Extending the information-theoretic approach from the (one) electron density to the pair density

Abstract

Within the framework of chemical reactivity theory, information-theoretic descriptors have predominantly focused on global and local measures, while nonlocal descriptors beyond Shannon entropy remain largely unexplored. By extending the information carrier from the one-electron density to the two-electron distribution function (pair density), this work introduces information-theoretic descriptors rooted in both one-electron and pair densities. This broadens the scope of the information-theoretic approach (ITA) and introduces new types of ITA descriptors, notably the joint, conditional, and mutual ITA quantities. To elucidate the interaction between electron correlation and localization, we compute and analyze a suite of ITA descriptors for one-electron and pair electrons, including the Shannon entropy, Fisher information, and Rényi entropy, for neutral atoms ranging from helium (He) to argon (Ar). The results demonstrate how the pair-density ITA enhances the interpretation of electronic correlations and its connection to spatial localization.