The long-range non-additive three-body dispersion interactions for the rare gases, alkali, and alkaline-earth atoms

Abstract

The long-range non-additive three-body dispersion interaction coefficients Z(111), Z(112), Z(113), and Z(122) are computed for many atomic combinations using standard expressions. The atoms considered include hydrogen, the rare gases, the alkali atoms (up to Rb), and the alkaline-earth atoms (up to Sr). The term Z(111) arising from three mutual dipole interactions is known as the Axilrod-Teller-Muto coefficient or the DDD (dipole-dipole-dipole) coefficient. Similarly, the terms Z(112), Z(113), and Z(122) arise from the mutual combinations of dipole (1), quadrupole (2), and octupole (3) interactions between atoms and they are sometimes known, respectively, as dipole-dipole-quadrupole, dipole-dipole-octupole, and dipole-quadrupole-quadrupole coefficients. Results for the four Z coefficients are given for the homonuclear trimers, for the trimers involving two like-rare-gas atoms, and for the trimers with all combinations of the H, He, and Li atoms. An exhaustive compilation of all coefficients between all possible atomic combinations is presented as supplementary data.

Density-functional approach to the three-body dispersion interaction based on the exchange dipole moment

“…18 They contain less approximations and are considered highly accurate. Very recent accurate benchmark results were also reported 19 (Tang'12) based on explicit evaluation of oscillator strength sum rules and are in very good agreement with KT's work. The data from that benchmark pertaining to this study are listed in column 7 of Table III.…”

“…The sum of the former for these 7 trimers is 0.001 20 kcal/mol and the sum of the latter is 0.001 25 kcal/ mol, with a mean absolute deviation (MAD) on these trimers of 0.000 05 kcal/mol. The accuracy of our non-damped threebody dispersion interaction was verified above in comparison with highly accurate benchmarks 18,19 (see Table III). The observed good agreement with respect to this energy component shows in turn that the energy difference E(CCSD(T)) − E(MP 2) is indeed mostly due to the three-body dispersion here.…”

“…The damping along each of the three interatomic distances is now inter-related via the three-body effective mean radiusR v dW, ABC , introduced here by Eqs. (18) and (19).…”

Three-Body Dispersion Potentials Involving Electric Octupole Coupling

“…Recent efforts have been spurred on by advances in ultracold spectroscopy and dynamics, especially three-atom and atom-molecule collisional processes involving alkali and alkaline Earth elements [6]. In a similar vein, interaction potentials among three Group 8 elements have been studied [7]. In this last work, the electric dipole approximation was relaxed and dispersion energies in which the perturbation operator included electric quadrupole and octupole coupling were computed.…”

“…The potentials obtained hold for all separation distances outside the region of wave function overlap and extending out to infinity, for oriented and isotropic systems. Approximating the speed of light to be infinite resulted in the reproduction of the potentials computed using static multipolar couplings, applicable in the near-zone [6,7]. Retardation corrected forms, applicable at very long-range, were obtained on taking the far-zone asymptote, in which virtual photons with low frequency contribute most significantly in mediating the interaction.…”