Conformal Coordinates for Molecular Geometry: From 3D to 5D

This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within ${ℝ}^5$ with an inner product different from the usual one. This model enables efficient computation of interatomic distances using what we call the Conformal Coordinate Matrix (C-matrix). The C-matrix not only simplifies the mathematical framework but also reduces the number of operations required for distance calculations compared to traditional methods.