Methods of molecular quantum mechanics : an introduction to electronic molecular structure
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書誌事項
Methods of molecular quantum mechanics : an introduction to electronic molecular structure
Wiley, 2009
- : pbk
- : cloth
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注記
Includes bibliographical references (p. [267]-273) and index
内容説明・目次
- 巻冊次
-
: pbk ISBN 9780470684412
内容説明
Methods of Molecular Quantum Mechanics This advanced text introduces to the advanced undergraduate and graduate student the mathematical foundations of the methods needed to carry out practical applications in electronic molecular quantum mechanics, a necessary preliminary step before using commercial programmes to carry out quantum chemistry calculations.
Major features of the book include:
Consistent use of the system of atomic units, essential for simplifying all mathematical formulae
Introductory use of density matrix techniques for interpreting properties of many-body systems
An introduction to valence bond methods with an explanation of the origin of the chemical bond
A unified presentation of basic elements of atomic and molecular interactions
The book is intended for advanced undergraduate and first-year graduate students in chemical physics, theoretical and quantum chemistry. In addition, it is relevant to students from physics and from engineering sub-disciplines such as chemical engineering and materials sciences.
目次
Preface.
1. Principles.
1.1 The Orbital Model.
1.2 Mathematical Methods.
1.3 Basic Postulates.
1.4 Physical Interpretation of the Basic Principles.
2. Matrices.
2.1 Definitions and Elementary Properties.
2.2 Properties of Determinants.
2.3 Special Matrices.
2.4 The Matrix Eigenvalue Problem.
3. Atomic Orbitals.
3.1 Atomic Orbitals as a Basis for Molecular Calculations.
3.2 Hydrogen-like Atomic Orbitals.
3.3 Slater-type Orbitals.
3.4 Gaussian-type Orbitals.
4. The Variation Method.
4.1 Variation Principles.
4.2 Nonlinear Parameters.
4.3 Linear Parameters and the Ritz Method.
4.4 Applications of the Ritz Method.
5. Spin.
5.1 The Zeeman Effect.
5.2 The Pauli Equations for One-electron Spin.
5.3 The Dirac Formula for N-electron Spin.
6. Antisymmetry of Many-electron Wavefunctions.
6.1 Antisymmetry Requirement and the Pauli Principle.
6.2 Slater Determinants.
6.3 Distributions Functions.
6.4 Average Values of Operators.
7. Self-consistent-field Calculations and Model Hamiltonians.
7.1 Elements of Hartree-Fock Theory for Closed Shells.
7.2 Roothaan Formulation of the LCAO-MO-SCF Equations.
7.3 Molecular Self-consistent-field Calculations.
7.4 Huckel Theory.
7.5 A Model for the One-dimensional Crystal.
8. Post-Hartree-Fock Methods.
8.1 Configuration Interaction.
8.2 Multiconfiguration Self-consistent-field.
8.3 Moller-Plesset Theory.
8.4 The MP2-R12 Method.
8.5 The CC-R12 Method.
8.6 Density Functional Theory.
9. Valence Bond Theory and the Chemical Bond.
9.1 The Born-Oppenheimer Approximation.
9.2 The Hydrogen Molecule H2.
9.3 The Origin of the Chemical Bond.
9.4 Valence Bond Theory and the Chemical Bond.
9.5 Hybridization and Molecular Structure.
9.6 Pauling's Formula for Conjugated and Aromatic Hydrocarbons.
10. Elements of Rayleigh-Schroedinger Perturbation Theory.
10.1 Rayleigh-Schroedinger Perturbation Equations.
10.2 First-order Theory.
10.3 Second-order Theory.
10.4 Approximate E2 Calculations: The Hylleraas Functional.
10.5 Linear Pseudostates and Molecular Properties.
10.6 Quantum Theory of Magnetic Susceptibilities.
11. Atomic and Molecular Interactions.
11.1 The H-H Nonexpanded Interactions up to Second Order.
11.2 The H-H Expanded Interactions up to Second Order.
11.3 Molecular Interactions.
11.4 Van der Waals and Hydrogen Bonds.
11.5 The Keesom Interaction.
12. Symmetry.
12.1 Molecular Symmetry.
12.2 Group Theoretical Methods.
12.3 Illustrative Examples.
References.
Author Index.
Subject Index.
- 巻冊次
-
: cloth ISBN 9780470684429
内容説明
Methods of Molecular Quantum Mechanics This advanced text introduces to the advanced undergraduate and graduate student the mathematical foundations of the methods needed to carry out practical applications in electronic molecular quantum mechanics, a necessary preliminary step before using commercial programmes to carry out quantum chemistry calculations.
Major features of the book include:
Consistent use of the system of atomic units, essential for simplifying all mathematical formulae
Introductory use of density matrix techniques for interpreting properties of many-body systems
An introduction to valence bond methods with an explanation of the origin of the chemical bond
A unified presentation of basic elements of atomic and molecular interactions
The book is intended for advanced undergraduate and first-year graduate students in chemical physics, theoretical and quantum chemistry. In addition, it is relevant to students from physics and from engineering sub-disciplines such as chemical engineering and materials sciences.
目次
Preface xiii
1 Principles 1
1.1 The Orbital Model 1
1.2 Mathematical Methods 2
1.2.1 Dirac Notation 2
1.2.2 Normalization 2
1.2.3 Orthogonality 3
1.2.4 Set of Orthonormal Functions 3
1.2.5 Linear Independence 3
1.2.6 Basis Set 4
1.2.7 Linear Operators 4
1.2.8 Sum and Product of Operators 4
1.2.9 Eigenvalue Equation 5
1.2.10 Hermitian Operators 5
1.2.11 Anti-Hermitian Operators 6
1.2.12 Expansion Theorem 6
1.2.13 From Operators to Matrices 6
1.2.14 Properties of the Operator 7
1.2.15 Transformations in Coordinate Space 9
1.3 Basic Postulates 12
1.3.1 Correspondence between Physical Observables and Hermitian Operators 12
1.3.2 State Function and Average Value of Observables 15
1.3.3 Time Evolution of the State Function 16
1.4 Physical Interpretation of the Basic Principles 17
2 Matrices 21
2.1 Definitions and Elementary Properties 21
2.2 Properties of Determinants 23
2.3 Special Matrices 24
2.4 The Matrix Eigenvalue Problem 25
3 Atomic Orbitals 31
3.1 Atomic Orbitals as a Basis for Molecular Calculations 31
3.2 Hydrogen-like Atomic Orbitals 32
3.2.1 Choice of an Appropriate Coordinate System 32
3.2.2 Solution of the Radial Equation 33
3.2.3 Solution of the Angular Equation 37
3.2.4 Some Properties of the Hydrogen-like Atomic Orbitals 41
3.2.5 Real Form of the Atomic Orbitals 43
3.3 Slater-type Orbitals 46
3.4 Gaussian-type Orbitals 49
3.4.1 Spherical Gaussians 49
3.4.2 Cartesian Gaussians 50
4 The Variation Method 53
4.1 Variational Principles 53
4.2 Nonlinear Parameters 57
4.2.1 Ground State of the Hydrogenic System 57
4.2.2 The First Excited State of Spherical Symmetry of the Hydrogenic System 59
4.2.3 The First Excited 2p State of the Hydrogenic System 61
4.2.4 The Ground State of the He-like System 61
4.3 Linear Parameters and the Ritz Method 64
4.4 Applications of the Ritz Method 67
4.4.1 The First 1s2s Excited State of the He-like Atom 67
4.4.2 The First 1s2p State of the He-like Atom 69
Appendix: The Integrals J, K, J' and K' 71
5 Spin 75
5.1 The Zeeman Effect 75
5.2 The Pauli Equations for One-electron Spin 78
5.3 The Dirac Formula for N-electron Spin 79
6 Antisymmetry of Many-electron Wavefunctions 85
6.1 Antisymmetry Requirement and the Pauli Principle 85
6.2 Slater Determinants 87
6.3 Distribution Functions 89
6.3.1 One- and Two-electron Distribution Functions 89
6.3.2 Electron and Spin Densities 91
6.4 Average Values of Operators 95
7 Self-consistent-field Calculations and Model Hamiltonians 99
7.1 Elements of Hartree-Fock Theory for Closed Shells 100
7.1.1 The Fock-Dirac Density Matrix 100
7.1.2 Electronic Energy Expression 102
7.2 Roothaan Formulation of the LCAO-MO-SCF Equations 104
7.3 Molecular Self-consistent-field Calculations 108
7.4 Huckel Theory 112
7.4.1 Ethylene (N = 2) 114
7.4.2 The Allyl Radical (N = 3) 115
7.4.3 Butadiene (N = 4) 119
7.4.4 Cyclobutadiene (N = 4) 120
7.4.5 Hexatriene (N = 6) 124
7.4.6 Benzene (N = 6) 126
7.5 A Model for the One-dimensional Crystal 129
8 Post-Hartree-Fock Methods 133
8.1 Configuration Interaction 133
8.2 Multiconfiguration Self-consistent-field 135
8.3 Moller-Plesset Theory 135
8.4 The MP2-R12 Method 136
8.5 The CC-R12 Method 137
8.6 Density Functional Theory 138
9 Valence Bond Theory and the Chemical Bond 141
9.1 The Born-Oppenheimer Approximation 142
9.2 The Hydrogen Molecule H 2 144
9.2.1 Molecular Orbital Theory 145
9.2.2 Heitler-London Theory 148
9.3 The Origin of the Chemical Bond 150
9.4 Valence Bond Theory and the Chemical Bond 153
9.4.1 Schematization of Valence Bond Theory 153
9.4.2 Schematization of Molecular Orbital Theory 154
9.4.3 Advantages of the Valence Bond Method 154
9.4.4 Disadvantages of the Valence Bond Method 154
9.4.5 Construction of Valence Bond Structures 156
9.5 Hybridization and Molecular Structure 162
9.5.1 The H2O Molecule 162
9.5.2 Properties of Hybridization 164
9.6 Pauling's Formula for Conjugated and Aromatic Hydrocarbons 166
9.6.1 Ethylene (One -Bond, n = 1) 169
9.6.2 Cyclobutadiene (n = 2) 169
9.6.3 Butadiene (Open Chain, n = 2) 171
9.6.4 The Allyl Radical (N = 3) 173
9.6.5 Benzene (n = 3) 176
10 Elements of Rayleigh-Schroedinger Perturbation Theory 183
10.1 Rayleigh-Schroedinger Perturbation Equations up to Third Order 183
10.2 First-order Theory 186
10.3 Second-order Theory 187
10.4 Approximate E2 Calculations: The Hylleraas Functional 190
10.5 Linear Pseudostates and Molecular Properties 191
10.5.1 Single Pseudostate 193
10.5.2 N-term Approximation 195
10.6 Quantum Theory of Magnetic Susceptibilities 196
10.6.1 Diamagnetic Susceptibilities 199
10.6.2 Paramagnetic Susceptibilities 203
Appendix: Evaluation of and 212
11 Atomic and Molecular Interactions 215
11.1 The H-H Nonexpanded Interactions up to Second Order 216
11.2 The H-H Expanded Interactions up to Second Order 220
11.3 Molecular Interactions 225
11.3.1 Nonexpanded Energy Corrections up to Second Order 226
11.3.2 Expanded Energy Corrections up to Second Order 227
11.3.3 Other Expanded Interactions 235
11.4 Van der Waals and Hydrogen Bonds 237
11.5 The Keesom Interaction 239
12 Symmetry 247
12.1 Molecular Symmetry 247
12.2 Group Theoretical Methods 252
12.2.1 Isomorphism 254
12.2.2 Conjugation and Classes 254
12.2.3 Representations and Characters 255
12.2.4 Three Theorems on Irreducible Representations 255
12.2.5 Number of Irreps in a Reducible Representation 256
12.2.6 Construction of Symmetry-adapted Functions 256
12.3 Illustrative Examples 257
12.3.1 Use of Symmetry in Ground-state H2O (1 A1) 257
12.3.2 Use of Symmetry in Ground-state NH3 (1 A1) 260
References 267
Author Index 275
Subject Index 279
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