.

0 (hodnocen0 x )

BK

First published

Mineola : Dover Publications, Inc., 1996

xiv, 466 stran : ilustrace ; 22 cm

ISBN 0-486-69186-1 (brožováno)

Dover books on chemistry and earth sciences

Obsahuje bibliografie a rejstřík

Reprint vydání z roku 1989

001462190

TABLE OF CONTENTS // Preface to Revised Edition Preface // ix // xi // Chapter 1. Mathematical Review // 1.1 Linear Algebra // 2 // 1 // 1.1.1 Three-Dimensional Vector Algebra 2 // 1.1.2 Matrices 5 // 1.1.3 Determinants 7 // 1.1.4 V-Dimensional Complex Vector Spaces 9 // 1.1.5 Change of Basis 75 // 1.1.6 The Eigenvalue Problem 15 // 1.1.7 Functions of Matrices 21 // 1.2 Orthogonal Functions, Eigenfunctions, and Operators 24 // 1.3 The Variation Method 31 // 1.3.1 The Variation Principle 31 // 1.3.2 The Linear Variational Problem 33 // Notes 38 // Further Reading 38 // Chapter 2. Many Electron Wave Functions and Operators 39 // 2.1 The Electronic Problem 40 // 2.1.1 Atomic Units 41 // 2.1.2 The Bom-Oppenheimer Approximation 43 // 2.1.3 The Antisymmetry or Pauli Exclusion Principle 45 // 2.2 Orbitals, Slater Determinants, and Basis Functions 46 // 2.2.1 Spin Orbitals and Spatial Orbitals 46 // 2.2.2 Hartree Products 47 // iii // IV MODERN QUANTUM CHEMISTRY // 2.2.3 Slater Determinants 49 // 2.2.4 The Hartree-Fock Approximation 53 // 2.2.5 The Minimal Basis H2 Model 55 // 2.2.6 Excited Determinants 58 // 2.2.7 Form of the Exact Wave Function and Configuration Interaction 60 // 2.3 Operators and Matrix Elements 64 // 2.3.1 Minimal Basis H2 Matrix Elements 64 // 2.3.2 Notations for One- and Two-Electron Integrals 67 // 2.3.3 General Rules for Matrix Elements 68 // 2.3.4 Derivation of the Rules for Matrix Elements 74 // 2.3.5 Transition from Spin Orbitals to Spatial Orbitals 81 // 2.3.6 Coulomb

and Exchange Integrals 85 // 2.3.7 Pseudo-Classical Interpretation of Determinantal Energies 87 // 2.4 Second Quantization 89 // 2.4.1 Creation and Annihilation Operators and Their Anticommutation Relations 89 // 2.4.2 Second-Quantized Operators and Their Matrix Elements 95 // 2.5 Spin-Adapted Configurations 97 // 2.5.1 Spin Operators 97 // 2.5.2 Restricted Determinants and Spin-Adapted Configurations 100 // 2.5.3 Unrestricted Determinants 104 // Notes 107 // Further Reading 107 // Chapter 3. The Hartree-Fock Approximation 108 // 3.1 The Hartree-Fock Equations 111 // 3.1.1 The Coulomb and Exchange Operators 112 // 3.1.2 The Fock Operator 114 // 3.2 Derivation of the Hartree-Fock Equations 115 // 3.2.1 Functional Variation 115 // 3.2.2 Minimization of the Energy of a Single Determinant 117 // 3.2.3 The Canonical Hartree-Fock Equations 120 // 3.3 Interpretation of Solutions to the Hartree-Fock Equations 123 // 3.3.1 Orbital Energies and Koopmans’Theorem 123 // 3.3.2 Brillouin’s Theorem 128 // 3.3.3 The Hartree-Fock Hamiltonian 130 // 3.4 Restricted Closed-Shell Hartree-Fock: The Roothaan Equations 131 // 3.4.1 Closed-Shell Hartree-Fock : Restricted Spin Orbitals 132 // 3.4.2 Introduction of a Basis : The Roothaan Equations 136 // 3.4.3 The Charge Density 138 // 3.4.4 Expression for the Fock Matrix 140 // 3.4.5 Orthogonalization of the Basis 142 // TABLE OF CONTENTS V // 3.4.6 The SCF Procedure 145 // ??? Expectation Values and Population Analysis 149 // 3.5 Model Calculations

on H2 and HeH+ 152 // 3.5.1 The Is Minimal STO-3G Basis Set 153 // 3.5.2 STO-3GH2 159 // 3.5.3 An SCF Calculation on STO-3GHeH+ 168 // 3.6 Polyatomic Basis Sets 180 // 3.6.1 Contracted Gaussian Functions 180 // 3.6.2 Minimal Basis Sets: STO-3G 184 // 3.6.3 Double Zeta Basis Sets: 4-31G 186 // 3.6.4 Polarized Basis Sets: 6-31G* and 6-31G** 189 // 3.7 Some Illustrative Closed-Shell Calculations 190 // 3.7.1 Total Energies 191 // 3.7.2 Ionization Potentials 194 // 3.7.3 Equilibrium Geometries 200 // 3.7.4 Population Analysis and Dipole Moments 203 // 3.8 Unrestricted Open-Shell Hartree-Fock : // The Pople-Nesbet Equations 205 // 3.8.1 Open-Shell Hartree Fock: Unrestricted Spin Orbitals 206 // 3.8.2 Introduction of a Basis : The Pople-Nesbet Equations 210 // 3.8.3 Unrestricted Density Matrices 212 // 3.8.4 Expression for the Fock Matrices 214 // 3.8.5 Solution of the Unrestricted SCF Equations 215 // 3.8.6 Illustrative Unrestricted Calculations 216 // 3.8.7 The Dissociation Problem and its Unrestricted Solution 221 // Notes // Further Reading 229 // Chapter 4. Configuration Interaction 231 // 4.1 Multiconfigurational Wave Functions and the // Structure of the Full Cl Matrix 233 // 4.1.1 Intermediate Normalization and an Expression for the Correlation Energy 237 // 4.2 Doubly Excited Cl 242 // 4.3 Some Illustrative Calculations 245 // 4.4 Natural Orbitals and the One-Particle Reduced Density Matrix 252 // 4.5 The Multiconfiguration Self-Consistent Field (MCSCF) // and Generalized Valence

Bond (GVB) Methods 258 // 4.6 Truncated Cl and the Size-Consistency Problem 261 // VI MODERN QUANTUM CHEMISTRY // Notes 269 // Further Reading 269 // Chapter 5. Pair and Coupled-Pair Theories 271 // 5.1 The Independent Electron Pair Approximation (IEPA) 272 // 5.1.1 Invariance under Unitary Transformations : An Example 277 // 5.1.2 Some Illustrative Calculations 284 // 5.2 Coupled-Pair Theories 286 // 5.2.1 The Coupled Cluster Approximation (CCA) 287 // 5.2.2 The Cluster Expansion of the Wave Function 290 // 5.2.3 Linear CCA and the Coupled Electron Pair Approximation (???) 292 // 5.2.4 Some Illustrative Calculations 296 // 5.3 Many-Electron Theories with Single Particle Hamiltonians 297 // 5.3.1 The Relaxation Energy via Cl, IEPA, CCA, and ??? 303 // 5.3.2 The Resonance Energy of Polyenes in Hückel Theory 309 // Notes 318 // Further Reading 319 // Chapter 6. Many-Body Perturbation Theory 320 // 6.1 Rayleigh-Schrödinger (RS) Perturbation Theory 322 // *6.2 Diagrammatic Representation of RS Perturbation Theory 327 // 6.2.1 Diagrammatic Perturbation Theory for 2 States 327 // 6.2.2 Diagrammatic Perturbation Theory for N States 335 // 6.2.3 Summation of Diagrams 336 // 6.3 Orbital Perturbation Theory: One-Particle Perturbations 338 // *6.4 Diagrammatic Representation of Orbital Perturbation Theory 348 // 6.5 Perturbation Expansion of the Correlation Energy 350 // 6.6 The A-Dependence of the RS Perturbation Expansion 354 // *6.7 Diagrammatic Representation of the Perturbation

Expansion of the Correlation Energy 356 // 6.7.1 Hugenholtz Diagrams 356 // 6.7.2 Goldstone Diagrams 362 // 6.7.3 Summation of Diagrams 368 // 6.1 A What Is the Linked Cluster Theorem? 369 // 6.8 Some Illustrative Calculations 370 // Notes 378 // Further Reading 379 // TABLE OF CONTENTS Vil // Chapter 7. The One-Particle Many-Body Green’s Function 380 // 7.1 Green’s Functions in Single Particle Systems 381 // 7.2 The One-Particle Many-Body Green’s Function 387 // 7.2.1 The Self-Energy 389 // 7.2.2 The Solution of the Dyson Equation 391 // 7.3 Application of the Formalism to H2 and HeH+ 392 // 7.4 Perturbation Theory and the Green’s Function Method 398 // 7.5 Some Illustrative Calculations 405 // Notes 409 // Further Reading 409 // Appendix A. Integral Evaluation with Is Primitive Gaussiane 410 // Appendix B. Two-Electron Self-Consistent-Field Program 417 // Appendix C. Analytic Derivative Methods and Geometry Optimization by M.C. Zerner 437 // Appendix D. Molecular Integrals for H2 as a Function of Bond Length 459 // Index // 461