Combination Rules for van der Waals Force Constants

Abstract

A family of combination rules, from which van der Waals coefficients for interactions between unlike molecules may be estimated in terms of those for the corresponding like interactions and the static polariabilities, is tested empirically and related to an approximate parameterization of the frequency-dependent polarizability function. The treatment includes two- and three-body dipole force constants and the higher-multipole terms of the second-order two-body dispersion energy. The rules give agreement within a few percent (about the same accuracy as the input data) when compared with accurate unlike coefficients for systems involving H, He, Ne, Ar, Kr, Xe, Li, Na, K, Rb, Cs, Hg, H2, N2, CH4, He(21S), He(23S), He+, Li+, Na+, K+, Rb+, Cs+. Knowledge of n like coefficients and polarizabilities permits calculation of n(n − 1) / 2 unlike two-body and n(n − 1)(n + 4) / 6 unlike three-body force constants.

Parallel temperatures in supersonic beams: Ultracooling of light atoms seeded in a heavier carrier gas

“…• In the case of molecular hydrogen H 2 seeded in argon, using to calculate the Ar-H 2 C 6 coefficient the combination rule and the data of Kramer and Herschbach [20], we get ρ s = 2.48 from which we predict a temperature ratio T 2,∞ /T 1,∞ = 0.16, a quite large effect!…”

“…Let us compare this result with our theory. Using the combination rule of Kramer and Herschbach [20] and data for oxygen from reference [27], we calculate the oxygen-argon C 6 coefficient C 6 (O − Ar) = 34 atomic units and ρ s = 1.06. Our theory then predicts a temperature ratio T 2,∞ /T 1,∞ = 0.76, substantially larger than the experimental value near 0.5.…”

Molecular Beam Chemistry: Reactions of Oxygen Atoms with Halogen Molecules.

“…28 This model will be described fully elsewhere. 16 29 The effective number of electrons were taken to be 6 for the 0 atom, 14 for halogen molecules, 7 for halogen atoms, and 13 for halogen monoxide diatomic molecules. The polarizability values were chosen to be consistent with literature values and atomic additivity.…”

Luminescence spectra of nitrogen in solid argon. II. Theory

“…Using the results of Table 5, Lastly, in the above, the Slater-Kirkwood approximation was used to find &/F in conjunction with the assumption that N g (13) is constant for a C + C transition. However, it has been shown by Kranier and Herschbach [14] that this approximation has a standard deviation of about 15% when used to cal-culate the C6 term for unlike interactions. This deviation in fact reflects the validity of this approximation.…”