What question did this study set out to answer?

The research aims to develop a conformal model for representing molecular geometry to enhance distance calculations.

February 5, 2026Journal of Computational Chemistry1 citationsOpen Access

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

JCJesus CamargoUniversidade Estadual do Oeste do Paraná CLCarlile LavorUniversidade Estadual de Campinas (UNICAMP)MSMichael Ferreira de SouzaBrazilian Institute of Geography and Statistics

Puntos clave

The research aims to develop a conformal model for representing molecular geometry to enhance distance calculations.
Introduces conformal model based on homogeneous coordinates.
Develops Conformal Coordinate Matrix (C-matrix) for computations.
Compares the efficiency of C-matrix with traditional distance calculation methods.
C-matrix simplifies the mathematical framework for molecular geometry.
Reduces operations needed for interatomic distance calculations compared to conventional methods.

Resumen

ABSTRACT This paper introduces the conformal model (an extension of the homogeneous coordinate system) for molecular geometry, where 3D space is represented within 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.

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