Solving the time-dependent Schrodinger equation for nuclear motion in one step: direct dynamics of non-adiabatic systems

A review of direct dynamics methods is given, focusing on their application to non-adiabatic photochemistry-i.e. systems in which a conical intersection plays an important role. Direct dynamics simulations use electronic structure calculations to obtain the potential energy surface only as it is required 'on-the-fly'. This is in contrast to traditional methods that require the surface to be globally known as an analytic function before a simulation can be performed. The properties and abilities, with descriptions of calculations made, of the three main methods are compared: trajectory surface hopping (TSH), ab initio multiple spawning (AIMS), and variational multi-configuration Gaussian wavepackets (vMCG). TSH is the closest to classical dynamics, is the simplest to implement, but is hard to converge, and even then not always accurate. AIMS solves the time-dependent Schrodinger more rigorously, but as its basis functions follow classical trajectories again suffers from poor convergence. vMCG is harder to implement, but its basis functions do not follow classical trajectories and it converges much faster.