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Methods of Molecular Quantum Mechanics: An Introduction to Electronic Molecular Structure

ISBN: 978-0-470-68442-9
298 pages
December 2009
Methods of Molecular Quantum Mechanics: An Introduction to Electronic Molecular Structure (0470684429) cover image

Description

This advanced text introduces to the advanced undergraduate and graduate student the mathematical foundations of the methods needed to carry out practical applications in electronic molecular quantum mechanics, a necessary preliminary step before using commercial programmes to carry out quantum chemistry calculations.

Major features of the book include:

  • Consistent use of the system of atomic units, essential for simplifying all mathematical formulae
  • Introductory use of density matrix techniques for interpreting properties of many-body systems
  • An introduction to valence bond methods with an explanation of the origin of the chemical bond
  • A unified presentation of basic elements of atomic and molecular interactions

The book is intended for advanced undergraduate and first-year graduate students in chemical physics, theoretical and quantum chemistry. In addition, it is relevant to students from physics and from engineering sub-disciplines such as chemical engineering and materials sciences.

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Table of Contents

Preface.

1 Principles.

1.1 The Orbital Model.

1.2 Mathematical Methods.

1.3 Basic Postulates.

1.4 Physical Interpretation of the Basic Principles.

2 Matrices.

2.1 Definitions and Elementary Properties.

2.2 Properties of Determinants.

2.3 Special Matrices.

2.4 The Matrix Eigenvalue Problem.

3 Atomic Orbitals.

3.1 Atomic Orbitals as a Basis for Molecular Calculations.

3.2 Hydrogen-Like Orbitals (HAOs).

3.3 Slater-Type Orbitals (STOs).

3.4 Gaussian-Type Orbitals (GTOs).

4 The Variation Method.

4.1 Variational Principles.

4.2 Non-Linear Parameters.

4.3 Linear Parameters and the Ritz Method.

4.4 Applications of the Ritz Method.

5 Spin.

5.1 The Zeeman Effect.

5.2 The Pauli Equations for 1-Electron Spin.

5.3 The Dirac Formula for N-Electron Spin.

6 Antisymmetry of Many-Electron Wavefunctions.

6.1 Antisymmetry Requirement and the Pauli Principle.

6.2 Slater Determinants.

6.3 Distribution Functions.

6.4 Average Values of Operators.

7 SCF Calculations and Model Hamiltonians.

7.1 Elements of Hartree-Fock Theory for Closed Shells.

7.2 Roothaan Formulation of the LCAO-MO-SCF Equations.

7.3 Molecular SCF Calculations.

7.4 Hückel Theory.

7.5 A Model for the 1-Dimensional Crystal.

8 Post-Hartree-Fock Methods.

8.1 Configuration Interaction (CI).

8.2 Multiconfiguration SCF.

8.3 Møller-Plesset (MP) Theory.

8.4 MP-R12 Method.

8.5 CC-R12 Method.

9.6 Density Functional Theory (DFT).

9 VB Theory and the Chemical Bond.

9.1 The Born-Oppenheimer Approximation.

9.2 The Hydrogen Molecule H2.

9.3 The Origin of the Chemical Bond.

9.3 Valence Bond (VB) Theory and the Chemical Bond.

9.4 Hybridization and Molecular Structure.

9.5 Pauling’s Formula for Conjugated and Aromatic Hydrocarbons.

10 Elements of Rayleigh-Schroedinger (RS) Perturbation Theory.

10.1 RS Perturbation Equations up to Third Order.

10.2 First-Order Theory.

10.3 Second-Order Theory.

10.4 Approximate E2 Calculations: the Hylleraas’ Functional.

10.5 Linear Pseudostates and Molecular Properties.

10.6 Quantum Theory of Magnetic Susceptibilities.

11 Atomic and Molecular Interactions.

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

11.2 The H-H Expanded Interactions up to Second Order.

11.3 Molecular Interactions.

11.4 Van der Waals and Hydrogen Bonds.

11.5 The Keesom Interaction.

12 Symmetry.

12.1 Molecular Symmetry.

12.2 Group Theoretical Methods.

12.3 Illustrative Examples.

References.

Author Index.

Subject Index.

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