Avoiding unphysical kinetic traps in Monte Carlo simulations of strongly attractive particles

We introduce a `virtual-move' Monte Carlo (VMMC) algorithm for systems of pairwise-interacting particles. This algorithm facilitates the simulation of particles possessing attractions of short range and arbitrary strength and geometry, an important realization being self-assembling particles endowed with strong, short-ranged and angularly specific (`patchy') attractions. Standard Monte Carlo techniques employ sequential updates of particles and suffer from low acceptance rates when attractions are strong. Our algorithm avoids this slowing-down by proposing simultaneous moves of collections (clusters) of particles according to gradients of interaction energies. One particle first executes a `virtual' trial move. We determine which of its neighbours move in a similar fashion by calculating individual bond energies before and after the proposed move. We iterate this procedure and update simultaneously the positions of all affected particles. Particles move according to an approximation of realistic dynamics without requiring the explicit computation of forces, and without the step size restrictions required when integrating equations of motion. We also employ a size- and shape-dependent hydrodynamic damping of cluster movements. We discuss the virtual-move algorithm in the context of other Monte Carlo cluster-move schemes, and demonstrate its utility by applying it to a model of biological self-assembly.