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Elementary Molecular Quantum Mechanics
Mathematical Methods and Applications
2nd Edition - August 7, 2013
Author: Valerio Magnasco
Hardback ISBN:
9 7 8 - 0 - 4 4 4 - 6 2 6 4 7 - 9
eBook ISBN:
9 7 8 - 0 - 4 4 4 - 6 2 6 6 6 - 0
The second edition of Elementary Molecular Quantum Mechanics shows the methods of molecular quantum mechanics for graduate University students of Chemistry and Physics. This… Read more
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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.
- 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
Students in chemical physics, theoretical and quantum chemistry also graduate students of chemistry/physics and undergraduate students of physical sciences
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
- No. of pages: 1012
- Language: English
- Published: August 7, 2013
- Imprint: Elsevier Science
- Hardback ISBN: 9780444626479
- eBook ISBN: 9780444626660
VM
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.