Collision-induced first overtone band of gaseous hydrogen from first principles.

Abstract

In previous work [Phys. Rev. A 40, 6931 (1989)] the interaction-induced dipole moments of ${\mathrm{H}}_{2}$ pairs have been obtained by treating the complex of the two molecules like one molecule in the self-consistent-field and size-consistent, coupled-electron pair approximations; from this dipole surface, the binary collision-induced absorption spectra have also been computed for the rototranslational and the fundamental band. In the present work, the radial transition matrix elements of the induced dipole components are obtained for the first overtone band of ${\mathrm{H}}_{2}$ at 1.2 \ensuremath{\mu}m. Two cases are here considered: ${\mathit{v}}_{1}$=0\ensuremath{\rightarrow}0, ${\mathit{v}}_{2}$=0\ensuremath{\rightarrow}2 (``single'' vibrational transition) and ${\mathit{v}}_{1}$=0->1, ${\mathit{v}}_{2}$=0\ensuremath{\rightarrow}1 (``double'' transition), where the ${\mathit{v}}_{\mathit{i}}$ are the vibrational quantum numbers of two interacting ${\mathrm{H}}_{2}$ molecules (i=1 or 2). The dependence of these dipole elements on the most important initial and final rotational states (j=0,. . .,3) is also evaluated. From these results, the spectral profiles of the collision-induced absorption of molecular hydrogen pairs in the infrared 1.2-\ensuremath{\mu}m (the first ${\mathrm{H}}_{2}$ overtone) band are obtained. The calculations are based on a proven isotropic potential model which we have extended to account for the effects of vibrational excitations. The comparison of the computated spectra with the measurements available at temperatures from 24 to 300 K shows agreement within the estimated uncertainties of the best measurements (\ensuremath{\approxeq}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.