Magnasco Elementary Methods of Molecular Quantum Mechanics

1. Auflage 2006
ISBN: 978-0-08-046680-4
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 749 Seiten

Elementary Methods of Molecular Quantum Mechanics shows the methods of molecular quantum mechanics for graduate University students of Chemistry and Physics. This readable book teaches in detail the mathematical methods needed to do working applications in molecular quantum mechanics, as a preliminary step before using commercial programmes doing quantum chemistry calculations.
This book aims to bridge the gap between the classic Coulson's Valence, where application of wave mechanical principles to valence theory is presented in a fully non-mathematical way, and McWeeny's Methods of Molecular Quantum Mechanics, where recent advances in the application of quantum mechanical methods to molecular problems are presented at a research level in a full mathematical way. Many examples and mathematical points are given as problems at the end of each chapter, with a hint for their solution. Solutions are then worked out in detail in the last section of each Chapter.
* Uses clear and simplified examples to demonstrate the methods of molecular quantum mechanics
* Simplifies all mathematical formulae for the reader
* Provides educational training in basic methodology

Professor of Theoretical Chemistry at the Department of Chemistry and Industrial Chemistry, (DCCI) University of Genoa, Italy.

Autoren/Hrsg.

Magnasco, Valerio

Inhaltsverzeichnis

1;Front cover;1
2;Elementary Methods of Molecular Quantum Mechanics;4
3;Copyright page;5
4;Contents;8
5;Preface;16
6;1 Basic Principles of Quantum Mechanics;20
6.1;1.1 The Orbital Model;20
6.2;1.2 The Fundamental Postulates of Quantum Mechanics;21
6.3;1.3 The Physical Principles of Quantum Mechanics;28
6.4;1.4 The Mathematics of Quantum Mechanics;38
6.5;1.5 Fundamental Physical Constants and Atomic Units;53
6.6;1.6 Problems 1;54
6.7;1.7 Solved Problems;60
7;2 Elementary Matrix Methods;76
7.1;2.1 Introduction;76
7.2;2.2 Elements of Matrix Algebra;77
7.3;2.3 Matrix Eigenvalue Problem;83
7.4;2.4 Functions of Hermitean Matrices;88
7.5;2.5 Problems 2;91
7.6;2.6 Solved Problems;97
8;3 The Particle in the Box;122
8.1;3.1 Introduction;122
8.2;3.2 The Free Particle in One Dimension;122
8.3;3.3 The 3-dimensional Box of Sides a, b, c;124
8.4;3.4 Particle in a 1-dimensional Box with Impenetrable Walls;125
8.5;3.5 Particle in a 1-dimensional Box of Finite Height;127
8.6;3.6 Problems 3;131
8.7;3.7 Solved Problems;132
9;4 The Hydrogen-Like System;136
9.1;4.1 Introduction;136
9.2;4.2 Separation of the Motion of the Centre-of-Mass;138
9.3;4.3 Separation of the Radial Equation in Spherical Coordinates;140
9.4;4.4 Solution of the Radial Equation;142
9.5;4.5 Solution of the Angular Equation;147
9.6;4.6 Hydrogen-Like Orbitals, Eigenvalues and Quantum Numbers;151
9.7;4.7 Properties of Ground and Excited States;157
9.8;4.8 Expectation Values for Ground and First Excited States;160
9.9;4.9 Slater and Gaussian Atomic Orbitals;161
9.10;4.10 Problems 4;166
9.11;4.11 Solved Problems;169
10;5 The Variation Method;182
10.1;5.1 Introduction;182
10.2;5.2 The Variation Method;183
10.3;5.3 Non-Linear Parameters;187
10.4;5.4 Linear Parameters and the Ritz Method;197
10.5;5.5 Atomic Applications of the Ritz Method;202
10.6;5.6 Molecular Applications of the Ritz Method;207
10.7;5.7 The Wentzel-Kramers-Brillouin (WKB) Method;216
10.8;5.8 Problems 5;219
10.9;5.9 Solved Problems;222
11;6 The Electron Spin;234
11.1;6.1 Introduction;234
11.2;6.2 Electron Spin According to Pauli and the Zeeman Effect;235
11.3;6.3 Theory of 1-Electron Spin;239
11.4;6.4 Matrix Representation of Spin Operators;244
11.5;6.5 Theory of 2-Electron Spin;246
11.6;6.6 Theory of N-Electron Spin;248
11.7;6.7 The Kotani Synthetic Method;252
11.8;6.8 Lowdin Spin Projection Operators;253
11.9;6.9 Problems 6;255
11.10;6.10 Solved Problems;258
12;7 Many-Electron Wavefunctions: Slater, Hartree-Fock and Related Methods;274
12.1;7.1 Introduction;275
12.2;7.2 Antisymmetry of the Electronic Wavefunction and the Pauli Principle;275
12.3;7.3 Electron Distribution Functions;282
12.4;7.4 Average Values of 1- and 2-Electron Operators;291
12.5;7.5 The Slater Rules;294
12.6;7.6 Pople's Two-Dimensional Chart of Quantum Chemistry;295
12.7;7.7 Hartree-Fock Theory for Closed Shells;298
12.8;7.8 Huckel theory;317
12.9;7.9 Semiempirical MO Methods;330
12.10;7.10 Post-Hartree-Fock Methods;336
12.11;7.11 Problems 7;351
12.12;7.12 Solved Problems;358
13;8 Molecular Symmetry and Group Theoretical Methods;382
13.1;8.1 Introduction;382
13.2;8.2 Symmetry and Quantum Mechanics;383
13.3;8.3 Molecular Symmetry;384
13.4;8.4 Symmetry Operations as Transformation of Coordinate Axes;387
13.5;8.5 Group Theoretical Methods;397
13.6;8.6 Applications;414
13.7;8.7 An Outline of Continuous and Permutation Groups;417
13.8;8.8 Problems 8;423
13.9;8.9 Solved Problems;432
14;9 Angular Momentum Methods for Atoms;458
14.1;9.1 Introduction;458
14.2;9.2 The Vector Model;459
14.3;9.3 Construction of States of Definite Angular Momentum;467
14.4;9.4 An Outline of Advanced Methods for Coupling Angular Momenta;473
14.5;9.5 Problems 9;477
14.6;9.6 Solved Problems;481
15;10 Valence Bond Theory and the Chemical Bond;492
15.1;10.1 Introduction;492
15.2;10.2 The Born-Oppenheimer Approximation;494
15.3;10.3 The Chemical Bond in H2;496
15.4;10.4 Elementary Valence Bond Methods;521
15.5;10.5 Pauling VB Theory for Conjugated and Aromatic Hydrocarbons;541
15.6;10.6 Hybridization and Directed Valency in Polyatomic Molecules;564
15.7;10.7 An Outline of Recent Advances in VB Theory;573
15.8;10.8 Problems 10;579
15.9;10.9 Solved Problems;582
16;11 Rayleigh-Schroedinger Perturbation Methods for Stationary States;596
16.1;11.1 Introduction;596
16.2;11.2 RS Perturbation Theory for Stationary States;597
16.3;11.3 Variational Approximations for the Second-Order Energy;605
16.4;11.4 Static Multipole Polarizabilities for H(1s);609
16.5;11.5 Electric Properties of Molecules;619
16.6;11.6 Problems 11;623
16.7;11.7 Solved Problems;625
17;12 Atomic and Molecular Interactions;636
17.1;12.1 Introduction;636
17.2;12.2 Interatomic Interactions;637
17.3;12.3 RS Perturbation Theory of the H-H+ Interaction;637
17.4;12.4 RS Perturbation Theory of the H-H Interaction;642
17.5;12.5 An Outline of a Perturbation Theory for Molecular Interactions;654
17.6;12.6 The Van der Waals Bond;669
17.7;12.7 Problems 12;674
17.8;12.8 Solved Problems;675
18;13 Evaluation of Molecular Integrals over STOs;682
18.1;13.1 Introduction;682
18.2;13.2 The Basic Integrals;683
18.3;13.3 1-Centre Integrals;686
18.4;13.4 Evaluation of the Electrostatic Potential J1s;689
18.5;13.5 The (1s2|1s2) Electron Repulsion Integral;693
18.6;13.6 General Formula for 1-Centre 2-Electron Integrals;694
18.7;13.7 2-Centre Integrals over 1s STOs;695
18.8;13.8 On the General Formulae for 2-Centre Integrals;709
18.9;13.9 A Short Note on Multicentre Integrals;712
18.10;13.10 Problems 13;715
18.11;13.11 Solved Problems;716
19;References;728
20;Author Index;736
21;Subject Index;742