Elementary Methods of Molecular Quantum Mechanics (eBook)

Front cover 1
Elementary Methods of Molecular Quantum Mechanics 4
Copyright page 5
Contents 8
Preface 16
1 Basic Principles of Quantum Mechanics 20
1.1 The Orbital Model 20
1.2 The Fundamental Postulates of Quantum Mechanics 21
1.3 The Physical Principles of Quantum Mechanics 28
1.4 The Mathematics of Quantum Mechanics 38
1.5 Fundamental Physical Constants and Atomic Units 53
1.6 Problems 1 54
1.7 Solved Problems 60
2 Elementary Matrix Methods 76
2.1 Introduction 76
2.2 Elements of Matrix Algebra 77
2.3 Matrix Eigenvalue Problem 83
2.4 Functions of Hermitean Matrices 88
2.5 Problems 2 91
2.6 Solved Problems 97
3 The Particle in the Box 122
3.1 Introduction 122
3.2 The Free Particle in One Dimension 122
3.3 The 3-dimensional Box of Sides a, b, c 124
3.4 Particle in a 1-dimensional Box with Impenetrable Walls 125
3.5 Particle in a 1-dimensional Box of Finite Height 127
3.6 Problems 3 131
3.7 Solved Problems 132
4 The Hydrogen-Like System 136
4.1 Introduction 136
4.2 Separation of the Motion of the Centre-of-Mass 138
4.3 Separation of the Radial Equation in Spherical Coordinates 140
4.4 Solution of the Radial Equation 142
4.5 Solution of the Angular Equation 147
4.6 Hydrogen-Like Orbitals, Eigenvalues and Quantum Numbers 151
4.7 Properties of Ground and Excited States 157
4.8 Expectation Values for Ground and First Excited States 160
4.9 Slater and Gaussian Atomic Orbitals 161
4.10 Problems 4 166
4.11 Solved Problems 169
5 The Variation Method 182
5.1 Introduction 182
5.2 The Variation Method 183
5.3 Non-Linear Parameters 187
5.4 Linear Parameters and the Ritz Method 197
5.5 Atomic Applications of the Ritz Method 202
5.6 Molecular Applications of the Ritz Method 207
5.7 The Wentzel-Kramers-Brillouin (WKB) Method 216
5.8 Problems 5 219
5.9 Solved Problems 222
6 The Electron Spin 234
6.1 Introduction 234
6.2 Electron Spin According to Pauli and the Zeeman Effect 235
6.3 Theory of 1-Electron Spin 239
6.4 Matrix Representation of Spin Operators 244
6.5 Theory of 2-Electron Spin 246
6.6 Theory of N-Electron Spin 248
6.7 The Kotani Synthetic Method 252
6.8 Lowdin Spin Projection Operators 253
6.9 Problems 6 255
6.10 Solved Problems 258
7 Many-Electron Wavefunctions: Slater, Hartree-Fock and Related Methods 274
7.1 Introduction 275
7.2 Antisymmetry of the Electronic Wavefunction and the Pauli Principle 275
7.3 Electron Distribution Functions 282
7.4 Average Values of 1- and 2-Electron Operators 291
7.5 The Slater Rules 294
7.6 Pople's Two-Dimensional Chart of Quantum Chemistry 295
7.7 Hartree-Fock Theory for Closed Shells 298
7.8 Huckel theory 317
7.9 Semiempirical MO Methods 330
7.10 Post-Hartree-Fock Methods 336
7.11 Problems 7 351
7.12 Solved Problems 358
8 Molecular Symmetry and Group Theoretical Methods 382
8.1 Introduction 382
8.2 Symmetry and Quantum Mechanics 383
8.3 Molecular Symmetry 384
8.4 Symmetry Operations as Transformation of Coordinate Axes 387
8.5 Group Theoretical Methods 397
8.6 Applications 414
8.7 An Outline of Continuous and Permutation Groups 417
8.8 Problems 8 423
8.9 Solved Problems 432
9 Angular Momentum Methods for Atoms 458
9.1 Introduction 458
9.2 The Vector Model 459
9.3 Construction of States of Definite Angular Momentum 467
9.4 An Outline of Advanced Methods for Coupling Angular Momenta 473
9.5 Problems 9 477
9.6 Solved Problems 481
10 Valence Bond Theory and the Chemical Bond 492
10.1 Introduction 492
10.2 The Born-Oppenheimer Approximation 494
10.3 The Chemical Bond in H2 496
10.4 Elementary Valence Bond Methods 521
10.5 Pauling VB Theory for Conjugated and Aromatic Hydrocarbons 541
10.6 Hybridization and Directed Valency in Polyatomic Molecules 564
10.7 An Outline of Recent Advances in VB Theory 573
10.8 Problems 10 579
10.9 Solved Problems 582
11 Rayleigh-Schroedinger Perturbation Methods for Stationary States 596
11.1 Introduction 596
11.2 RS Perturbation Theory for Stationary States 597
11.3 Variational Approximations for the Second-Order Energy 605
11.4 Static Multipole Polarizabilities for H(1s) 609
11.5 Electric Properties of Molecules 619
11.6 Problems 11 623
11.7 Solved Problems 625
12 Atomic and Molecular Interactions 636
12.1 Introduction 636
12.2 Interatomic Interactions 637
12.3 RS Perturbation Theory of the H-H+ Interaction 637
12.4 RS Perturbation Theory of the H-H Interaction 642
12.5 An Outline of a Perturbation Theory for Molecular Interactions 654
12.6 The Van der Waals Bond 669
12.7 Problems 12 674
12.8 Solved Problems 675
13 Evaluation of Molecular Integrals over STOs 682
13.1 Introduction 682
13.2 The Basic Integrals 683
13.3 1-Centre Integrals 686
13.4 Evaluation of the Electrostatic Potential J1s 689
13.5 The (1s2|1s2) Electron Repulsion Integral 693
13.6 General Formula for 1-Centre 2-Electron Integrals 694
13.7 2-Centre Integrals over 1s STOs 695
13.8 On the General Formulae for 2-Centre Integrals 709
13.9 A Short Note on Multicentre Integrals 712
13.10 Problems 13 715
13.11 Solved Problems 716
References 728
Author Index 736
Subject Index 742