Properties of Atoms in Molecules:  Atoms Forming Molecules

This paper studies the evolution of the electron densities of two separated atoms into an equilibrium molecular distribution. A range of interactions is considered: from closed-shell with and without charge transfer, through polar-shared, to equally shared interactions. The changes in the density are monitored in terms of the properties of the density at the bond critical point and the shape of the interatomic surface. The effect of these changes on the properties of the atoms defined as proper open systems is determined. The “harpoon mechanism” operative in the formation of LiF is found to exert dramatic effects on the electron density and on the atomic and molecular properties. The virial and the Ehrenfest force theorems in their molecular, atomic, and local forms, together with the Hellmann−Feynman theorem, provide an understanding of the similarities and differences in the bonding resulting from closed-shell, shared, and polar interactions. The effect of the long-range dispersion forces on the electron density and the resulting changes in the kinetic and potential energies, the former decreasing and the latter increasing on the initial approach of the atoms, are investigated. In addition to the changes in the total energy and its kinetic and potential energy components as a function of the internuclear separation R, the atomic contributions to these quantities are also reported. The atomic Ehrenfest force is the force acting on the electron density in an atomic basin and the one measured in an atomic force microscope. It is shown to change from an intially attractive interaction, to a repulsive one at a separation slightly greater than R e where the Hellmann−Feynman forces on the nuclei vanish.