Conical intersections within linear-response time-dependent density functional theory

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for many popular electronic-structure methods, given the propensity of such regions to possess conical intersections (CXs), i.e., (highly-connected) points of degeneracy between potential energy surfaces (PESs). CXs constitute the mechanistic bedrock of our theoretical framework to understand the ultrafast, non-radiative decay processes in photochemistry and photophysics. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to CXs, it is vital that the performance of electronic-structure methods is routinely examined in this context. As such, this thesis scrutinises the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to correctly describe (i) ground-to-excited state and (ii) excited-to-excited state minimum-energy CXs (MECXs), the latter experiencing much less attention in the literature than the former. Initially, we compare the performance of AA LR-TDDFT in terms of the location, topology and topography of the MECXs it affords in two prototypical molecules, protonated formaldimine (S/S and S/S) and pyrazine (S/S), to those afforded by two popular wavefunction-based methods. Such a comparison highlights a connection between two observations made previously in the literature regarding defective ground-to-excited state intersections within AA LR-TDDFT; both are shown in this thesis to emanate from the same defective PES feature. The thesis then examines the accumulated topological phase of the corresponding adiabatic electronic wavefunction in both aforementioned S/S and S/S MECX cases, and goes on to provide a detailed investigation of trajectory-surface hopping dynamics in protonated formaldimine, focused on the influence of the defective AA LR-TDDFT S/S intersection.