Development of Methodology, Functionality and Optimisation Tools for the Fermionic "Zombie" Coherent State Method

Zombie states are a novel addition to the Coupled Coherent States (CCS) family of methods. These have been successfully used for simulation of the dynamics of various quantum systems which primarily have been bosonic. Usually, such methods would be generalised, to describe fermions, by application of fermionic coherent states. These are constructed using either Grassmann algebra or a Lie group with appropriate topological properties which are not well suited to numeric calculations. Zombie states are constructed as a superposition of "dead" and "alive" electronic states. Antisymmetry is preserved by the addition of a simple sign-change rule to the creation and annihilation operators. CCS methods are characterised by their high chemical accuracy and low computational cost when compared to similar methods. Therefore, Zombie states are intended to maintain these properties for electron dynamic simulations.

This thesis presents developments to the formulation and implementation of the Zombie states method which are verified by application to a range of chemical systems. Firstly, the Zombie states method is formulated using the general coherent state definition; it is shown how this naturally gives rise to the sign-change rule. It is then demonstrated that imaginary time propagation can be used to find exact ground state energies with minimal computational cost, which greatly improves the method's practicality. Smaller basis sets incur lower computational costs. However, an incomplete sized basis set of random Zombie states does not accurately recover the ground state. Thus, necessitating the development of sampling and optimisation techniques. Hence, gradient descent is adopted to find optimal sets of Zombie state amplitudes that can recover the ground state energy using a small basis set. Finally, the Zombie state method is extended to find excited states by incorporation of Gram-Schmidt orthogonalisation. These excited states energies can be found with minimal additional computational cost and with no requirement for a reference state.