All-atom computations with irreversible Markov chains

TL;DR

This paper introduces an all-atom ECMC method for simulating multi-particle Coulomb interactions efficiently, achieving O(N log N) complexity without spatial cutoffs or time-step errors, suitable for soft matter and biological systems.

Contribution

It extends ECMC to all-atom Coulomb models with new factorization and lifting schemes, enabling efficient, accurate simulations of complex charged systems.

Findings

Achieves O(N log N) complexity for charge-neutral systems

Demonstrates equivalence of line-charge and standard Coulomb models

Provides efficient simulation of water and Coulomb gases

Abstract

The event-chain Monte Carlo (ECMC) method is an irreversible Markov process based on the factorized Metropolis filter and the concept of lifted Markov chains. Here, ECMC is applied to all-atom models of multi-particle interactions that include the long-ranged Coulomb potential. We discuss a line-charge model for the Coulomb potential and demonstrate its equivalence with the standard Coulomb model with tin-foil boundary conditions. Efficient factorization schemes for the potentials used in all-atom water models are presented, before we discuss the best choice for lifting schemes for factors of more than three particles. The factorization and lifting schemes are then applied to simulations of point-charge and charged-dipole Coulomb gases, as well as to small systems of liquid water. For a locally charge-neutral system in three dimensions, the algorithmic complexity is O(N log N) in the number N of particles. In ECMC, a Particle-Particle method, it is achieved without the interpolating mesh required for the efficient implementation of other modern Coulomb algorithms. An event-driven, cell-veto-based implementation samples the equilibrium Boltzmann distribution using neither time-step approximations nor spatial cutoffs on the range of the interaction potentials. We discuss prospects and challenges for ECMC in soft condensed-matter and biological physics.