Topology of density difference and force analysis .1. Homopolar bond formation

The density difference Delta rho(r) of a molecule A-B is defined as the difference of the density rho(r) of the molecule A-B and the density rho(A)(r) + rho(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 H-2 molecule formation reaction and the interaction of two He atoms. By the topological analysis of Delta rho(r), and by using the Hellmann-Feynman force and its partition into the AD, EC, and EGC forces, the characteristic behaviors of the Delta rho(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 Delta rho(r) rather than that of the total density rho(r).