An enhanced version of the heat exchange algorithm with excellent energy conservation properties

TL;DR

This paper introduces an improved heat exchange algorithm for molecular dynamics simulations that significantly reduces energy drift, ensuring better energy conservation during thermal gradient modeling.

Contribution

The authors identify the cause of energy drift in the original heat exchange algorithm and propose an additional integration step to enhance energy conservation.

Findings

The new algorithm exhibits excellent energy conservation in Lennard-Jones liquid simulations.

The improved method maintains all advantages of the original algorithm.

Energy drift is caused by operator splitting truncation errors.

Abstract

We propose a new algorithm for non-equilibrium molecular dynamics simulations of thermal gradients. The algorithm is an extension of the heat exchange algorithm developed by Hafskjold and co-workers [Mol. Phys. 80, 1389 (1993); Mol. Phys. 81, 251 (1994)], in which a certain amount of heat is added to one region and removed from another by rescaling velocities appropriately. Since the amount of added and removed heat is the same and the dynamics between velocity rescaling steps is Hamiltonian, the heat exchange algorithm is expected to conserve the energy. However, it has been reported previously that the original version of the heat exchange algorithm exhibits a pronounced drift in the total energy, the exact cause of which remained hitherto unclear. Here, we show that the energy drift is due to the truncation error arising from the operator splitting and suggest an additional coordinate integration step as a remedy. The new algorithm retains all the advantages of the original one whilst exhibiting excellent energy conservation as illustrated for a Lennard-Jones liquid and SPC/E water.