Internal stresses in molecules II. a local view of chemical binding in the H molecule

Abstract

Earlier work on internal stresses in one-electron systems is now extended to many-electron systems. The expressions for local stresses and local force densities involve electrostatic fields arising from given electronic and nuclear charge distributions and, therefore, the stress at any point in 3-D space again assumes a maxwellian form. As an illustration of the stress formalism, the interaction between two many-electron systems has been considered, taking the formation of the hydrogen molecule from its constituent atoms as a simple example. Using the double-zeta gaussian wavefunctions of Snyder and Basch, the stresses and fields experienced by an observer at three points on the internuclear axis are evaluated as functions of the internuclear distance R, and their respective variations are rationalized by means of classical arguments. The most interesting observation is that, depending on the location of the point considered, the interaction stress or the total stress or both may either vanish or pass through an extremum at an R value close to R. The consequences of a charge build-up in the binding region are clearly apparent. The picture of chemical binding in the H molecule that emerges from these calculations is a local one in which binding occurs due to variations of electrostatic pressure from point to point in such a manner as to cause the vanishing of either the total electrostatic force density or the difference force density or both at certain points on the internuclear axis; this complements the existing viewpoints on binding in the molecule. It may not be too early to say that the stress formalism which includes the Hellmann-Feynman force viewpoint as a special case has the potential to develop into a powerful interpretive tool for understanding molecular phenomena.