Canonical Force Distributions in Pairwise Interatomic Interactions from the Perspective of the Hellmann-Feynman Theorem.

Force-based canonical approaches have recently given a unified but different viewpoint on the nature of bonding in pairwise interatomic interactions. Differing molecular categories (covalent, ionic, van der Waals, hydrogen, and halogen bonding) of representative interatomic interactions with binding energies ranging from 1.01 to 1072.03 kJ/mol have been modeled canonically giving a rigorous semiempirical verification to high accuracy. However, the fundamental physical basis expected to provide the inherent characteristics of these canonical transformations has not yet been elucidated. Subsequently, it was shown through direct numerical differentiation of these potentials that their associated force curves have canonical shapes. However, this approach to analyzing force results in inherent loss of accuracy coming from numerical differentiation of the potentials. We now show that this serious obstruction can be avoided by directly demonstrating the canonical nature of force distributions from the perspective of the Hellmann-Feynman theorem. This requires only differentiation of explicitly known Coulombic potentials, and we discuss how this approach to canonical forces can be used to further explain the nature of chemical bonding in pairwise interatomic interactions. All parameter values used in the canonical transformation are determined through explicit physical based algorithms, and it does not require direct consideration of electron correlation effects.