Collective Moves in Monte Carlo

Unlike Molecular Dynamics, Monte Carlo based simulation methods, where the phase space is sampled by random changes to the system (the so called moves), do not suffer the restriction of a small displacement per simulation step. One of the most established Monte Carlo based methods in the area of atomistic systems is Metropolis MC, where the propagation of the system is sampled by a Markov chain. For every simulation step, a completely random modification to the system is proposed and accepted or rejected due to an acceptance criterion that satisfies detailed balance. This is very efficient for problems with only a few degrees of freedom such as the simulation of single molecule deposition or protein folding.

In condensed systems there are lots of degrees of freedom (Order of 104 particles) and completely random changes are unlikely to result in a step towards equilibration, leading to very low acceptance rates. This limits the number of degrees of freedom that can be changed in one simulation step to the order of 1. While the embedding of Metropolis MC in other algorithms such as replica exchange, simulated annealing or multiple try Monte Carlo. is efficient in individual cases, this basic restriction to the propagation of the system is a bottleneck to any molecular simulation based on Metropolis Monte Carlo.

There are several advanced approaches to the increase of efficiency of the Monte Carlo sampling methods, including a force biased move construction for the simulation of water, cluster MC algorithms, approaches using generalized ensembles and feedback effects. Similarly, we are testing different modifications to the Metropolis Monte Carlo protocol that changes more than one degree of freedom per Monte Carlo step while preserving detailed balance.

To check the quality of these moves, we use a heated up crystal structure, and try to rearrange the system to the original state.