Contents

• Declaration
• Acknowledgements
• Abstract
• List of Publications
• Contents
• Introduction
  • The Schrödinger Equation
  • The Born-Oppenheimer Approximation
  • The Hartree Approximation
  • The Variational Method
  • Hartree-Fock Theory
    • Matrix Elements and Notation
    • Initial Guess
    • Restricted Closed Shell Hartree-Fock
    • Restricted Open Shell Hartree-Fock
    • Unrestricted Hartree-Fock
    • Spin Properties of Hartree-Fock Wavefunctions
    • The cost of HF Theory
  • Multiple Determinant Wavefunctions
    • Configuration Interaction
    • Quadratic Configuration Interaction
    • Coupled Cluster Theory
    • Møller-Plesset Perturbation Theory
    • Gaussian-2 Theory
  • Basis Sets
  • Molecular Properties
• Density Functional Theory
  • Introduction
  • The Hohenberg-Kohn Theorems
  • The Constrained Search Formulation
  • Density Matrices
  • The Exchange Correlation Hole
  • The Uniform Electron Gas
  • The Almost Uniform Electron Gas
  • Kohn-Sham Theory
  • Exchange-Correlation Functionals
    • The Becke Exchange Functional
    • The Perdew-Wang 91 Functional
    • The Gill Functional
    • The Lee-Yang-Parr Functional
    • The Wigner Functional
    • Hybrid Density Functionals
  • Numerical Evaluation of Exchange-Correlation Integrals
    • Voronoi Polyhedra
    • Radial Integration
    • Angular Integration
    • Translational and Rotational Invariance
    • Standard Quadrature Grid
    • Standard Electronic Orientation
    • XC Linear Scaling
  • The Kohn-Sham matrix
• Density Functional Partitions^9.2
  • Introduction
  • General Theory
  • Energy Partitions
  • Application
  • Discussion
  • Conclusions
• Empirical Density Functionals^11.2
  • Introduction
  • General Theory
  • Results
  • Conclusions
• Faster Integral Calculation
  • Introduction
  • Traditional (0)^(m) Generation
  • The Bra Concentric Case
  • The Non-Concentric Case
  • Convergence Test
  • Constructing Moments
  • Matrix Equations
  • General Algorithm
  • Theoretical Performance Analysis
  • Empirical Performance Analysis
  • Conclusion
• The CASE Approximation
  • Introduction to Linear Methods
    • The Fast Multipole Method
    • The Continuous Fast Multipole Method
    • ONX: Order N Exchange
    • The KWIK Algorithm
  • The CASE Approximation
  • The Hydrogen Atom
  • Molecular Results
  • Conclusions
• Efficient Short-Range Integrals
  • Introduction
  • Integral Generation
  • Boxing Scheme
  • Integral Screening
  • Results and Discussion
  • Concluding Remarks
• Coulomb-Attenuated Exchange Energy Density Functionals^20.2
  • Introduction
  • Coulomb-Attenuated Dirac Exchange Functional
  • Coulomb-Attenuated Exact Exchange Functional
  • The Hydrogen Atom
  • Conclusion
• A Family of Attenuated Coulomb Operators
  • Introduction
  • The CASE(m) Approximation
  • Addition Integrals
  • Results
    • The Hydrogen Atom
    • Madelung Constant of NaCl
  • Conclusions
• Effects of Coulomb Attenuation on Chemical Properties
  • Introduction
  • Wavefunctions
  • Chemical Energetics
  • Effect of Basis Set
  • Geometry Optimizations
  • Vibrational Frequencies
  • Conclusions
• Reintroducing the Background^26.2
  • Introduction
  • An Expression for E_L
  • A Gaussian Basis for G(k)
  • The Ugly Fact
  • G_m(k) Chemistry
  • Conclusions
• Concluding Remarks
• Bibliography