Molecular Flow Monte Carlo

Abstract

In this paper, we suggest a novel sampling method for Monte Carlo molecular simulations. In order to perform efficient sampling of molecular systems, it is advantageous to avoid extremely high energy configurations while also retaining the ability to quickly generate new and independent trial states. Thus, we introduce a continuous normalizing flow method which can quickly generate independent states for various proposal distributions using a first-order differential equation. We define this continuous normalizing molecular flow approach based on two-body intermolecular interactions to achieve a probability distribution transformation method which yields distributions which have probability densities of zero when molecule pairs are in close proximity; while in all other cases, the probability density is compressed such that it is spatial uniform. This transform provides the proposal distribution which generates no states of extremely high energy. We find that an inverse square flow is applicable as the continuous normalizing molecular flow. Using the transformed distribution, we can perform the Metropolis-Hastings method more efficiently. The high efficiency of the proposed method is demonstrated using simple molecular systems.