A new Coriolis perturbation in the methane spectrum III. Intensities and optical spectrum

Abstract

In two previous papers (Jahn 1938) the perturbations of the rotational levels of the low-frequency fundamental vibration v 4 of the methane molecule were evaluated. These perturbations were caused by the Coriolis term in the vibrational-rotational Hamiltonian which couples the rotational levels of this fundamental with the rotational levels of the infra-red inactive vibration v 2 . In the present paper we use this energy spectrum to calculate the theoretical infra-red absorption spectrum of the vibration v 4 . For this purpose we need the intensities of the rotational fine structure fines and these are here calculated, taking into account the nuclear spin weights of the states. We do not, however, take into account the effect of the Coriolis perturbation itself on the intensities, since the perturbation of the levels compared with the difference of their total vibrational energy is very small indeed, so that any intermixture of the wave functions of the two sets of levels can be neglected. From the theoretical spectrum so obtained we calculate the absorption envelope which would be observed with slit widths of approximately 0.5 cm. -1 and compare this with the experimental envelope. Attention is drawn to the fact that a third overtone absorption band of methane has a complex rotational structure which is very similar indeed to that of the fundamental here under discussion, and the reason for this is given. The general importance of Coriolis perturbations in the spectra of polyatomic molecules is stressed, and the general nature of the problems which will be met with in the rotational analysis of the spectra of these molecules is outlined.