Geometrical Eigen-subspace Framework Based Molecular Conformation Representation for Efficient Structure Recognition and Comparison

TL;DR

This paper introduces a spectral decomposition-based eigen-subspace framework for molecular conformation representation, enabling efficient structure recognition and comparison through invariant and intrinsic features derived from atomic eigen-coordinates and eigen-subspace projections.

Contribution

It presents a novel spectral approach utilizing eigen-coordinates and eigen-subspace projections for precise, invariant molecular structure comparison, enhancing efficiency and rationality.

Findings

Eigen-coordinates precisely specify atomic positions in eigen-space.

Refined atomic eigen-subspace projection array acts as a competent invariant.

Intermolecular EPF distance demonstrates high efficiency in structure recognition.

Abstract

We have developed an extended distance matrix approach to study the molecular geometric configuration through spectral decomposition. It is shown that the positions of all atoms in the eigen-space can be specified precisely by their eigen-coordinates, while the refined atomic eigen-subspace projection array adopted in our approach is demonstrated to be a competent invariant in structure comparison. Furthermore, a visual eigen-subspace projection function (EPF) is derived to characterize the surrounding configuration of an atom naturally. A complete set of atomic EPFs constitute an intrinsic representation of molecular conformation, based on which the interatomic EPF distance and intermolecular EPF distance in the eigen-space can be reasonably defined. Exemplified with a few cases, the intermolecular EPF distance shows exceptional rationality and efficiency in structure recognition and comparison.