Use of non-additive information measures in exploring molecular electronic structure: stockholder bonded atoms and role of kinetic energy in the chemical bond

Abstract

The entropic principles of information theory are used for defining molecular fragments. The additive and non-additive components of the entropy-deficiency and Fisher-information functionals are introduced. The implications of the adopted constraints for predicted in situ charge sensitivities of molecular fragments in donor–acceptor systems are examined and the exhaustive, local partitioning of the molecular electron/probability density into atomic pieces is discussed as an illustration. The alternative information principles using the free-atom references, which define the atomic “promolecule”, formulated in terms of the local electron density/probability of bonded atoms and their share/enhancement factors, are shown to give rise the stockholder partitioning of Hirshfeld. It is alternatively characterized by the common (subsystem independent), molecular local enhancements for each bonded atom or by the equality of the molecular and promolecular share factors. This unbiased division is shown to exactly remove the non-additive component of the missing-information of electron probabilities; in the conditional probability representation the entropy-deficiency of stockholder atoms is shown to generate the exactly vanishing additive component. The additivity of information contributions in the hypothetical (non-interacting) Kohn-Sham (KS) system in the resolution defined by the KS molecular orbitals (MO) is stressed and their non-additivity in the atomic-orbital (AO) resolution is emphasized. The non-additive Fisher information of the real (interacting) molecular system in both the MO and AO resolutions is then examined: the former is linked to the electron localization function (ELF) while the latter defines the so called contra-gradience(CG) criterion for localizing chemical bonds in the molecule. The bonding basins of the negative CG density in the valence-shell identify regions of an increased electron delocalization due to formation of the chemical bond. Representative plots of these local probes of the molecular electron distributions are presented and discussed.