The Hellmann-Feynman theorem: a perspective.

The Hellmann-Feynman theorem has, with a few exceptions, not been exploited to the degree that it merits. This is due, at least in part, to a widespread failure to recognize that its greatest value may be conceptual rather than numerical, i.e., in achieving insight into molecular properties and behavior. In this brief overview, we shall discuss three examples of significant concepts that have come out of the Hellmann-Feynman theorem: (1) The forces exerted upon the nuclei in molecules are entirely Coulombic in nature. (2) The total energies of atoms and molecules can be expressed rigorously in terms of just the electrostatic potentials at their nuclei that are produced by the electrons and other nuclei. (3) Dispersion forces are due to the attractions of nuclei to their own polarized electronic densities. To summarize, energy and force analyses should not be viewed as competitive but rather as complementary.