Quantum dynamics simulations using Gaussian wavepackets: the vMCG method

Gaussian wavepacket methods are an attractive way to solve the time-dependent Schrödinger equation (TDSE). They have an underlying trajectory picture that has a natural connection to semi-classical mechanics, allowing a simple pictorial interpretation of an evolving wavepacket. They also have better scaling with system size compared to conventional grid-based techniques. Here we review the variational multi-configurational Gaussian (vMCG) method. This is a variational solution to the TDSE, with explicit coupling between the Gaussian basis functions, resulting in a favourable convergence on the exact solution. The implementation of the method and its performance will be discussed with examples from non-adiabatic photo-excited dynamics and tunneling to show that it can correctly describe both of these strongly quantum mechanical processes. Particular emphasis is given to the implementation of the direct dynamics variant, DD-vMCG, where the potential surfaces are calculated on-the-fly via an interface to quantum chemistry programs.