Coriolis perturbations in the methane spectrum. IV. Four general types of Coriolis perturbation

In previous papers (Jahn 1938, Childs and Jahn 1939) a new Coriolis perturbation in the methane spectrum was investigated. This perturbation arose from a coupling of the rotational levels of an infra-red active threefold degenerate vibration with those of an inactive twofold degenerate vibration. In the present paper, which is a continuation of this work, it is our purpose to show that in a regular tetrahedral molecule there are in all four possible distinct types of Coriolis perturbation. Two of these do not produce a splitting of the rotational levels but merely a displacement of the rotational level as a whole, whilst the other two produce a splitting as well as a displacement, one of these latter perturbations being identical with the type of perturbation previously investigated. General formulae are derived for the matrix elements of these new types of perturbation, and in the case of the new perturbation which produces a splitting of the levels, we factorize the perturbation matrices up to the tenth rotational quantum number, using the group-theoretical method previously developed. These results will be useful in elucidating the rotational structure of the overtones and combination tones of methane.