Electronic charge density distortions due to dispersion: physically meaningful DMA multipoles for H2, HeH, and He⋯He

Abstract

Feynman attributed long-range dispersion forces to the attraction of each nucleus to the local dipolar distortion of the electronic charge distribution. Here we take a step toward the first demonstration of Feynman's statement with full configuration-interaction wave functions. We have used Stone's distributed multipole analysis (DMA) to obtain the local multipoles in H₂ in the b³Σ⁺_u and X¹Σ⁺_g states and the local dipoles in HeH and He⋯He in their ground states. Except for the H₂ singlet, these states have repulsive potentials with shallow wells due to van der Waals dispersion. For H₂, the DMA dispersion dipole on each nucleus, computed ab initio with the d-aug-cc-pV6Z basis, shows excellent agreement with the sum of the R⁻⁷ and R⁻⁹ terms predicted by perturbation theory. The DMA dipoles of HeH and He⋯He also agree quite well with the prediction of perturbation theory. The signs and the R-dependence of the DMA dispersion dipoles are fully consistent with Feynman's statement. For H₂, we also find strong agreement between the results of perturbation theory and the dispersion terms in the DMA quadrupoles, DMA octopoles, DMA hexadecapoles, the total quadrupoles, and the total hexadecapoles. The dynamic correlation effects on the multipoles have physical meaning when computed with sufficiently large basis sets.