given by:

G =

0 @

+ _

\Gamma _

+ _

1 A

(A.3)

where _

is the reciprocal of the mass of Y, and so on.

The secular equation is then given by

fi fi fi fi fi fi

a \Gamma e \Gamma * d

c b \Gamma e \Gamma *

fi fi fi fi fi fi

= 0 (A.4)

where

a = f

+ _

)

b = f

+ _

)

c = f

+ _

) \Gamma f

d = f

+ _

) \Gamma f

e = f

Solving for *,

* =

(a \Gamma x) + (b \Gamma x) \Sigma (a \Gamma b)

1 +

4cd

(a \Gamma b)

(A.5)

137 Table A.1: Various degrees of approximations in vibrational frequency calculations. All frequencies are in cm

\Gamma 1

species *

F ull

Y O

Eqn: A:6

Y O

EF F F

Y O

CuYO complexes (linear Cu-Y-O):

[CuN O]

2292 2291 2303

[Cu(H

O)N O]

2248 2249 2238

[Cu(H

O)CO]

2243 2243 2214

[Cu(H

O)CO]

2336 2328 2303

CuYO complexes (non-linear Cu-Y-O):

[CuN O] 1699 1703 1723 [Cu(H

O)N O] 1572 1598 1569

[Cu(H

O)CO] 1914 1922 1914

Cu(YO)

complexes:

[Cu(N O)

] 1587,1721 1617,1744 1632,1750

[Cu(N O)

]

1854,1927 1899,1941 1885,1948

=) * = a \Gamma e +

(a \Gamma b)

; b \Gamma e \Gamma

(a \Gamma b)

(A.6)

upto first order in cd=(a \Gamma b)

Within the EFFF approximation, * = a; b, and so, *

EF F F

Y O

= 2ss

+ *

In the actual normal mode analysis, however, e results in a constant downward shift of both the uncoupled a and b terms, whereas the interaction matrix elements c and d further repel the downward shifted (a \Gamma e) and (b \Gamma e) terms.

Similar analyses can be made for other cases, for instance, for the case of bent CuYO complexes, or that of larger CuYO containing complexes; however, effects not considered in the present discussion--especially stretches and bends due to bonds other than Y-O and Cu-Y--are likely to have a much smaller effect on the uncoupled terms a and b, than the effects already pointed out above. The above table shows Y-O stretch frequencies calculated within the normal mode analyses, with the Cu-Y stretch taken into account (using Eqn. A.6), and within the EFFF approximation. In general, the EFFF approximation introduces an error of just a few percent in the normal mode harmonic Y-O stretch frequency. The direction of the error depends on

138 the relative magnitudes of e and cd=(a \Gamma b). Coupling of the Cu-Y and Y-O modes results in a downward shift of *

EF F F

Y O

relative to the normal mode result, whereas e

(or f

), which is a measure of the covalency in the bonds has the opposite effect.

In the case of dicarbonyl and dinitrosyl complexes, the 2 \Theta 2 F and G matrices are replaced by their appropriate 4 \Theta 4 counterparts. A few representative symmetric and antisymmetric Y-O stretchs in Cu(YO)

complexes are also shown in the above

table.

139 Appendix B Natural Internal Coordinates

For a system consisting of N atoms, local internal coordinates are usually defined as a set of 3N-6 (or 3N-5 for linear systems) bond lengths, bond angles and dihedral angles. Geometry optimizations to determine equilibrium geometries (local minima in potential energy hypersurface) are generally quite easy as guessing starting geometries is usually quite straightforward. These calculations are efficiently performed in terms of internal coordinates rather than in terms of the 3N cartesian coordinates due to the lower dimensionality of the problem in the former coordinate system; usually, an initial diagonal Hessian (second energy derivative or "force-constant" matrix) is used, which is refined after every geometry step.

In contrast, transition state (saddle-point) determinations are significantly harder. The diagonal Hessian almost never works, and a Hessian computed for a structure that is the best guess for the transition state--the hardest in most cases--should be provided. Another possible problem with transition state calculations is that internal coordinates are strongly coupled. A common example to illustrate this might be a bond length in a ring geometry, and the angle on the opposite side of the ring. Clearly, changing one directly affects the other. Another way of saying the same thing is that there are large off-diagonal matrix elements in the Hessian computed in the internal coordinate system.

The most effective way of handling this problem is to use the "natural internal coordinates" of Pulay [104, 105]. These are symmetry-adapted linear (non-linear in the case of ring geometries) combinations of local internal coordinates. In this new coordinate system, the Hessian is diagonally dominant, and the transition state calculation converges the fastest.

Thus, for the system of interest, the Hessian is computed in any coordinate system (the cartesian system, in the implementation used in the present study) at the best guess for the transition state. Natural internal coordinates are determined by the

140 procedure outlined in Ref. [104, 105], and the Hessian is transformed to the natural internal coordinate system. The geometry optimization is then performed in this coordinate system with the "pre-conditioned" Hessian.

In the present study, as the option of using natural internal coordinates was not available in ADF, the optimizer in GAMESS [106] (which had this utility built-in) was used; ADF was used to calculate the initial hessian, and energies and gradients at each optimization step, and GAMESS supplied ADF with successive geometries until convergence was reached. IRC searches for the bare model were also performed with this protocol starting at the transition state and following the steepest descent paths along each direction of the normal mode with the imaginary frequency [107].

In the following, we list the natural internal coordinates used for the structures in Figure 8.1(d)-(f), for each model used. Internal coordinates like (1-2), (1-2-3), and (1-2-3-4) stand for the bond lengths, bond angles and dihedral angles between the numbered atoms, respectively, and (1-2, 2-3-4) stands for the angle between the bond between atoms 1 and 2, and the plane formed by atoms 2, 3 and 4.

B.1 Natural internal coordinates for bare model Figure 8.1(d)

1. (1-2)

2. (1-3) 3. (2-4) 4. (3-5) 5. (4-5) 6. (2-3-1) + cos 144

ffi

[(1-2-4) + (1-3-5)] + cos 72

ffi

[(2-4-5) + (3-5-4)]

7. (cos 144

ffi

\Gamma cos 72

ffi

)[(1-2-4) \Gamma (1-3-5)] + (1 \Gamma cos 144

ffi

)[(2-4-5) \Gamma (3-5-4)]

8. (2-4-5-3) + cos 144

ffi

[(1-2-4-5) + (1-3-5-4)] + cos 72

ffi

[(3-1-2-4) + (2-1-3-5)]

9. (cos 144

ffi

\Gamma cos 72

ffi

)[(1-3-5-4) \Gamma (1-2-4-5)] + (1 \Gamma cos 144

ffi

)[(2-1-3-5) \Gamma

(3-1-2-4)]

141 Figure 8.1(e) and 8.1(f )

1. (1-2)

2. (2-3) 3. (3-4) 4. (4-5) 5. (1-2-3) 6. (2-3-4) 7. (3-4-5) 8. (1-2-3-4) 9. (2-3-4-5)

B.2 Natural internal coordinates for water-ligand model Figure 8.1(d) 1-9. same as for bare model

10. (1-6) 11. (1-7) 12. (6-8) 13. (6-10) 14. (7-9) 15. (7-11) 16. 5.(6-1-7) + (2-1-3) 17. (7-1-3) \Gamma (6-1-2) + (7-1-2) \Gamma (6-1-3) 18. (7-1-3) + (6-1-2) \Gamma (7-1-2) \Gamma (6-1-3)

142 19. (7-1-3) \Gamma (6-1-2) \Gamma (7-1-2) + (6-1-3) 20. 2.(8-6-10) \Gamma (10-6-1) \Gamma (8-6-1) 21. (10-6-1) \Gamma (8-6-1) 22. (1-6, 6-8-10) 23. 2.(9-7-11) \Gamma (9-7-1) \Gamma (11-7-1) 24. (9-7-1) \Gamma (11-7-1) 25. (1-7, 9-7-11) 26. (8-6-1-2) + (8-6-1-3) + (8-6-1-7) + (10-6-1-2) + (10-6-1-3) + (10-6-1-7) 27. (9-7-1-2) + (9-7-1-3) + (9-7-1-6) + (11-7-1-2) + (11-7-1-3) + (11-7-1-6) Figure 8.1(e) and 8.1(f ) Same as for Figure 8.1(d) except for:

16. 2.(6-1-7) \Gamma (2-1-6) \Gamma (2-1-7) 17. (2-1-6) \Gamma (2-1-7) 18. (6-1-2-3) + (7-1-2-3) 19. (2-1, 1-6-7)

B.3 Natural internal coordinates for T-site model Figure 8.1(d) 1-9. same as for bare model

10. (1-6) 11. (1-7) 12. (6-10) 13. (7-10) 14. (6-8)

143 15. (7-9) 16. (10-11) 17. (10-12) 18. (11-13) 19. (12-14) 20. (6-1-7) \Gamma (10-6-1) + (7-10-6) \Gamma (1-7-10) 21. (1-6-10-7) \Gamma (6-10-7-1) + (10-7-1-6) \Gamma (7-1-6-10) 22. (2-1-6) + (3-1-6) \Gamma (2-1-7) \Gamma (3-1-7) 23. (2-1-6) \Gamma (3-1-6) + (2-1-7) \Gamma (3-1-7) 24. (2-1-6) \Gamma (3-1-6) \Gamma (2-1-7) + (3-1-7) 25. (8-6-1) \Gamma (8-6-10) 26. (8-6-10-1) 27. (9-7-1) \Gamma (9-7-10) 28. (9-7-10-1) 29. 4.(11-10-12) \Gamma (6-10-11) \Gamma (7-10-11) \Gamma (6-10-12) \Gamma (7-10-12) 30. (6-10-11) + (7-10-11) \Gamma (6-10-12) \Gamma (7-10-12) 31. (6-10-11) \Gamma (7-10-11) + (6-10-12) \Gamma (7-10-12) 32. (6-10-11) \Gamma (7-10-11) \Gamma (6-10-12) + (7-10-12) 33. (13-11-10) 34. (13-11-10-6) \Gamma (13-11-10-7) 35. (14-12-10) 36. (14-12-10-7) \Gamma (14-12-10-6)

144 Figure 8.1(e) and 8.1(f ) Same as for Figure 8.1(d) except for:

22. (2-1-6) \Gamma (2-1-7) 23. (6-1-2-3) \Gamma (7-1-2-3) 24. (2-1, 1-6-7)

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158 Vita Ramamurthy Ramprasad Birthdate Birthplace

March 27, 1969 Madras, India

Research Interests State-of-the-art atomic-scale computation using quantum chemistry and physics electronic structure and classical force field techniques, applied to studying a variety of material classes, properties and phenomena.

Education 08/92-03/97: Ph. D. in Materials Science and Engineering

University of Illinois at Urbana-Champaign Thesis Title: Density Functional Study of NO Decomposition with Cu-exchanged Zeolites 08/90-05/92: M. S. in Materials Science and Engineering

Washington State University Thesis Title: Analysis of the Thermodynamic Properties of Small Metal Clusters 08/86-05/90: B. Tech. in Metallurgical Engineering

Indian Institute of Technology, Madras

Research Experience

ffl 08/92-03/97: Research Assistant, University of Illinois at UrbanaChampaign; investigation of electronic and surface band structure, catalytic reactions, chemisorption and vibrational phenomena using electronic structure methods; systems include CO and NO in Cu-exchanged zeolites, CO on Pd(110) and O on Al(111).

159 ffl Summers of '96, '95 and '94: Research Associate, Chemical and

Physical Sciences Laboratory, Ford Motor Company, Dearborn, MI; examined possible catalytic NO decomposition mechanisms in the presence of Cu-exchanged zeolites with quantum chemistry methods.

ffl 08/90-05/92: Research Assistant, Washington State University, Pullman; developed empirical interaction potentials and Fortran77 code to study small metal clusters.

Publications

1. W. F. Schneider, K. C. Hass, R. Ramprasad and J. B. Adams, `First-principles

analysis of elementary steps in the catalytic decomposition of NO by Cu-exchanged zeolites', submitted to J. Phys. Chem.

2. R. Ramprasad, K. C. Hass, W. F. Schneider, J. B. Adams, `Cu-dinitrosyl species in

zeolites: a density functional molecular cluster study', submitted to J. Phys. Chem.

3. R. Ramprasad, W. F. Schneider, K. C. Hass and J. B. Adams, `A theoretical study

of CO and NO vibrational frequencies in Cu-water clusters and implications for Cuexchanged zeolites', J. Phys. Chem., in print.

4. R. Ramprasad, K. M. Glassford, J. B. Adams and R. I. Masel, `CO on Pd(110):

Determination of the optimal adsorption site', Surf. Sci. 1996, 360, 31.

5. W. F. Schneider, K. C. Hass, R. Ramprasad and J. B. Adams, `Cluster models of

Cu binding and CO and NO adsorption in Cu-exchanged zeolites', J. Phys. Chem. 1996, 100, 6032.

6. R. Ramprasad, K. C. Hass and W. F. Schneider, `Cluster model studies of Cu complexes in zeolites', Ford Technical Report, August 1994.

7. J. B. Adams, A. Rockett, J. Kieffer, W. Xu, M. Nomura, K. A. Kilian, D. F. Richards

and R. Ramprasad, `Atomic-level computer simulation', J. Nucl. Mater. 1994, 216, 265.

8. R. Ramprasad, K. M. Glassford and J. B. Adams, `Ab initio study of Pd carbonyls

and CO/Pd(110)', Materials Research Society Conference Proceedings Vol. 344: Materials and Processes for Environmental Protection (Spring 1994, San Fransisco).

9. R. Ramprasad, D. A. Drabold and J. B. Adams, `Density-functional study of chemisorption of oxygen on Al(111)', Materials Research Society Conference Proceedings Vol. 317: Mechanisms of Thin Film Evolution (Fall 1993, Boston).

10. R. Ramprasad and R. G. Hoagland, `Thermodynamic properties of small zinc clusters', Modelling Simul. Mater. Sci. Eng. 1993, 1, 189.

11. R. Ramprasad and R. G. Hoagland, `Thermodynamic properties of small clusters of