Development and Applications of New Basis Set Sampling and Basis Set Handling Procedures for the Coupled Coherent States Family of Methods

The Coupled Coherent States family of methods have shown themselves capable of simulating the quantum dynamics of many different systems. The ability of these methods to accurately describe quantum behaviour is dependent on using a basis set which covers a sufficient area of phase space. If the area covered is too small, the basis set will be unable to adequately describe the dynamics of the system, however if the area is too large and the basis functions become too widely spaced, coupling will be lost between
the coherent states and the simulation will fall into the semiclassical regime. In some situations the loss of this coupling becomes accelerated, through trajectories guiding the basis functions far from each other in phase space for example, limiting the ability of these methods to accurately describe quantum behaviour.

This thesis demonstrates two techniques for preserving a correct description of the wavefunction in phase space. Firstly a combination of initial sampling using swarms of basis function trains and basis function cloning during propagation of the wavefunction is shown to correct a disagreement seen between the two formulations of the Multi-
Configurational Ehrenfest method when simulating the high dimensional spin boson model. This combination gives a good agreement with benchmark calculations found using the Multi-Configurational Time-Dependent Hartree method. The techniques used to correct this disagreement have been used previously for on-the-fly ab initio direct dynamics simulations, reported in references [1] and [2], and so this investigation provides validation for the results obtained in those publications. Secondly a system of adaptive reprojection of the wavefunction is shown to allow a large grid of coherent states to be reduced to only the area of interest, while keeping the basis set in that region. It is also demonstrated that this will still hold even if the equations of motion tend to move basis
functions far away from this area. This adaptive reprojection technique is tested against the high harmonic generation of an electron bound to a pseudo-atomic potential in one dimension, yielding results which are in good agreement with benchmark calculations carried out using the Time-Dependent Schrodinger equation.