Density (de)localization and statistical correlation in the Van der Waals interactions and the chemical bond between two hydrogens

Abstract

Localization and statistical correlation of the molecule H2 and the Van der Waals system H(1s)−H(1s) are studied as a function of its internuclear distance by the use of Shannon entropies, mutual information, and density distribution variance and covariance. Comparative analysis of the behavior of the different localization measures are made, as well as the comparison between the statistical correlation ones. A comparative analysis between the two systems is performed, where the Kullback–Leibler statistical distance between the two probability densities is computed and discussed. We show that there is a region where the valence bond and the VdW densities are closer. Hence, statistical analysis is able to detect regions with notable similarities between the Heitler and London density, based on valence bond wave function and the VdW density, based on the correspondent wave function. This leads to the concern if VdW interactions could be detected using valence bond wave functions by analyzing its correlation and localization properties.