Methods of Molecular Quantum Mechanics An Introduction to Electronic Molecular Structure

by Magnasco, Valerio

• ISBN13: 9780470684429
• ISBN10: 0470684429
• Edition: 1st
• Format: Hardcover
• Copyright: 2009-12-21
• Publisher: Wiley

Summary

This provides an advanced text introducing graduate students to the mathematical foundations of methods needed to do working applications in molecular quantum mechanics. It contains a consistent use of atomic units from the very beginning for simplifying mathematical formulae, and presents a unified presentation of basic elements of atomic and molecular interactions, with particular emphasis on practical use of second-order calculation techniques.

Author Biography

Dr Valerio Magnasco, MRSC, is full Professor of Theoretical Chemistry at the University of Genoa, Italy, presently at the Department of Chemistry and Industrial Chemistry (DCCI) of the Faculty of Mathematical, Physical and Natural Sciences of the University. He is Member of the Royal Society of Chemistry (UK, RSC), the American Institute of Physics (US, AIP), the Physical Chemistry Division of the Italian Chemical Society (Italy, SCI), the Class of Sciences of Accademia Ligure di Scienze e Lettere (Italy, Genova). He is supervising a research group working on the theoretical study of atomic and molecular interactions, and is author or co-author of over 170 scientific papers mostly published on international journals, and of one book on Molecular Quantum Mechanics.

Table of Contents

Preface

Principles

The Orbital Model

Mathematical Methods

Basic Postulates

Physical Interpretation of the Basic Principles

Matrices

Definitions and Elementary Properties

Properties of Determinants

Special Matrices

The Matrix Eigenvalue Problem

Atomic Orbitals

Atomic Orbitals as a Basis for Molecular Calculations

Hydrogen-Like Orbitals (HAOs)

Slater-Type Orbitals (STOs)

Gaussian-Type Orbitals (GTOs)

The Variation Method

Variational Principles

Non-Linear Parameters

Linear Parameters and the Ritz Method

Applications of the Ritz Method

Spin

The Zeeman Effect

The Pauli Equations for 1-Electron Spin

The Dirac Formula for N-Electron Spin

Antisymmetry of Many-Electron Wavefunctions

Antisymmetry Requirement and the Pauli Principle

Slater Determinants

Distribution Functions

Average Values of Operators

SCF Calculations and Model Hamiltonians

Elements of Hartree-Fock Theory for Closed Shells

Roothaan Formulation of the LCAO-MO-SCF Equations

Molecular SCF Calculations

Hückel Theory

A Model for the 1-Dimensional Crystal

Post-Hartree-Fock Methods

Configuration Interaction (CI)

Multiconfiguration SCF

Møller-Plesset (MP) Theory

MP-R12 Method

CC-R12 Method

Density Functional Theory (DFT)

VB Theory and the Chemical Bond

The Born-Oppenheimer Approximation

The Hydrogen Molecule H_2.

The Origin of the Chemical Bond

Valence Bond (VB) Theory and the Chemical Bond

Hybridization and Molecular Structure

Pauling's Formula for Conjugated and Aromatic Hydrocarbons

Elements of Rayleigh-Schroedinger (RS) Perturbation Theory

RS Perturbation Equations up to Third Order

First-Order Theory

Second-Order Theory

Approximate E2 Calculations: the Hylleraas' Functional

Linear Pseudostates and Molecular Properties

Quantum Theory of Magnetic Susceptibilities

Atomic and Molecular Interactions

The H-H Non-Expanded Interactions up to Second Order

The H-H Expanded Interactions up to Second Order

Molecular Interactions

Van der Waals and Hydrogen Bonds

The Keesom Interaction

Symmetry

Molecular Symmetry

Group Theoretical Methods

Illustrative Examples

References

Author Index

Subject Index

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