Accelerating direct quantum dynamics using graphical processing units

Methods using a swarm of Gaussian basis functions to represent the nuclear wavefunction are a very appealing way to solve the time-dependent Schrödinger equation (TDSE) as they avoid the conventional scaling bottleneck of grid-based methods and provide a grid-free trajectory representation of the dynamics understudy. When coupled with direct (on-the-fly) dynamics, these methods offer the ability to simulate quantum dynamics of larger systems in full nuclear configuration space and avoid the requirement of a priori fitting of a potential energy surface. During such simulations, it is often assumed that the limiting factor is the computational cost of the quantum chemistry calculations. To combat this, in the present paper the direct dynamics variational multi-configurational Gaussian (DD-vMCG) method is combined with electronic structure calculations accelerated by Graphical Processing Units (GPUs). For the systems studied, a protonated ammonia dimer and the imidazole dimer, it is shown that the cost of the term responsible for the quantum behaviour of the nuclear dynamics means that the computational time associated with the quantum chemistry quickly becomes a small part of the overall computational time. Using these simulations, an estimated scaling of the vMCG method, with respect to the number of Gaussian basis functions is reported. This can be used to identify when quantum chemistry is the limiting factor and when GPU acceleration will have a significant effect for both ground and excited state simulations.