On the Estimation of Centre of Mass in Periodic Systems

TL;DR

This paper introduces a computationally efficient method for accurately estimating the centre of mass in periodic systems, improving upon previous approaches that involved non-physical averaging.

Contribution

It proposes a new, efficient approach to compute the intrinsic mean for centre of mass estimation in periodic systems, addressing previous computational complexity issues.

Findings

The new method provides more accurate centre of mass estimates.

It reduces computational complexity compared to analytical solutions.

Applicable to most chemical systems with periodic boundaries.

Abstract

Calculation of the centre of mass of a group of particles in a periodically-repeating cell is an important aspect of chemical and physical simulation. One popular approach calculates the centre of mass via the projection of the individual particles' coordinates onto a circle [Bai \& Breen, \emph{J. Graph. Tools}, \textbf{13}(4), 53, (2008)]. However, this approach involves averaging of the particles in a non-physically meaningful way resulting in inaccurate centres of mass. Instead the intrinsic weighted average should be computed, but the analytical calculation of this is computationally expensive and complex. Here, we propose a more computationally efficient approach to compute the intrinsic mean that is suitable for the majority of chemical systems.