Contents

• Contents
• The Quantum Many-Body Problem
  • Introduction
  • Thomas-Fermi Theory
  • Dirac Exchange
  • Hartree-Fock Theory
    • The Self-Consistent Field
    • Correlation
  • Density Functional Theory
    • The Hohenberg-Kohn Theorems
    • The Kohn-Sham Formulation
  • Plane-Wave Implementation of DFT
    • Bloch's Theorem
    • Kohn-Sham Equations in Plane-Wave Form
    • -point Sampling
    • Pseudopotentials
    • Energy Minimisation
  • The CASTEP Code
• Exchange and Correlation
  • Fundamentals
    • The Exchange-Correlation Hole
    • Exact Definition of Exchange and Correlation
    • Properties of the Exchange-Correlation Hole
    • The Pair-Correlation Function
    • Self-Interaction Effects
  • Exchange-Correlation Approximations
    • The Local Density Approximation
    • The Generalised Gradient Approximation
    • Meta-Generalised Gradient Approximation
    • Hybrid Functionals
    • Non-Local Functionals
  • Quantum Monte Carlo
  • Summary
• Assessment of Semi-Empirical GGA Functionals
  • Introduction
  • The HCTH Functional
    • The General Form
    • Details of the Implementation
    • Testing: The Hellmann-Feynman Theorem
  • Properties of group IV and III-V Semiconductors
    • Lattice Constants
    • Bulk Moduli
    • Cohesive Energies
    • Electronic Bandstructures
    • Charge Density Differences
    • Pseudopotential Considerations
  • Performance of Other HCTH-Type Functionals
    • Computational Results
  • Conclusions
• The Weighted Density Approximation
  • Introduction
  • Theory of the WDA
    • The Functional Form
    • The WDA Potential
    • Model Pair-Correlation Functions
    • Self-Interaction
    • Asymptotic Properties
  • Computational Implementation
    • Reciprocal-Space Representation
    • The Sum Rule
    • Energy Density
    • The Scalar Fields: and
    • WDA Potential
    • Implementation Tests
  • Algorithm Development
  • Self-Consistent WDA Calculations
    • Interpolation Grid Convergence
    • Results
  • Summary
• Investigation of Model Pair-Correlation Functions
  • Introduction
  • The Model Functions
  • Bulk Properties of Si
    • Structural Properties
    • Electronic Structure
  • Exchange-Correlation Holes in Si[110]
    • Comparison with the VMC Method
    • Generation Procedure
    • Results
    • Discussion
  • Development
    • Existing Problems
    • A New Model Function
    • Implementation Details
    • Results for the Homogeneous Electron Gas
  • Summary
• Model Electron Gas Systems
  • Introduction
  • The Cosine-Wave Electron Gas
    • Overview of a VMC Study
    • Details of the Calculations
    • The WDA Results
  • Quasi Two-Dimensional Electron Gas
    • The Model Potential
    • Computational Results
  • Strong Isotropic Confinement
    • The Model Potential
    • Computational Results
  • Summary
• Conclusions and Future Work
• Derivation of the Exact Exchange-Correlation Energy
• Coefficients for HCTH and HCTH-related GGAs
• Publications
• Bibliography