Topology of density difference and force analysis

Abstract

The density difference Δρ(r) of a molecule A-B is defined as the difference of the density ρ(r) of the molecule A-B and the density ρ_A(r) + ρ_B(r) put at the position of the atoms A and B. We investigate here the topological features of the density difference and define electron density flow (EDF) as representing the direction and the amount of the electron density flow in the course of the nuclear displacement processes. As such examples, we study H₂ molecule formation reaction and the interaction of two He atoms. By the topological analysis of Δρ(r), and by using the Hellmann-Feynman force and its partition into the AD, EC, and EGC forces, the characteristic behaviors of the Δρ(r) map are clarified. In particular, the electron cloud preceding and incomplete following are represented by using the concept of the EDF. The natures of the covalent bond are clarified based on the topological properties of the difference density Δρ(r) rather than that of the total density ρ(r).