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• Preface to Revised editionPreface1. Mathematical Review1.1 Linear Algebra1.1.1 Three-dimensional vector algebra1.1.2 Matrices1.1.3 Determinants1.1.4 N-Dimensional Complex Vector spaces1.1.5 Change of Basis1.1.6 The Eigenvalue Problem1.1.7 Functions of Matrices1.2 Orthogonal functions, Eigenfunctions, and Operators1.3 The Variation Method1.3.1 The Variation principle1.3.2 The Linear Variational ProblemNotes, Further Reading2. Many Electron Wave functions and operators2.1 The Electronic Problem2.1.1 Atomic Units2.1.2 The Born-Oppenheimer Approximation2.1.3 The Antisymmetry or Pauli Exclusion Principle2.2 Orbitals, Slater Determinants, and Basis functions2.2.1 Spin Orbitals and Spatial Orbitals2.2.2 Hartree Products2.2.3 Slater Determinants2.2.4 The Hartree-Fock Approximation2.2.5 The Minimal Basis H subscript 2 Model2.2.6 Excited Determinants2.2.7 Form of the Exact Wave function and Configuration Interaction2.3 Operators and Matrix Elements2.3.1 Minimal Basis H subscript 2 matrix Elements2.3.2 Notations for One- and Two-Electron Integrals2.3.3 General Rules for Matrix Elements2.3.4 Derivation of the Rules for Matrix Elements2.3.5 Transition from Spin Orbitals to Spatial Orbitals2.3.6 Coulomb and Exchange Integrals2.3.7 Pseudo-Classical interpretation of Determinantal Energies2.4 Second Quantization2.4.1 Creation and annihilation Operators and Their Anticommutation Relations2.4.2 Second-Quantized Operators and Their Matrix Elements2.5 Spin-Adapted Configurations2.5.1 Spin Operators2.5.2 Restricted Determinants and Spin-Adapted Configurations2.5.3 Unrestricted DeterminantsNotes, Further Reading3. The Hartree-Fock Approximation3.1 The Hartree-Fock Equations3.1.1 The Coulomb and Exchange Operators3.1.2 The Fock Operator3.2 Derivation of the Hartree-Fock Equations3.2.1 Functional Variation3.2.2 Minimization of the Energy of a Single Determinant3.2.3 The Canonical Hartree-Fock Equations3.3 Interpretation of Solutions to the Hartree-Fock Equations3.3.1 Orbital energies and Koopmans' Theorem3.3.2 Brillouin's Theorem3.3.3 The Hartree-Fock Hamiltonian3.4 Restricted Closed-Shell hartree-Fock: The Roothaan Equations3.4.1 Closed-Shell Hartree-Fock: Restricted Spin Orbitals3.4.2 Introduction of a Basis: The Roothaan Equations3.4.3 The Charge Density3.4.4 Expression for the Fock Matrix3.4.5 Orthogonalization of the Basis3.4.6 The SCF Procedure3.4.7 Expectation Values and Population Analysis3.5 Model Calculations on H subscript 2 and HeH superscript +3.5.1 The 1s Minimal STO-3G Basis Set3.5.2 STO-3G H subscript 23.5.3 An SCF Calculation on STO-3G HeH superscript +3.6 Polyatomic Basis Sets3.6.1 Contracted Gaussian functions3.6.2 Minimal Basis Sets: STO-3G3.6.3 Double Zeta Basis Sets: 4-31G3.6.4 Polarized Basis Sets: 6-31G and 6-31G3.7 Some Illustrative Closed-Shell Calculations3.7.1 Total Energies3.7.2 Ionization Potentials3.7.3 Equilibrium Geometries3.7.4 Population Analysis and Dipole Moments3.8 Unrestricted Open-Shell Hartree-Fock: The Pople-Nesbet Equations3.8.1 Open-Shell Hartree-Fock: Unrestricted Spin Orbitals3.8.2 Introduction of a Basis: The Pople-Nesbet Equations3.8.3 Unrestricted Density Matrices3.8.4 Expression for the Fock Matrices3.8.5 Solution of the Unrestricted SCF Equations3.8.6 Illustrative Unrestricted Calculations3.8.7 The Dissociation Problem and its Unrestricted SolutionNotes, Further Reading4. Configuration Interaction4.1 Multiconfigurational Wave Functions and the Structure of the Full CI Matrix4.1.1 Intermediate Normalization and an Expression for the Correlation Energy4.2 Doubly Excited CI4.3 Some Illustrative Calculations4.4 Natural Orbitals and the One-Particle Reduced Density Matrix4.5 The Multiconfiguration Self-Consistent Field (MCSCF) and Generalized Valence Bond (GVB) Methods4.6 Truncated CI and the Size-Consistency ProblemNotes, Further Reading5. Pair and Coupled-Pair Theories5.1 The Independent Electron Pair Approximation (IEPA)5.1.1 Invariance under Unitary Transformations: an example5.1.2 Some Illustrative Calculations5.2 Coupled-Pair Theories5.2.1 The Coupled Cluster Approximation (CCA)5.2.2 The Cluster Expansion of the Wave Function5.2.3 Linear CCA and the Coupled Electron Pair Approximation (CEPA)5.2.4 Some Illustrative Calculations5.3 Many-Electron Theories with Single Particle Hamiltonians5.3.1 The Relaxation Energy via CI, IEPA, CCA, and CEPA5.3.2 The Resonance Energy of Polyenes in Hückel TheoryNotes, Further Reading6. Many-Body Perturbation Theory6.1 Rayleigh-Schrödinger (RS) Perturbation Theory6.2 Diagrammatic Representation of RS Perturbation Theory6.2.1 Diagrammatic Perturbation Theory for 2 States6.2.2 Diagrammatic Perturbation Theory for N States6.2.3 Summation of Diagrams6.3 Orbital Perturbation Theory: One-Particle Perturbations6.4 Diagrammatic Representation of Orbital Perturbation Theory6.5 Perturbation Expansion of the Correlation Energy6.6 The N-Dependence of the RS Perturbation Expansion6.7 Diagrammatic Representation of the Perturbation Expansion of the Correlation Energy6.7.1 Hugenholtz Diagrams6.7.2 Goldstone Diagrams6.7.3 Summation of Diagrams6.7.4 What Is the Linked Cluster Theorem?6.8 Some Illustrative CalculationsNotes, Further Reading7. The One-particle Many-Body Green's Function7.1 Green's Functions in single Particle Systems7.2 The One-Particle Many-Body Green's Function7.2.1 The Self-Energy7.2.2 The solution of the Dyson Equation7.3 Application of the formalism to H subscript 2 and HeH superscript +7.4 Perturbation Theory and the Green's Function Method7.5 Some Illustrative CalculationsNotes, Further ReadingAppendix A. Integral Evaluation with 1s Primitive GaussiansAppendix B. Two-Electron Self-Consistent-Field ProgramAppendix C. Analytic Derivative methods and Geometry OptimizationAppendix D. Molecular Integrals for H subscript 2 as a Function of Bond LengthIndex