# 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.

## Key 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.

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Source: https://tomesphere.com/paper/1701.07917