Cook Ab Initio Valence Calculations in Chemistry

1. Auflage 2013
ISBN: 978-1-4831-6121-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 282 Seiten, Web PDF

Ab Initio Valence Calculations in Chemistry describes the theory and practice of ab initio valence calculations in chemistry and applies the ideas to a specific example, linear BeH2. Topics covered include the Schrödinger equation and the orbital approximation to atomic orbitals; molecular orbital and valence bond methods; practical molecular wave functions; and molecular integrals. Open shell systems, molecular symmetry, and localized descriptions of electronic structure are also discussed. This book is comprised of 13 chapters and begins by introducing the reader to the use of the Schrödinger equation to solve the electronic structure of molecular systems. This discussion is followed by two chapters that describe the chemical and mathematical nature of orbital theories in quantum chemistry. Two general ways of using chemical and physical information in looking for approximate solutions of the Schrödinger equation are highlighted: model approximations and numerical approximations. Attention then turns to atomic orbitals as the basis of a description of molecular electronic structure; practical molecular wave functions; and a general strategy for performing molecular valence calculations. The final chapter examines the nature of the valence electronic structure by using invariance with respect to transformations among the occupied molecular orbitals and among the atomic orbitals. This text will be of interest to students and practitioners of chemistry, biochemistry, and quantum mechanics.

Autoren/Hrsg.

Cook, D. B.

Inhaltsverzeichnis

1;Front Cover;1
2;Ab Initio Valence Calculations in Chemistry;4
3;Copyright Page;5
4;Table of Contents;10
5;PREFACE;6
6;ACKNOWLEDGEMENTS;8
7;CHAPTER 1. INTRODUCTION;12
8;CHAPTER 2. THE SCHRÖDINGER EQUATION;15
8.1;2.1 NOTATION AND DEFINITIONS;15
8.2;2.2 THE SCHRÖDINGER EQUATION;16
8.3;2.3 THE PAULI PRINCIPLE;20
8.4;2.4 CONSTRAINTS ON THE SCHRÖDINGER EQUATION;20
8.5;2.5 PROPERTIES OF THE MOLECULAR WAVE FUNCTION;21
8.6;2.6 DENSITY FUNCTIONS;22
8.7;2.7 SOLUTIONS OF THE SCHRODINGER EQUATION;24
8.8;2.8 ATOMIC UNITS;27
9;CHAPTER 3. THE ORBITAL APPROXIMATION;29
9.1;3.1 THE ORBITAL MODEL;29
9.2;3.2 THE SCHRÖDINGER EQUATION IN AN ORBITAL BASIS;30
9.3;3.3 ELECTRON SPIN AND THE IMPOSITION OF THE PAULI PRINCIPLE;33
9.4;3.4 FULL STATEMENT OF THE ORBITAL MODEL;37
9.5;3.5 THE VARIATION METHOD;37
9.6;3.6 USE OF THE VARIATION PRINCIPLE;43
9.7;3.7 THE LINEAR VARIATION METHOD;44
9.8;3.8 ADDENDUM - THE FORMAL CONTENT OF CHAPTER 3;46
10;CHAPTER 4. ATOMIC ORBITALS;50
10.1;4.1 THE ONE-CONFIGURATION MODEL;50
10.2;4.2 THE ROOTHAAN-HARTREE-FOCK METHOD FOR ATOMS;52
10.3;4.3 THE INTERPRETATION OF THE RHF EQUATION;59
10.4;4.4 THE USE OF NON-ORTHOGONAL BASIS FUNCTIONS;62
10.5;4.5 SUMMARY;63
11;CHAPTER 5. THE MOLECULAR ORBITAL AND VALENCE BOND METHODS;65
11.1;5.1 SURVEY OF THE MOLECULAR ORBITAL AND VALENCE BOND METHODS;65
11.2;5.2 THE MOLECULAR-ORBITAL (MO) METHOD;68
11.3;5.3 THE VALENCE BOND (VB) METHOD;75
11.4;5.4 THE EVALUATION OF VB MATRIX ELEMENTS - THE SLATER/LÖWDIN RULES;78
12;CHAPTER 6. PRACTICAL MOLECULAR WAVE FUNCTIONS;86
12.1;6.1 FURTHER APPROXIMATIONS?;86
12.2;6.2 MOLECULAR INTEGRAL CONSIDERATIONS;86
12.3;6.3 APPROXIMATE ATOMIC ORBITALS;88
12.4;6.4 CONTRACTION TECHNIQUES;93
12.5;6.5 SUMMARY OF APPROXIMATIONS;94
12.6;6.6 EXAMPLE - THE BERYLLIUM AND HYDROGEN ATOMS;96
13;CHAPTER 7. THE GENERAL STRATEGY;102
13.1;7.1 "SYSTEMS ANALYSIS';102
13.2;7.2 COMPUTATION OF MOLECULAR INTEGRALS;103
13.3;7.3 THE MATRIX LCAO MO EQUATIONS;103
13.4;7.4 THE DIAGONALISATION OF SYMMETRIC MATRICES;106
13.5;7.5 COMPLICATIONS;111
13.6;7.6 THE VIRTUAL ORBITALS;112
14;CHAPTER 8. MOLECULAR INTEGRALS - COMPUTATION AND STORAGE;115
14.1;8.1 MOLECULAR INTEGRALS;115
14.2;8.2 NOTATION;115
14.3;8.3 MOLECULAR INTEGRALS USING AN STO BASIS;117
14.4;8.4 MOLECULAR INTEGRALS USING A GTF BASIS;123
14.5;8.5 PHYSICAL INTERPRETATION AND ORDERS OF MAGNITUDE;127
14.6;8.6 THE COMPUTER STORAGE OF MOLECULAR INTEGRALS - CONVENTIONS;130
14.7;8.7 FORMATION OF THE MATRIX G(R);136
14.8;8.8 THE USE OF AN INTEGRAL FILE IN THE VB METHOD;139
14.9;8.9 APPLICATION TO BeH2;140
15;CHAPTER 9 . ORBITAL TRANSFORMATIONS;144
15.1;9.1 RECAPITULATION;144
15.2;9.2 ORBITAL TRANSFORMATIONS AMONG THE AO'S;145
15.3;9.3 TRANSFORMATIONS AMONG THE MO'S;147
15.4;9.4 THE RHF EQUATIONS IN A NON-ORTHOGONAL BASIS;148
15.5;9.5 TRANSFORMATION INDUCED IN THE ELECTRON REPULSION INTEGRALS;151
15.6;9.6 ORBITAL TRANSFORMATIONS AND THE VB METHOD;152
15.7;9.7 ORTHOGONALISATION METHODS;155
15.8;9.8 COMPOSITE ORTHOGONALISATION METHODS;164
15.9;9.9 APPLICATION TO BeH2;166
16;CHAPTER 10. POPULATION ANALYSIS AND PHYSICAL INTERPRETATION;170
16.1;10.1 QUALITATIVE AND QUANTITATIVE INFORMATION;170
16.2;10.2 POPULATION ANALYSIS;171
16.3;10.3 POPULATION ANALYSIS IN PRACTICE;174
16.4;10.4 COMPUTATION OF MOLECULAR PROPERTIES;176
17;CHAPTER 11. OPEN SHELL SYSTEMS;180
17.1;11.1 UNPAIRED ELECTRONS;180
17.2;11.2 DIFFERENT ORBITALS FOR DIFFERENT SPINS* (DODS);181
17.3;11.3 THE OPEN SHELL LCAOMO METHOD;184
17.4;11.4 COMMENTS ON THE UNPAIRED ELECTRON METHODS;190
17.5;11.5 APPLICATION TO BeH2;190
18;CHAPTER 12. THE USE OF MOLECULAR SYMMETRY;193
18.1;12.1 MOLECULAR SYMMETRY AND AO'S;193
18.2;12.2 MOLECULAR SYMMETRY AND MOLECULAR INTEGRALS;195
18.3;12.3 STORAGE COMPRESSION USING MOLECULAR SYMMETRY;208
18.4;12.4 EXTENSION TO GENERAL LINEAR TRANSFORMATIONS;210
18.5;12.5 SYMMETRY ORBITALS AND THE MO METHOD;212
18.6;12.6 THE USE OF SYMMETRY ORBITALS IN STORAGE COMPRESSION;216
18.7;12.7 SUMMARY;218
18.8;SUGGESTIONS FOR FURTHER READING;219
19;CHAPTER 13. LOCALISED DESCRIPTIONS OF ELECTRONIC STRUCTURE;220
19.1;13.1 CHEMICAL CONSEQUENCES OF INVARIANCE;220
19.2;13.2 LOCALISED MOLECULAR ORBITALS AND THE TWO ELECTRON BOND;220
19.3;13.3 THE DIRECT CALCULATION OF LMO's;225
19.4;13.4 OPTIMUM BOND HYBRIDS;228
19.5;13.5 THE SEPARATE ELECTRON PAIR MODEL;233
19.6;13.6 DIRECT CALCULATION OF OPTIMUM "HYBRIDS";240
19.7;SUGGESTIONS FOR FURTHER READING;241
20;APPENDIX A: GTF MOLECULAR INTEGRALS;246
21;APPENDIX B: PROGRAM PACKAGES;251
22;APPENDIX C: SAMPLE PROGRAMS;253
23;INDEX;274