Collision-induced light scattering spectra of the inert gases and hydrogen at high densities provide evidence of nonadditive three-body interaction effects, for which a quantitative theory is needed. In this work, we derive and evaluate the three-body polarizability Δα(3) for interacting molecules with negligible electronic overlap. Our results, based on nonlocal response theory, account for dipole-induced-dipole (DID) interactions, quadrupolar induction, dispersion, and concerted induction-dispersion effects. The contribution of leading order comes from a DID term that scales as α3d−6 in the molecular polarizability α and a representative distance d between the molecules in a cluster. Quadrupolar induction effects are also large, however, ranging from ∼35% to 104% of the leading DID terms for equilateral triangular configurations of the species studied in this work, at separations approximately 1 a.u. beyond the van der Waals minima in the isotropic pair potentials. For the same configurations, the dispersion terms range from 2% to 7% of the total Δᾱ(3). The dispersion and induction-dispersion contributions are derived analytically in terms of integrals over imaginary frequency, with integrands containing the polarizability α(iω) and the γ hyperpolarizability. For H, He, and H2, the integrals have been evaluated accurately by 64-point Gauss–Legendre quadrature; for heavier species, we have developed approximations in terms of static polarizabilities, static hyperpolarizabilities, and van der Waals interaction energy coefficients (C6 and C9). In the isotropic interaction-induced polarizability Δᾱ, the three-body terms are comparable in magnitude to the two-body terms, due to a cancellation of the first-order, two-body DID contributions to Δᾱ. For the heavier species in this work (Ar, Kr, Xe, N2, CH4, and CO2) in the configurations studied, the three-body contributions to Δᾱ range from −7 to −9% of the two-body terms for equilateral triangular arrays and from 35% to 47% of the two-body terms for linear, centrosymmetric systems.
Compressed gases and liquids containing molecules of Td and D∞h symmetry absorb far-infrared radiation, due to transient dipole moments induced during molecular collisions. In earlier theoretical work on far-infrared absorption by CH4/N2 mixtures, good agreement was obtained between calculated and experimental spectra at low frequencies, but at higher frequencies—from 250 to 650 cm−1—calculated absorption intensities fell significantly below the experimental values. In this work, we focus on an accurate determination of the long-range, collision-induced dipoles of Td⋯D∞h pairs, including two polarization mechanisms not treated in the earlier line shape analysis: dispersion and nonuniformity in the local field gradient acting on the Td molecule. Since these mechanisms produce transitions with ΔJ=±3 or ±4 for CH4 and ΔJ=0 or ±2 for N2, their inclusion is expected to increase the calculated absorption intensities in the high frequency wings for CH4/N2 mixtures. This should improve agreement with the experimental spectra, and permit more accurate determination of anisotropic overlap terms in the collision-induced dipole. We give numerical values for the long-range dipole coefficients of CH4 or CF4 interacting with H2, N2, CO2, or CS2; the dipole coefficients have been derived with spherical-tensor methods and evaluated using single-molecule moments and susceptibilities from recent ab initio calculations or experiments. The dispersion dipoles are given rigorously in terms of integrals involving the imaginary-frequency polarizability α(iω) and the hyperpolarizabilities β(0;iω,−iω) and B(0;iω,−iω). To obtain numerical estimates for the dispersion dipoles, we have developed constant-ratio approximations that require only the static susceptibilities and C6 van der Waals coefficients.
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