Identity for Kullback-Leibler divergence in density functional reactivity theory

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Theoretical Chemistry

Background:

• Density functional reactivity theory (DFRT) utilizes electron density functionals to understand chemical reactivity.
• The Kullback-Leibler divergence, also known as information gain or relative Shannon entropy, is a key DFRT component with emerging applications.
• Previous uses include rationalizing atomic partitioning and quantifying molecular electrophilicity/nucleophilicity.

Purpose of the Study:

• To investigate the local behavior of the Kullback-Leibler divergence.
• To introduce and validate a novel mathematical identity for the Kullback-Leibler divergence.
• To explore the implications of this identity for advancing the DFRT framework.

Main Methods:

• Examination of the local behavior of the Kullback-Leibler divergence.
• Derivation of a new mathematical identity involving the Kullback-Leibler divergence.
• Numerical verification of the derived identity using neutral atoms (He to Kr) with varying reference densities.

Main Results:

• A novel identity for the Kullback-Leibler divergence has been established.
• The identity's validity is confirmed through numerical calculations on atomic systems.
• Analytical properties and local behaviors of three newly introduced functions are discussed.

Conclusions:

• The novel identity and associated functions offer new perspectives for DFRT.
• This work enhances understanding of the local behavior of molecular properties within DFRT.
• The findings contribute to the ongoing development and application of DFRT in chemistry.