A New Perspective on the Homogeneous Coordinate System for Calculating Interatomic Distances and Their Derivatives in Terms of Internal Coordinates

In many chemical physics calculations, efficient computation of interatomic distances and their derivatives using internal coordinates is essential for understanding molecular structure and dynamics. This paper explores the homogeneous coordinate system as an alternative framework to simplify these calculations. It is proven that computing interatomic distances using the Euclidean model of 3D space requires almost 60% more operations than the homogeneous model, which may represent a significant difference in molecular dynamics simulations.