Quantum theory and collisional propensity rules for rotationally inelastic collisions between polyatomic molecules (NH3 and CO2) and an uncorrugated surface

Abstract

We present the general quantum theory of collisions of a symmetric top molecule with an uncorrugated surface. The similarities between the description of collisions of a molecule with a structureless atom and a flat surface allow us to exploit earlier gas-phase results. We then derive several collisional propensity rules: (1) In experiments in which both inversion states in the initial J,K doublets of para-NH3 are equally populated, both inversion states of all collisionally excited levels must also be equally populated. If, however, the initial inversion level can be state selected, then unequal populations will be observed in collisionally excited inversion doublets. (2) For transitions from the J=0 level of ortho-NH3 into rotational levels of the K=3 stack, a strong propensity will exist toward conservation of the inversion symmetry for transitions into levels with J′ odd, but toward a change in the inversion symmetry for transitions into levels with J′ even. (3) If the odd terms in the angular expansion of the potential dominate, then for transitions out of rotational levels with J>0 in the K=0 stack of ortho-NH3 into rotational levels of the K=3 stack, a strong propensity will exist toward population of the upper level of the inversion doublet if the initial state has even J, and toward population of the lower level if the initial state has odd J. Using the similarities between the wave functions of a symmetric top and those of a linear polyatomic molecule with degenerate bending modes, we derived several propensity rules for the specific case of collisions of CO2 (0000) with an uncorrugated surface. In collisions which excite the low-lying (0110) bending vibration, if the initial rotational quantum number is small, then we predict that the probability of transition into a final state with J′ odd will be much larger than for transition into a final state with J′ even.