Reduced Matrix Elements for collisionally induced transitions of ¹²CH₄

Reduced matrix elements (RMEs) for collisionally induced transitions are an important component of semi-classical line shape calculations. They give the quantum mechanical probability for a transition in the radiating molecule occurring due to a collision with one of the bath molecules. The RMEs for both the radiating and perturbing molecules are part of the quantum mechanical component of a semi-classical calculation. Evaluating the reduced matrix elements requires wavefunctions for the molecules in question. In this work, RMEs for ro-vibrational states of methane are evaluated using ab initio wavefunctions. These RMEs are compared with RMEs evaluated using a Hamiltonian model to the fourth order in the T _d formalism. Comparisons are made for the ground and ν ₃ states, where the ν ₃ state is treated as an isolated state by an Effective Hamiltonian. The formulas for the reduced matrix elements are developed in both formalisms. The comparison shows good agreement for low angular momentum states, where the isolated state approximation should be valid. Using sum rules as a check of the RMEs revealed that all symmetry components of the wavefunctions are needed in a line shape calculation. Line shape parameters are evaluated using the ab initio RMEs for a number of ν ₃ transitions measured by Benner et al. [JQSRT 50, 65, 1993].