Modern Electronic Structure Theory

The following sections are included:

• INTRODUCTION

• PREFACE GENERAL

• PREFACE TO PART II

• CONTENTS

The following sections are included:

• Introduction

• Qualitative Considerations
  • Quantum Chemistry of Some Model Systems
  • Molecular Orbitals and Electron Correlation
  • Slater Orbitals and Gaussian Orbitals
  • Correlating Orbitals

• Gaussian Basis Sets
  • Basis Set Convergence
  • Contracted Gaussians from Fits to STO's
  • Contracted Gaussians from Atomic Calculations
  • Segmented Versus General Contractions
  • Even-Tempered Sequences
  • Polarization Functions
  • Correlated Calculations

• Basis Sets for SCF Calculations
  • Small Basis Sets
  • Larger Basis Sets
  • Extended Basis Sets

• Basis Sets for Correlated Calculations
  • Nondynamical Correlation
  • Small Basis Sets
  • Atomic Natural Orbitals
  • Correlation-Consistent Basis Sets
  • Basis Set Recommendations

• Basis Sets and Molecular Properties
  • Basis Functions and Energy Derivatives
  • Spectroscopic Constants
  • Electric Properties
  • Magnetic Properties
  • Basis Set Recommendations

• Basis Set Superposition Error
  • Counterpoise Correction
  • Basis Set Improvements and BSSE

• Basis Sets: Miscellaneous Topics
  • Excited and Ionized States
  • Core Correlation
  • Bond Functions

• Molecular Integrals — Introduction

• Charge Distributions
  • Properties of GTO's
  • Hermite Gaussian Functions
  • Overlap Distributions
  • Overlap Distributions by Recursion

• Simple One-Electron Integrals
  • Multipole Moments
  • Momentum and Kinetic Energy Integrals

• Coulomb Integrals
  • Electrostatics for Gaussian Charge Distributions
  • The Incomplete Gamma Function
  • Hermite Integrals
  • Cartesian Integrals
  • The Obara–Saika Scheme
  • Integral Prescreening

• Integrals over CGTO's
  • Cartesian Gaussian Integrals
  • Spherical Harmonic Gaussian Integrals

• Property Integrals
  • Geometrical Derivative Integrals
  • Derivatives of London Orbitals
  • Spin-Orbit Integrals

• Rys Quadrature

• Molecular Symmetry and Integrals
  • Symmetry-Distinct Integrals over CGTO's
  • Symmetry-Adapted Basis Functions
  • Computational Implementations
  • Differentiated Integrals and Symmetry

• Conclusions

• Acknowledgments

• References

The following sections are included:

• Introduction

• Response Theory for an Exact State
  • Introduction to Time-Dependent Perturbation Theory
  • Equations for the Time Development of Exact States
    • Parametrization
    • Time-Dependent Equations
  • Solution of the Generalized Ehrenfest Equations
    • General Perturbations
    • Periodic Perturbations
  • Response Functions for Exact States
    • General Expansions
    • Linear Response Functions
    • Quadratic Response Functions
    • Cubic Response Functions
  • Residues of Response Functions
    • Linear Response Functions
    • Quadratic Response Functions
    • Cubic Response Functions
  • Equations of Motion
    • Response Functions
    • Residues of Response Functions
    • Sum Rules
  • Molecular Properties from Response Functions
    • Interaction Operators
    • Linear Response Functions
    • Quadratic Response Functions
    • Cubic Response Functions
  • Equivalences for Dipole Properties
  • Response Functions in Static External Fields
  • The Time-Dependent Hellmann–Feynman Theorem
  • Response Functions for Approximate Wave Functions
    • Ansatzes for Time-Dependant Wave Functions
    • Equations for the Time Evolution
    • Equivalences of Molecular Properties

• Response Theory for an SCF State
  • Parametrization
  • Matrix Equations for the Time Development
  • First- and Second-Order Equations
  • Simultaneous Diagonalization of S^[2] and E^[2]
  • First- and Second-Order Time Solutions
  • Response Functions
  • Response Functions and Molecular Properties
  • Elimination of Summation over Intermediate States
  • Linear Transformations with ^eE^[2] and ^eS^[2]

• Response Theory for an MCSCF State
  • Parametrization
  • Matrix Equations for the Time Development
  • Response Functions
  • Computational Aspects in the Calculation of MCSCF-Response Functions and their Residues

• Examples of SCF and MCSCF Response Calculations
  • Introduction
  • Ne: Hyperpolarizability
  • N₂: Polarizability and Hyperpolarizability
  • FH: Polarizability and Hyperpolarizability
  • H₂O: Polarizability and Hyperpolarizability
  • Polyynes: Polarizability and Hyperpolarizability
  • Ne: Mixed Electric–Magnetic Hyperpolarizability Anisotropy

• Summary

• Acknowledgments

• Appendix. Iterative Algorithms for Large Response Matrix Equations
  • The Generalized Eigenvalue Equation
  • The Response Linear Sets of Equations
  • Results

• References

The following sections are included:

• Introduction

• Theoretical Aspects
  • Electron Correlation Requirements
  • Basis Set Requirements

• Composite Techniques
  • Gaussian-1 (G1) Theory
  • Gaussian-2 (G2) Theory
  • Simplifications to G2 Theory

• Applications of G1 and G2 Theories
  • Comparison with Accurate Experimental Data
  • Predictions for Other Compounds

• Future Extensions and Prospects

• Acknowledgments

• References

The following sections are included:

• Introduction

• The Kohn-Sham Formalism

• The Adiabatic Connection

• Exchange–Correlation Energy and Holes

• Exchange–Correlation Models

• Correlation in Chemical Bonds

• The Role of Exact Exchange (Hartree–Fock)

• Future Directions and Conclusions

• References

The following sections are included:

• Introduction

• Basic Considerations in Coupled-Cluster Theory

• Outline of Procedures for Derivation of Explicit Coupled-Cluster Equations
  • Normal-Product Hamiltonian
  • Energy Equations
  • Amplitude Equations
  • Factorized Equations

• Generalized Many-Body Perturbation Theory

• Simplified CC Methods for Triple and Quadruple Excitations
  • Iterative Methods
  • Non-Iterative Methods

• Open-Shell Applications

• Coupled-Cluster Energy Functional

• Coupled-Cluster Treatment of Properties

• Excited States
  • Comparison with Exact Results
  • EOM-CC for Properties and Oscillator Strengths
  • Excited States of Ethylene

• Acknowledgments

• Appendix A. Diagram Methods
  • Amplitude Diagrams

• Appendix B. Quadratic Configuration Interaction

• References

The following sections are included:

• Introduction

• Conventional Correlation Methods — Overview

• Pseudospectral Method — Motivation and Theory

• Conventional Møller–Plesset Perturbation Theory

• Pseudospectral Møller–Plesset Perturbation Theory

• Conclusion

• Acknowledgments

• References

The following sections are included:

• Introduction

• Partitioning Theory

• Effective Hamiltonians

• Bloch's Formulation

• Unitary Wave Operators

• Intruder States

• Energy Derivatives

• Conclusions

• References

The following sections are included:

• Introduction

• General Treatment
  • Parameter Dependence of the Wave Function and Energy
  • Derivatives of Variational Energy Expressions
  • Non-Variational Energy Expressions
  • Hellmann–Feynman Forces
  • Effective Density Matrix Formalism

• Derivatives for Self-Consistent Field Wave Functions
  • Historical Background
  • First Derivatives of the SCF Energy
  • Computational Considerations
  • Multiconfigurational Self-Consistent Field (MCSCF) Gradients
  • Derivatives in Density-Functional Theory
  • SCF and MCSCF Second Derivatives
  • Higher Derivatives

• Derivatives for Dynamical Electron Correlation

• Related Methods
  • Numerical Differentiation
  • Simultaneous Variation of the Geometrical and Electronic Variables

• The Calculation of Vibrational Spectra
  • Introduction
  • Empirical Scaling of Force Fields

• Acknowledgment

• References

The following sections are included:

• Introduction

• Identification of Molecular Species
  • Background
    • Early History
    • HCO⁺ and HNC
    • Cyanoethynyl and Butadiynyl
  • Extraterrestrial
    • Astrophysical Significance and Observations
    • Molecular Structure Calculations of
  • Recent Work and Future Directions

• Molecular Abundance Determinations

• Molecular Formation and Destruction Processes
  • Overview
  • Radiative Association
  • Photodissociation

• Concluding Remarks

• Acknowledgments

• References

The following sections are included:

• Introduction

• Overview of Transition Metal Bonding

• Methods

• Molecular Ions
  • The Metal–Rare-Gas Ion Systems
  • The Metal Ion–H₂ and –N₂ Systems
  • The Metal Ion–Benzene Systems
  • The Metal Ion–H₂O, –NH₃, and –CO Systems
  • The Transition Metal Ion–Methyl Systems
  • The Transition Metal Ion–Acetylene and –Ethylene Systems
  • The Transition Metal Ion–Methylene Systems
  • Doubly Charged Systems

• Neutral Systems: ML_n
  • The Transition Metal–Methyl Systems
  • The Transition Metal Oxides and Superoxides
  • The Transition Metal Carbonyl Systems
  • Transition Metal–Metal Bonding
  • The Calculation of Reaction Barriers

• Spectroscopy of Transition Metal Systems
  • The Vibrational Spectrum of CuCH₃
  • Vibrational Frequencies of the TiF_nCl_4−n (n = 0−4) Systems
  • Vibrational Frequencies for Other Transition Metal Systems
  • Electronic Transitions in the Scandium and Yttrium Halides
  • The Electronic Spectrum of FeH

• Conclusions

• References

The following sections are included:

• Introduction
  • Applications
  • Experiments
  • Theories
  • Massively Parallel Computing

• Schwinger Multichannel Method
  • Formulation
    • Basic Scattering Equations
    • Schwinger Variational Principle
    • Modified Schwinger Principle
  • Computational Form
    • Working Equations
    • One- and Two-Electron Integrals
    • Transformation Steps
    • Solution of Equations
  • Parallel Implementation
    • Design Philosophy
    • Integrals
    • Transformation
    • Solution of Equations
    • Resource Requirements
    • Performance and Optimization

• Applications
  • Elastic Scattering by Polyatomics
    • Alkanes
    • C₂H₄ and C₃H₆
    • [1.1.1] Propellane
    • Hydrides
    • CF₄ and SiF₄
  • Inelastic Scattering
    • Formaldehyde
    • Ethylene
    • [1.1.1] Propellane
    • Hydrogen Molecule
    • Nitrogen Molecule
    • Carbon Monoxide

• Future Directions

• Acknowledgments

• References

The following sections are included:

• INDEX