Triple dipole terms

The effect of the Axilrod-Teller term (also known as the triple-dipole correction) is to make the interaction energy more negative when three molecules are linear but to weaken it when the molecules form an equilateral triangle. This is because the linear arrangement enhances the correlations of the motions of the electrons, whereas the equilateral arrangement reduces it. 

Ternary spectral moments of collision-induced absorption in hydrogen gas are analyzed in the H2 fundamental band in terms of pairwise additive and irreducible contributions to the interaction-induced dipole moment, Eqs. (1 - 7) [51]. Numerical results show that irreducible dipole components, especially of the exchange quadrupole-induced ternary dipole component, are significant for agreement with spectroscopic measurements, such as ternary spectral moments (Fig. 1) [53], an observed diffuse triple transition 3<3i centered at 12,466 cm-1 [52, 54, 55], and the intercollisional dip in compressed hydrogen gas, pp. 188 -190. 

If the structure is decided by an effective potential ues (r), it was demonstrated in the mean spherical approximation (MSA) that the direct correlation function c(r) should rapidly approach — pMerr (r) for large r (see Section IE). According to Reatto and Tau [131], this relationship, which is asymptotically exact for large distance and low density, holds quite well when the long-range dispersion term of the AS potential, - Cg / r6, and the AT triple-dipole potential, < m3 (r) > (8n/3)vp/r6, are considered, so that the direct correlation function reads... 

If the potential is anharmonic, the higher terms of the potential energy according to Eq. 2.1-16 are not negligible, the mechanical anharmonicity gives rise to overtones, vibrations with the double, triple, or multiple frequency of the fundamentals. Overtones are also produced by the higher terms of the dipole moment according to Eq. 2.3-1, the electrical anharmonicity. Since both equations may contain mixed terms, combinations of two or more normal vibrations, i.e., sums or differences, are produced. These appear in the spectra, but usually only with small intensity. Also Raman spectra show overtones and combinations due to mechanical and electrical anharmonicities (see below). 

In the third order of long-range perturbation theory for a system of three atoms A, B and C, the leading nonadditive dispersion term is the Axilrod-Teller-Mutd triple-dipole interaction [58. 59]... 

These results suggest that three-body terms that are repulsive at the equilibrium geometry must be included to bring the calculated rotational constants in line with experiment. Hutson and coworkers have investigated the effect of several three-body terms on reducing the discrepancies with experiment. Specifically, the inclusion of terms accounting for (i) the anisotropic Axilrod-Teller triple dipole (DDD) interaction, and (ii) the... 

From a detailed examination of the three-body SAPT energies for the argon liquid, Bukowski et al. (Bukowski and Szalewicz 2001) have concluded that the bulk of the three-body dispersion energy can be estimated using the AxUrod-Teller-Muto triple dipole term. For isotropic local distributed polarizabihties this takes the form (Stone 1996)... 

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