Long-range, collision-induced dipoles of Td–D∞h molecule pairs: Theory and numerical results for CH4 or CF4 interacting with H2, N2, CO2, or CS2

Abstract

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.