Use of non-additive Fisher information in probing chemical bonds

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 chi={chi(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.)[chi; r] = f(total) [chi; r] - f(add.)[chi; r], where f(total)[chi; r] is the molecular (overall) distribution and f(add.)[chi; 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.)[chi; r] <0. i.e., f(total)[chi; r]