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

Area of Science:

• Quantum Chemistry
• Chemical Physics
• Information Theory

Background:

• Information-theoretic descriptors traditionally focus on global and local measures.
• Nonlocal descriptors beyond Shannon entropy are underexplored in chemical reactivity.
• Existing methods primarily use one-electron density, limiting scope.

Purpose of the Study:

• To extend the information-theoretic approach (ITA) by incorporating the two-electron distribution function (pair density).
• To introduce novel ITA descriptors, including joint, conditional, and mutual quantities.
• To analyze the interplay between electron correlation and localization using these new descriptors.

Main Methods:

• Computation and analysis of information-theoretic descriptors (Shannon entropy, Fisher information, Rényi entropy).
• Application to one-electron and pair densities for neutral atoms (Helium to Argon).
• Extension of the information-theoretic approach to include pair density information.

Main Results:

• Successful introduction of new ITA descriptors based on pair density.
• Demonstration of enhanced interpretation of electronic correlations.
• Clearer understanding of the connection between electronic correlations and spatial localization.

Conclusions:

• The pair-density ITA significantly broadens the scope of information-theoretic descriptors in chemical reactivity.
• Novel ITA quantities provide deeper insights into electron correlation and localization phenomena.
• This approach offers a more comprehensive framework for analyzing atomic electronic structure.