A new Coriolis perturbation in the methane spectrum II. Energy levels

Abstract

In the first part of this work (Jahn 1938) we found the correct vibrational-rotational wave functions with which to evaluate any tetrahedrally symmetrical perturbation of the rotational levels of a threefold degenerate mode of vibration of the methane molecule. In this second part we use these wave functions to calculate the perturbation due to the Coriolis term which couples the rotational levels of the one quantum threefold degenerate vibration v 4 and the rotational levels of the one quantum twofold degenerate vibration v 2 . This Coriolis term was derived in part I from the general vibrational-rotational Hamiltonian of the molecule. To carry out the perturbation calculation we shall need those combinations of the vibrational-rotational wave functions of v 2 which transform according to irreducible representations of the tetrahedral group, and these are derived here. We find also general formulae for the matrix elements in question and use these to calculate explicitly the perturbed rotational energy levels of v 4 up to the tenth rotational quantum number. The rotational levels of v 2 are of course correspondingly perturbed, but the calculation of these is reserved for another publication.