A Density-Based Continuous Local Symmetry Measure

TL;DR

This paper introduces a new framework for evaluating local molecular symmetry using electron density localization, enhancing understanding of structure-property relationships in chemistry.

Contribution

The study presents a novel continuous local symmetry measure based on electron density, addressing gaps in fuzzy symmetry quantification and local symmetry analysis.

Findings

Quantitative global and local symmetry representations for molecules.

Reveals distinctive features of local symmetry and chirality.

Provides insights into structure-property relationships.

Abstract

Although continuous symmetry theory has attracted increasing attention in modern chemistry, local symmetry remains under-investigated. As a consequence, the relationship between symmetry and chemical behavior is often obscured, limiting the practical use of fuzzy symmetry measures. In this study, we introduce a novel framework for evaluating local symmetry based on electron density localization, and present continuous symmetry representations for several representative molecules. Our approach not only quantitatively captures global symmetry, but also reveals distinctive features of symmetry in a local chemical environment. The related concept, local chirality or chirotopicity, is also discussed. Overall, the proposed local symmetry and chirality measures provide valuable insights into molecular structure and structure-property relationships.