Pauli energy and information-theoretic approach for evaluating dynamic and nondynamic electron correlation

Abstract

Even though the quantification of different correlation regimes among electrons is controversial and a robust and generally applicable approach in this context is still lacking, accurately accounting for the electron correlation is a must. As the prominent and most well-known terms used to classify correlation effects, dynamic and nondynamic electron correlation is of concern herein. In this work, we consider a different tack to qualitative and quantitative description of the dynamic and nondynamic correlations, where Pauli energy and information-theoretic approach are considered for the purpose. To do so, several versions of the Pauli energy based on approximate kinetic energy density (KED) functionals and information-theoretic (IT) quantities like Fisher information, Shannon entropy, Onicescu information energy, and Ghosh–Berkowitz–Parr entropy with the two representations of electron density and shape function have been utilized. It is shown that although some KEDs may not reproduce the accurate Pauli energy results, their prediction for dynamic and nondynamic electron correlation can be desirable. There are also KEDs providing much better Pauli energy results than others, while their shortcomings can still be unveiled when they are used to describe electron correlation regimes. On the other hand, to more balanced treatment of electron correlation effects we propose to use the IT quantities with significantly different views from the perspectives of electron density distribution, scaling properties, and physiochemical meanings in the framework of Pauli energy. The efficiency and usefulness of the developed models have been demonstrated for both the dynamic and nondynamic electron correlation in molecular systems.