Time-dependent density functional theory (TDDFT) is an alternate formulation of time-dependent N-body quantum mechanics which allows one to describe a system via the single-particle density, n, rather than the full N-body wave function. While this reformulation is in theory exact in practice it necessitates at least two approximations. First, the exchange-correlation potential which encodes the two-particle interactions present in the time-dependent Schrdinger equation into the language of the single-particle description is not precisely known. Even if one had perfect knowledge of this potential a further approximation would be required when attempting to extract the values of observables as the exact relation between the one-particle density and most observables of interest is also unknown.
This dissertation investigates these issues using ion-atom collision systems as a testbed. First, the observable problem is explored in antiproton-helium, proton-helium, and He^{2+}-He collision systems. Total cross sections for all charge transfer processes in these systems, the observables of choice in the present situation, are determined using a two-centred extension of a correlation-integral model that was originally applied to single-centred situations.
Following this theoretical total cross section results for all ionization/capture processes in the He^{+}-He collision system are presented in the approximate impact energy range 10-1000 keV/amu. Calculations were performed within the framework of a spin-dependent extension of TDDFT. These cross sections are used as a benchmark to test an accurate exchange-correlation potential generated via the Krieger-Li-Iafrate approximation applied within the exchange-only limit in which correlation is ignored. The results of two models, one where electron translation factors in the orbitals used to calculate the potential are ignored and another where partial electron translation factors are included, are compared with available experimental data as well as a selection of previous theoretical calculations
