Theory of vibrationrotation interactions in spherical top molecules Part I. A new overtone band
Abstract
The possibility of a new overtone band in the infrared absorption spectrum of tetrahedral XY _{4} molecules is investigated theoretically. This band is associated with the E vibrational part of the first overtone of an infrared active fundamental. The new band is active only through vibrationrotation interactions. Its intensity is very small compared to that of the F_{2} vibrational part of the same overtone. Formulas for relative intensities and matrix elements of the Hamiltonian are calculated. The selection rules imply a single P, Q, and R branch. The tetrahedral splittings of the vibrationrotation levels are determined by only two parameters: D_{t} and γ' _{3t} ≡ {1}/{3} (Z _{3s} + 6Z _{3t}) . A possible favorable case for the observation of the band may be CD _{4} at about 4700 cm ^{1}. With the assumption that γ' _{3 t} ≫ D_{t}, the tetrahedral splittings and relative intensities are calculated numerically through J = 7 for this case.
 Publication:

Journal of Molecular Spectroscopy
 Pub Date:
 May 1965
 DOI:
 10.1016/00222852(65)900834
 Bibcode:
 1965JMoSp..16...35F