Elementary Molecular Quantum Mechanics

Elementary Molecular Quantum Mechanics

Mathematical Methods and Applications

2nd Edition - August 1, 2013

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  • Author: Valerio Magnasco
  • Hardcover ISBN: 9780444626479
  • eBook ISBN: 9780444626660

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Description

The second edition of Elementary 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.

Key Features

  • 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

Readership

Students in chemical physics, theoretical and quantum chemistry also graduate students of chemistry/physics and undergraduate students of physical sciences

Table of Contents

  • Dedication

    Preface

    Part 1: Mathematical Methods

    Chapter 1. Mathematical foundations and approximation methods

    1.1 Mathematical Foundations

    1.2 The Variational Method

    1.3 Perturbative Methods for Stationary States

    1.4 The Wentzel–Kramers–Brillouin Method

    1.5 Problems 1

    1.6 Solved Problems

    Chapter 2. Coordinate systems

    2.1 Introduction

    2.2 Systems of Orthogonal Coordinates

    2.3 Generalized Coordinates

    2.4 Cartesian Coordinates (x,y,z)

    2.5 Spherical Coordinates (r,θ,φ)

    2.6 Spheroidal Coordinates (μ,ν,φ)

    2.7 Parabolic Coordinates (ξ,η,φ)

    2.8 Problems 2

    2.9 Solved Problems

    Chapter 3. Differential equations in quantum mechanics

    3.1 Introduction

    3.2 Partial Differential Equations

    3.3 Separation of Variables

    3.4 Solution by Series Expansion

    3.5 Solution Near Singular Points

    3.6 The One-dimensional Harmonic Oscillator

    3.7 The Atomic One-electron System

    3.8 The Hydrogen Atom in an Electric Field

    3.9 The Hydrogen Molecular Ion H2+

    3.10 The Stark Effect in Atomic Hydrogen

    3.11 Appendix: Checking the Solutions

    3.12 Problems 3

    3.13 Solved Problems

    Chapter 4. Special functions

    4.1 Introduction

    4.2 Legendre Functions

    4.3 Laguerre Functions

    4.4 Hermite Functions

    4.5 Hypergeometric Functions

    4.6 Bessel Functions

    4.7 Functions Defined by Integrals

    4.8 The Dirac δ-Function

    4.9 The Fourier Transform

    4.10 The Laplace Transform

    4.11 Spherical Tensors

    4.12 Orthogonal Polynomials

    4.13 Padé Approximants

    4.14 Green’s Functions

    4.15 Problems 4

    4.16 Solved Problems

    Chapter 5. Functions of a complex variable

    5.1 Functions of a Complex Variable

    5.2 Complex Integral Calculus

    5.3 Calculus of Residues

    5.4 Problems 5

    5.5 Solved Problems

    Chapter 6. Matrices

    6.1 Definitions and Elementary Properties

    6.2 The Partitioning of Matrices

    6.3 Properties of Determinants

    6.4 Special Matrices

    6.5 The Matrix Eigenvalue Problem

    6.6 Functions of Hermitian Matrices

    6.7 The Matrix Pseudoeigenvalue Problem

    6.8 The Lagrange Interpolation Formula

    6.9 The Cayley–Hamilton Theorem

    6.10 The Eigenvalue Problem in Hückel’s Theory of the π Electrons of Benzene

    6.11 Problems 6

    6.12 Solved Problems

    Chapter 7. Molecular symmetry

    7.1 Introduction

    7.2 Symmetry and Quantum Mechanics

    7.3 Molecular Symmetry

    7.4 Symmetry Operations as Transformation of the Coordinate Axes

    7.5 Applications

    7.6 Problems 7

    7.7 Solved Problems

    Chapter 8. Abstract group theory

    8.1 Introduction

    8.2 Axioms of Group Theory

    8.3 Examples of Groups

    8.4 Multiplication Table

    8.5 Subgroups

    8.6 Isomorphism

    8.7 Conjugation and Classes

    8.8 Direct-Product Groups

    8.9 Representations and Characters

    8.10 Irreducible Representations

    8.11 Projectors and Symmetry-Adapted Functions

    8.12 The Symmetric Group

    8.13 Molecular Point Groups

    8.14 Continuous Groups

    8.15 Rotation Groups

    8.16 Problems 8

    8.17 Solved Problems

    Chapter 9. The electron spin

    9.1 Introduction

    9.2 Electron Spin according to Pauli and the Zeeman Effect

    9.3 Theory of One-Electron Spin

    9.4 Matrix Representation of Spin Operators

    9.5 Theory of Two-Electron Spin

    9.6 Theory of Many-Electron Spin

    9.7 The Kotani’ Synthetic Method

    9.8 Löwdin’ Spin Projection Operators

    9.9 Problems 9

    9.10 Solved Problems

    Chapter 10. Angular momentum methods for atoms

    10.1 Introduction

    10.2 The Vector Model

    10.3 Construction of States of Definite Angular Momentum

    10.4 An Outline of Advanced Methods for Coupling Angular Momenta

    10.5 Problems 10

    10.6 Solved Problems

    Part 2: Applications

    Chapter 11. The physical principles of quantum mechanics

    11.1 The Orbital Model

    11.2 The Fundamental Postulates of Quantum Mechanics

    11.3 The Physical Principles of Quantum Mechanics

    11.4 Problems 11

    11.5 Solved Problems

    Chapter 12. Atomic orbitals

    12.1 Introduction

    12.2 Hydrogen-like Atomic Orbitals

    12.3 Slater-type Orbitals

    12.4 Gaussian-type Orbitals

    12.5 Problems 12

    12.6 Solved Problems

    Chapter 13. Variational calculations

    13.1 Introduction

    13.2 The Variational Method

    13.3 Non-linear Parameters

    13.4 linear Parameters and the Ritz Method

    13.5 Atomic Applications of the Ritz Method

    13.6 Molecular Applications of the Ritz Method

    13.7 Variational Principles in Second Order

    13.8 Problems 13

    13.9 Solved Problems

    Chapter 14. Many-electron wavefunctions and model Hamiltonians

    14.1 Introduction

    14.2 Antisymmetry of the Electronic Wavefunction and the Pauli’s Principle

    14.3 Electron Distribution Functions

    14.4 Average Values of One- and Two-Electron Operators

    14.5 The Slater’s Rules

    14.6 Pople’s Two-Dimensional Chart of Quantum Chemistry

    14.7 Hartree–Fock Theory for Closed Shells

    14.8 Hückel’s Theory

    14.9 Semiempirical MO Methods

    14.10 Problems 14

    14.11 Solved Problems

    Chapter 15. Valence bond theory and the chemical bond

    15.1 Introduction

    15.2 The Chemical Bond in H2

    15.3 Elementary VB Methods

    15.4 Pauling’s VB Theory for Conjugated and Aromatic Hydrocarbons

    15.5 Hybridization and Directed Valency in Polyatomic Molecules

    15.6 Problems 15

    15.7 Solved Problems

    Chapter 16. Post-Hartree–Fock methods

    16.1 Introduction

    16.2 Matrix Elements between Slater Determinants

    16.3 Spinless Pair Functions and the Correlation Problem

    16.4 Configurational Interaction Methods

    16.5 Multiconfigurational-SCF Method

    16.6 Møller-Plesset Perturbation Theory

    16.7 Second Quantization

    16.8 Diagrammatic Theory

    16.9 The Density Functional Theory

    16.10 Problems 16

    16.11 Solved Problems

    Chapter 17. Atomic and molecular interactions

    17.1 Introduction

    17.2 Electric Properties of Molecules

    17.3 Interatomic Potentials

    17.4 Molecular Interactions

    17.5 The Pauli Repulsion Between Closed Shells

    17.6 The Van der Waals Bond

    17.7 Accurate Theoretical Results for Simple Diatomic Systems

    17.8 A Generalized Multipole Expansion for Molecular Interactions

    17.9 Problems 17

    17.10 Solved problems

    Chapter 18. Evaluation of molecular integrals

    18.1 Introduction

    18.2 The Basic Integrals

    18.3 One-centre Integrals

    18.4 Evaluation of the Electrostatic Potential J1S

    18.5 The (1S2|1S2) Electron Repulsion Integral

    18.6 General Formula for One-centre Two-electron Integrals

    18.7 Two-centre Integrals Over 1S STOS

    18.8 On the General Formulae for Two-centre Integrals

    18.9 A Short Note on Multicentre Integrals

    18.10 Molecular Integrals Over GTOS

    18.11 Problems 18

    18.12 Solved Problems

    Chapter 19. Relativistic molecular quantum mechanics

    19.1 Introduction

    19.2 The Schroedinger’s Relativistic Equation

    19.3 The Klein–Gordon Relativistic Equation

    19.4 Dirac’s Relativistic Equation for the Electron

    19.5 Spinors: Small and Large Components

    19.6 Dirac’s Equation for a Central Field

    19.7 One-Electron Molecular Systems: H2+ and HHe+2

    19.8 Two-Electron Atomic System: The He Atom

    19.9 Two-Electron Molecular Systems: H2 and HHe+

    19.10 Many-Electron Atoms and Molecules

    19.11 Problems 19

    19.12 Solved Problems

    Chapter 20. Molecular vibrations

    20.1 Introduction

    20.2 Separation of Translational and Rotational Motions

    20.3 Normal Coordinates in Classical and Quantum Mechanics

    20.4 The Born–Oppenheimer Approximation

    20.5 Electronically Degenerate States and the Renner’s Effect in NH2

    20.6 The Jahn–Teller Effect in CH4+

    20.7 The Von Neumann–Wigner Non-crossing Rule in Diatomics

    20.8 Conical Intersections in Polyatomic Molecules

    20.9 Problems 20

    20.10 Solved Problems

    References

    Author Index

    Subject Index

Product details

  • No. of pages: 1012
  • Language: English
  • Copyright: © Elsevier Science 2013
  • Published: August 1, 2013
  • Imprint: Elsevier Science
  • Hardcover ISBN: 9780444626479
  • eBook ISBN: 9780444626660

About the Author

Valerio Magnasco

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

Affiliations and Expertise

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

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