Quantum sum formulae for the collision-induced spectroscopies: Molecular systems as H2-H2

Quantum expressions for the second moment of collision-induced spectra are developed in the low-density limit. Previous work by Moraldi is extended to account for the rotational structure of colliding linear molecules; isotropic interaction is assumed. Computations of the lowest three moments are presented for the case of infrared absorption and Raman scattering of molecular hydrogen pairs at temperatures from 77 to 300 K. The radial distribution functions of pairs, mean energy and angular momentum, which are required for that purpose, are obtained for the case of H₂ molecules interacting with H₂, and compared with their classical counterparts. The simple classical approximations with lowest-order Wigner-Kirkwood quantum corrections serve as an accurate representation of the quantum expressions at large separations and may be sufficient for massive systems at high temperatures.