Quantum States of Confined Atomic and Molecular Systems in a Basis of Explicitly Correlated Gaussians

Abstract

A model for describing the ground and excited states of a hydrogen atom (or amolecule) confined to a soft-wall cuboidal potential energy trap, which allows a small part of the wave function to leak across the boundary, is proposed and implemented. Explicitly Correlated Gaussian (ECG) functions are used to expand these wave functions that are symmetry adapted with respect to the trapping potential. These quantum systems are studied without assuming the Born-Oppenheimer approximation, to achieve highly accurate results. Both the electronic and nuclear densities of all the states are visualized using density plots. This novel method to understand the behavior of a trapped hydrogen atom (or a molecule), when extended to multiple hydrogen molecules, has potential for predicting the cage occupancy of different clathrate molecules used for hydrogen storage, because current data regarding these are highly contested. Since the cage occupancy directly corresponds to the % hydrogen by weight, the work described in the thesis can potentially be used to advance the field of hydrogen storage in clathrates. In addition, the studies shed more light on the confinement of small quantum systems subjected to a partially penetrable potential, which can, when developed further, help in the understanding of several response properties such as polarizability, hyperpolarizability, dipole moment etc under these confinement conditions.