Molecular dynamics simulations are very powerful, providing microscopic insight into chemical processes in the gas phase, clusters and condensed phases. However, two outstanding challenges of the standard algorithms are: 1) Extending simulations to longer timescales, to allow the description of phenomena such as the nucleation and growth of clusters. 2) Including quantum statistics at a reasonable computational cost, to enable simulations of chemistry in ultra-cold clusters. I will describe two algorithms to address these limitations. First, I will present a method to perform bosonic path integral molecular dynamics simulations (PIMD). While widely used to study quantum effects in chemistry and physics, PIMD assumes that the particles are distinguishable, completely neglecting quantum statistics. This approximation breaks down for ultra-cold clusters. The main difficulty with indistinguishable particles is the enumeration of all particle permutations, which scales exponentially with system size. We developed a recursive algorithm that reduced the scaling from exponential to cubic, allowing the first applications of PIMD to large bosonic systems, from supersolids to superfluid helium clusters. Secondly, I will present a method to expedite MD simulations to longer timescales using stochastic resetting. Processes such as cluster nucleation and growth are often characterized by broad transition time distributions in which extremely slow events have a non-negligible probability. Stochastic resetting, i.e., restarting simulations at random times, was recently shown to significantly accelerate processes of that nature. We employ resetting for enhanced sampling of molecular simulations for the first time. We use it to speed up long-timescale processes by up to an order of magnitude in systems ranging from toy models to a molecule undergoing a conformational change in the gas phase. We also recover the mean transition time without resetting from accelerated simulations at a single restart rate.

Algorithms for long timescales and quantum statistics in molecular dynamics simulations

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