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Contents
List of Figures
List of Tables
Introduction
The Many-Electron Problem
One-Electron Methods
The Hartree Approximation
The Hartree-Fock Approximation
Configuration Interaction
Density Functional Methods
Kohn-Sham Equations
Quantum Monte Carlo Calculations
Layout of Thesis
Quantum Monte Carlo Methods
The Variational Principle
Monte Carlo Methods
Importance Sampling
The Metropolis Algorithm
Variational Quantum Monte Carlo
Trial Wavefunctions
Evaluating the Local Energy
Evaluating the Kinetic Energy
Electrostatic Energies
Accumulating Averages
Performing VMC calculations of Parallel Computers
Diffusion Quantum Monte Carlo
The Method
A DMC Algorithm
The Fixed-Node Approximation
DMC With Non-Local Pseudopotentials
Performing DMC Calculations on Parallel Computers
Quantum Monte Carlo Calculations on Solids
Supercell Calculations
Wavefunctions for Solid Calculations
Germanium and Silicon - The Diamond Structure
Choice of Slater Determinant
Coulomb Interactions in Supercell Calculations
Isolated Simulation Cell
Periodic Boundary Conditions
Ewald Summation
Electron-Ion Coulomb Interactions
Optimising Trial Wavefunctions
Motivation
VMC Calculations
DMC Calculations
Optimisation Method
Why Minimise the Variance of the Energy?
Previous Applications of Variance Minimisation
The Variance Minimisation Method
Control of the Reweighting Factors
Choice of Average Local Energy,
Generating Configurations
Optimising the
function
Which Part of
to Optimise?
Choice of Parameters
Adding a new Function to Chi
Results of Optimising the Function in Germanium Solid
Optimising the
u
Function
Choice of Functional Form for new term in the Jastrow Factor
Implementation of the new Jastrow Function
Results of Optimising the new Jastrow Factor
Removing the
Prefactor in
A New
u
function
Form of the New
u
function
Tests on Jellium
Applying the New
u
Function to Solids
Optimising Wavefunctions for Atoms
Choice of Atomic Wavefunction
Results
Cohesive Energies
Variance Minimisation on Parallel Computers
Variance Minimisation with Non-Local Pseudopotentials
Keeping the Non-Local part Fixed during Optimisation
Evaluating the non-local Integral during Optimisation
Limits of Variance minimisation
VMC Calculations
DMC Calculations
Finite Size Effects
Introduction
Motivation
Previous Methods of Removing Finite Size Effects
Analysis of e-e energy
Comparison of Hartree-Fock and LDA Results
Electron-Electron Interaction in More Detail
New Proposed Energy Expression
Short range of Exchange-Correlation Hole
Use
Interaction
Choices for the
f
function
Tests on the Homogeneous Electron Gas
VMC Results
Finite Size Effects in Inhomogeneous Solids
Electron-Ion and Ion-Ion Interactions
Results for Silicon
VMC Results
HF Results
DMC Results
Variance Minimisation with the New Interaction
Conclusions
QMC Calculations of Excitation Energies
Previous Work on Excitation Energies
QMC Calculations
Hartree-Fock Calculations
Density Functional Calculations
Experimental Determination of Excited States
QMC Methods for Calculating Excitation Energies
Addition and Subtraction of Electrons
Trial Wavefunction
Electron-Electron Interaction
New Electron-Electron Interaction
Hartree-Fock Analysis of New Interactions
New Interaction, Eq.()
Enhanced Version from Eq.()
Addition and Subtraction of Electrons in VMC
VMC Results
Addition and Subtraction of Electrons in DMC
DMC Results
Promoting Electrons
Trial Wavefunctions for Promoted States
Spin Contamination
One and Two-body Functions for Promotion Calculations
Electron-Electron Interaction for Promoted States
DMC Results
Calculating Band Widths
Excitonic Effects
Summary and Comparison of the Methods
Alternative Methods for Calculating Excited States within QMC
Spectrum Folding
DMC Decay Curves
Conclusions
Updating the Slater Determinant
References
About this document ...
Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996