Nonadiabatic dynamics has been an essential part of quantum chemistry since the 1930’s. Nonadiabatic effects play a crucial role in photo-physical and photo-chemical reactions for both small and large molecules in both gas and condensed phases. Modeling dynamics of photoinduced reactions has been a new frontier of chemistry. Many dynamical phenomena, such as intersystem crossing, non-radiative relaxation, and charge energy transfer, require a nonadiabatic description which incorporates transitions between electronic states.
In Chapter 2, the property of scattering region in the semiclassical limit is investigated. We suggest that a nuclear wavepacket close enough to the conical intersection will propagate ballistically in a straight line through the scattering region with distance λ+, the impact parameter, away from the conical intersection. Upon taking the semiclassical limit, we have proven that in a certain neighborhood of the conical intersection, the adiabatic propagation and ballistic propagation are both valid. The resulted complete propagator is governed by the semiclassical propagation along the reference path which connects the initial and final points, and an integration over the impact parameter, hence only depends on the initial and final classical states of the system.
In Chapter 3, we identify the main differences between the effects of Kramers symmetry on the systems with even and odd number of electrons, the ways how the aforementioned symmetry affects the structure of the Conical Seams (CSs), and how it shows up in semiclassical propagation of nuclear wavepackets, crossing the CSs. We identify the topological invariants, associated with CSs,
in three cases: even and odd number of electrons with time-reversal symmetry, as well as absence of the latter. We obtain asymptotically exact semiclassical analytical solutions for wavepackets scattered on a CS for all three cases, identify topological features in a non-trivial shape of the scattered wavepacket, and connect them to the topological invariants, associated with CSs. We argue that, due to robustness of topology, the non-trivial wavepacket structure is a topologically protected evidence of a wavepacket having passed through a CS, rather than a feature of a semiclassical approximation.
In Chapter 4, we present, in detail, an algorithm based on Monte-Carlo sampling of the semiclassical time-dependent wavefunction, that involves running simple surface hopping dynamics, followed by a post-processing step which adds little cost. The method requires only a few quantities from quantum chemistry calculations, can systematically be improved, and provides excellent agreement with exact quantum mechanical results. Here we show excellent agreement with exact solutions for scattering results of standard test problems. Additionally, we find that convergence of the wavefunction is controlled by complex valued phase factors, the size of the nonadiabatic coupling region, and the choice of sampling function. These results help in determining the range of applicability of the method, and provide a starting point for further improvement
