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

TL;DR

This paper presents a conformal coordinate model extending 3D molecular geometry into 5D space, enabling more efficient interatomic distance computations with a new C-matrix approach.

Contribution

It introduces a novel conformal coordinate system and C-matrix for molecular geometry, improving computational efficiency over traditional methods.

Findings

C-matrix simplifies distance calculations

Reduces computational operations

Extends 3D to 5D conformal representation

Abstract

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.