Use of non-additive Fisher information in probing chemical bonds

Abstract

The contra-gradience (CG) criterion, related to the non-additive Fisher information and kinetic-energy of electrons in the resolution determined by the basis-functions χ = { χ i} of standard SCF LCAO MO calculations of molecular electronic structure, e.g., Atomic Orbitals (AO), is used to locate the bonding regions in physical space, and to generate the associated quantitative information-theoretic (IT) descriptors of these chemical bond basins in molecules. The key quantity is the interference, non-additive contribution to the molecular Fisher information density, f nadd.[ χ ; r ] = f total[ χ ; r ] − f add.[ χ ; r ], where f total[ χ ; r ] is the molecular (overall) distribution and f add.[ χ ; r ] denotes its AO-additive part. This scalar field is used to determine the bonding volumes in molecules, identified as the largest (closed) basins of f nadd.[ χ ; r ] < 0, i.e., f total[ χ ; r ] < f add.[ χ ; r ], enclosed by the zero CG surface f nadd.[ χ ; r ] = 0. This CG criterion thus identifies regions of the physical space exhibiting a diminished overall Fisher information content, compared to the reference AO-additive level. These bonding volumes represent a locally-decreased gradient content of the system wave-function, thus reflecting less “order” (more “uncertainty”) in the molecular distribution of electrons, marking their relative delocalization via the system chemical bonds. The graphical representations of both the closed bonding and core areas of a diminished CG density are presented for illustrative molecules together with the associated numerical IT descriptors measuring the integrals of f nadd.[ χ ; r ] over the volumes in question. These examples convincingly validate the applicability of the CG probe in exploring the bonding patterns in molecules from the novel, Fisher information/kinetic-energy perspective.