Funnel Hopping Monte Carlo: Efficient Monte Carlo simulations for multi-funnel systems*

Monte Carlo simulations are a popular tool used in physics, chemistry and biology to study the behavior of atomic systems at finite temperatures.

However, in many cases, the potential energy landscape is divided into multiple funnels separated by high energy barriers, which can prevent a complete sampling within available simulation time.

Our newly developed method, named funnel hopping Monte Carlo (FHMC), overcomes this problem by introducing non-local Monte Carlo moves from one low energy region to another, bypassing the high energy barriers entirely.

These new moves are generated by sampling Gaussian mixtures, that have been fit to the Boltzmann distributions of each funnel in advance to the simulation.

The method was first tested on the 38 and 75 atom Lennard-Jones clusters, for which conventional Monte Carlo simulations fail to converge, due to their double funnel energy landscape.

By integrating our method into the parallel tempering scheme, we were able to reduce the number of energy and force evaluations needed for a convergence of the simulations significantly.

Recently we also extended the method to periodic systems for which we will present results from ongoing applications.