Absorption spectra of ${\mathrm{H}}_2$-${\mathrm{H}}_2$ pairs in the fundamental band

For the computation of the induced-dipole moment, the collisional complex consisting of two ${\mathrm{H}}_2$ molecules is treated like one molecule in the self-consistent-field and size-consistent, coupled electron pair approximations that separates correctly at distant range. The basis set accounts for 95% of the correlation energies. The radial transition matrix elements of the induced-dipole components are obtained for the two cases $v_1$=$v_2$=0 and $v_1$=0,$v_2$=1, where the $v_i$ are the vibrational quantum numbers of the interacting ${\mathrm{H}}_2$ molecules (i=1 or 2). The dependence of these elements on the most important rotational states (${\mathit{j}}_1$, ${\mathit{j}}_1$’,${\mathit{j}}_2$,${\mathit{j}}_2$ ’=0,...,3) involved is obtained and seen to be significant in the fundamental band. The results are recast in a simple, but accurate analytical form that is used in a quantum formalism for computations of the spectral moments (sum rules) and line shapes of the collision-induced absorption spectra of molecular hydrogen pairs in the infrared 2.4-μm band. The calculations are based on a proven isotropic potential model that we have extended to account for effects of vibrational excitations. Numerical consistency of the line-shape calculations with the sum rules is observed at the 1% level. The comparison of the computational results with the available measurements at temperatures from 20 to 300 K shows agreement within the estimated uncertainties of the best measurements (≊10%). This fact suggests that theory is capable of predicting these spectra reliably at temperatures for which no measurements exist, with an accuracy that compares favorably with that of good laboratory measurements.