On the estimation of center of mass in periodic systems

Calculation of the center of mass of a group of particles in a periodically repeating cell is an important aspect of chemical and physical simulations. One popular approach calculates the center of mass via the projection of the individual particles' coordinates onto a circle [Bai and Breen, J. Graph. Tools, 13(4), 53 (2008)]. However, this approach involves averaging the particles in a non-physically meaningful way, resulting in inaccurate centers 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.