# Quantum Monte Carlo Calculations of Electronic Excitations

*A. Williamson*, 1996

## Summary

This thesis is concerned with developing quantum Monte Carlo techniques to calculate electronic excitations. Variational and diffusion quantum Monte Carlo calculations for the ground-state electronic properties of atoms and solids are reported. The importance of the choice of trial wavefunction in these calculations is highlighted. Methods for optimising this trial wavefunction, based on the minimisation of the variance of the local energy are developed for both atomic and solid wavefunctions. New forms of variational trial wavefunction are introduced that are more suitable for optimisation and are also much faster to evaluate.

The existence of finite size effects when simulating periodic systems is illustrated. The source of these finite size errors is tracked down to the Ewald method which introduces spurious correlations between electrons in different simulation cells. A new electron-electron interaction which consists of the Coulomb interaction between point particles at short range, and a long ranged averaged (Hartree) interaction is proposed. Hartree-Fock, variational and diffusion quantum Monte Carlo results for the energy of diamond-structure silicon are presented which demonstrate the effectiveness of this new method.

Variational and diffusion quantum Monte Carlo results for the quasiparticle bandstructure of diamond-structure silicon using both highly optimized trial wavefunctions and the new electron-electron interaction are reported. These are based on two separate methods of calculating excited states, (i) the addition and subtraction of electrons, (ii) the promotion of electrons from the valence band into the conduction band. These two methods of calculating excited states are compared and contrasted with each other and other more traditional methods of calculating quasiparticle bandstructures, such as the local density approximation to density functional theory.

The results show that if a careful choice of trial/guiding wavefunction is made, and the electron-electron interaction is chosen to reduce the Coulomb finite size effects, it is possible to calculate electronic excitation energies within diffusion quantum Monte Carlo that represent a significant improvement over those calculated using the local density approximation.