Spatial localization of electron pairs in molecules using the Fisher information density

Highlights: • The phase-space-defined Fisher information density is derived and studied. • This function reveals the regions of maximal concentration of electron pairs. • The features of this function are linked with the local electron momentum uncertainty. - Abstract: Starting from the quasi-probability distribution function by electron positions r and momenta p and applying the minimum information principle subject to the certain physically-grounded constrains, we obtained the approximate expression for phase-space-defined Fisher information density (PS-FID). It provides information about an electron momentum in the position representation and reveals the electronic shell structure for atoms with Z ⩽ 20 as well as the regions of maximal concentration of bonding and lone electron pairs in molecules. Also, this function enables to recognize the different types of chemical bonds as polar and non-polar covalent bonds, the charge-shift bond as well as the weak non-covalent molecular interactions. We found that the PS-FID behavior results from the local electron momentum uncertainty that is linked with both information about electron real-space position (which, in turn, is related with electronic steric factor) and the Pauli principle