Inversion and internal rotation in methyl-d-amine: Theory

A theory has been developed for an analysis of the microwave spectrum of the CH₂DNH₂-type molecule which has an asymmetric internal rotor. First, the Hamiltonian matrix was expressed on the basis of localized wavefunctions, each of which corresponds to a conformer vibrating in the vicinity of a potential minimum. Next, by a symmetrization, the Hamiltonian matrix was factored into four submatrices. By solving these matrices, a general view of the energy-level structure has been given, which should be useful for an interpretation of the observed rotational spectrum. It has been shown that the inversion splitting in each level of the trans form molecule should be sensitive to the amount of trans-gauche coupling through tunneling and therefore the relative height of a trans level with respect to a gauche level can be determined from an observation of the inversion splitting in the trans levels.