Knowledge Bank

The mocrowave spectra of several simple molecules are made more complicated by an excited internal degree of freedom. Using the matrix formulation of quantum mechanics we have established the Hamiltonian elements for a molecule with a restricted internally rotating methyl group. The matrix elements for both the kinetic and potential energies have been determined in a J, K, k, $MJ$ representation, where k refers to the angular momentum of the methyl group rotation. The direction cosine matrix elements are also obtained in this representation. They can be used in the methods developed for rigid asymmetric tops in order to calculate dipole intensities and Stark effects. Some applications of these methods to the microwave spectrum of nitromethane recently reported by Tannenbaum, Johnson, Myers and Gwinn will also be discussed.