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

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 H_2.

_{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.}