Theoretical Investigations of Translation—Rotation Energy Transfer: (H2, He) and (D2, He) Systems

Abstract

The classical analysis of translation—rotation energy transfer in (H2, He) and (D2, He) systems is reported. The accurate, a priori potential surface obtained by Krauss and Mies has been employed in a generalized, three-body Monte Carlo calculation to obtain, as a function of temperature, relaxation times and collision numbers for the 0→2 and the 2→0 rotational transitions in both H2 and D2. A negative dependence upon temperature is obtained in each case. The relaxation times for the 0→2 transition in H2 range from 7.725×10−8 sec at 100°K to 3.491×10−8 sec at 700°K. For the 2→0 deexcitation the corresponding values are 9.00×10−8 and 4.30×10−8 sec. When a van der Waals attraction term, whose magnitude is estimated from PVT data, is added to the Krauss—Mies surface, the values for the 0→2 transition decrease to 3.1×10−8 sec at 100°K and 2.0×10−8 sec at 700°K. Corresponding decreases occur for the 2→0 transition. Calculated relaxation times for D2 are 50%—100% smaller than those obtained for H2. These results are in satisfactory agreement with available experimental data and appear to be more accurate than previous theoretical results. The energy-transfer mechanism has been investigated and found to be smooth and continuous with transfer occurring in about 10−13 sec. The most favorable approach angle for transfer is found to be about 60°. Two other empirical potential surfaces have been employed to estimate the effect of potential well depth and the assumption of pairwise additivity of molecular potentials. It is found that as the well depth increases, the relaxation time decreases in a manner previously predicted by Parker. The assumption of pairwise additivity is found to yield results for the relaxation times which are low by about a factor of 2. The magnitude of this error, coupled with calculations employing off-center, pairwise potentials, indicates that the repulsive centers in H2 are located about 0.16 Å from the nuclei.