Force analysis by molecular orbitals — partition of the Hellmann–Feynman force into one-electron orbital contributions

Abstract

The Hellmann–Feynman force acting on a nucleus is partitioned into forces from molecular orbitals (MO forces) and forces from the other nuclei. The MO forces are analyzed for second-row diatomics by employing the relative coordinate. It is found that the forces exerted by inner valence orbitals, which are constituted of mainly 2s basis functions, are predominant. The origin of the MO forces on the relative coordinate as well as on each nucleus is analyzed in terms of basis function components. The components due to the overlap of nucleus-centered basis functions can be correlated to bonding in the conventional sense, although the values of the total MO forces do not necessarily correlate like that. It is also shown that core orbitals make significant contributions to the forces by causing distortion of charge distribution near the nuclei. Using the concept of the MO force, we show interpretations of vibrational structures in photoelectron spectra and geometrical changes in ionization processes.