Valence shell structures in the distributions of the Laplacian of the electron density and the one-electron potential for diatomic molecules

Abstract

The valence shell charge concentration, VSCC, in an atom is defined by Bader as the outermost spherical region for which ∇2ρ(r)<0. We compare and contrast an alternate definition of the VSCC as the outermost spherical region for which ∇2ρ(r)/2ρ(r)<0. The quantity ∇2ρ(r)/2ρ(r), termed the one-electron potential (OEP), is implicit in the (exact) one-electron Schrödinger equation. In a homonuclear diatomic bound by shared interaction, the VSCCs of the atoms are merged. Provided that the merged VSCCs persist, the diatomic is enclosed by an outermost zero-valued surface encompassing the VSCC of the molecule. The outermost ∇2ρ(r)=0 surface is termed the reactive surface while the outermost OEP=0 surface is termed the molecular envelope. In cases where the VSCCs are not revealed in the atoms, the reactive surfaces and molecular envelopes are incomplete or absent in the diatomics. We show that in many diatomics the molecular envelope is present although the reactive surface is missing. In an ionic diatomic bound by closed-shell interaction, the VSCC of the cation can disappear. Otherwise, fragments of the cationic VSCC, termed ligand-opposed charge-concentration (LOCC), may remain opposite to the anion. In general, the LOCC is absent when the VSCC is not revealed in the atom. We show that the LOCC is more widespread in the distribution of OEP than ∇2ρ(r).