The conceptual power of the Hellmann-Feynman theorem

The power of the Hellmann-Feynman theorem is primarily conceptual. It provides insight and understanding of molecular properties and behavior. In this overview, we discuss several examples of concepts coming out of the theorem. (1) It shows that the forces exerted upon the nuclei in a molecule, which hold the molecule together, are purely Coulombic in nature. (2) It indicates whether the role of the electronic charge in different portions of a molecule's space is bond-strengthening or bond-weakening. (3) It demonstrates the importance of the electrostatic potentials at the nuclei of a molecule, and that the total energies of atoms and molecules can be expressed rigorously in terms of just these potentials, with no explicit reference to electron-electron interactions. (4) It shows that dispersion forces arise from the interactions of nuclei with their own polarized electronic densities. Our discussion focuses particularly upon the contributions of Richard Bader in these areas.