Topological analysis of information-theoretic quantities in density functional theory

We have witnessed considerable research interest in the recent literature about the development and applications of quantities from the information-theoretic approach (ITA) in density functional theory. These ITA quantities are explicit density functionals, whose local distributions in real space are continuous and well-behaved. In this work, we further develop ITA by systematically analyzing the topological behavior of its four representative quantities, Shannon entropy, two forms of Fisher information, and relative Shannon entropy (also called information gain or Kullback-Leibler divergence). Our results from their topological analyses for 103 molecular systems provide new insights into bonding interactions and physiochemical properties, such as electrophilicity, nucleophilicity, acidity, and aromaticity. We also compare our results with those from the electron density, electron localization function, localized orbital locator, and Laplacian functions. Our results offer a new methodological approach and practical tool for applications that are especially promising for elucidating chemical bonding and reactivity propensity.

Automated summary

Considerable research interest has been observed in recent literature regarding the development and applications of information-theoretic approach (ITA) quantities in density functional theory. These ITA quantities are explicit density functionals with continuous and well-behaved local distributions in real space. By systematically analyzing the topological behavior of four representative ITA quantities, namely Shannon entropy, two forms of Fisher information, and relative Shannon entropy, our work further develops ITA. The topological analyses for 103 molecular systems provide new insights into bonding interactions and physiochemical properties, such as electrophilicity, nucleophilicity, acidity, and aromaticity. Comparisons with results from other functions demonstrate the potential of our results as a methodological approach and practical tool for elucidating chemical bonding and reactivity propensity.