Knowledge Bank

Last year we reported on progress during the preliminary stages of an analysis of the far infrared spectrum of methylamine, using a newly developed effective Hamiltonian (derived essentially from group theoretical considerations) to take into account a variety of effects of the tunneling splittings arising from the methyl group internal rotation and the amino group umbrella motion. Work on the vibrational ground state has now been completed, and we have obtained a fit of about 950 energy level differences with $0\le K\le 19$ and $K\le J\le 30$, using 30 molecular parameters. The standard deviation of the fit is $0.00061cm-1$, which is only slightly larger than the expected measurement precision. Perhaps the most interesting result to emerge from the ground state fit concerns the determination of the structural parameter $\rho$, which relates the moment of inertia'' of the top to the moment of inertia'' of the whole molecule. One of us found, in earlier fits of microwave data $alone1$, that two values of $\rho$, differing by about 2% were obtained, depending on whether internal-rotation splittings or umbrella-motion splittings were treated. On the basis of the present work, it is now clear that there are two Coriolis terms involving interaction of the large-amplitude angular momentum with the overall angular momentum, since there are two large-amplitude motions in methylamine. In the traditional IAM procedure the value of $\rho$ is determined by requiring the coefficient of the Coriolis term to vanish in the effective Hamiltonian. In the present case we can make the internal-rotation coefficient, or the umbrella-motion coefficient, or some linear combination of the two vanish, but we cannot make both vanish simultaneously. Thus, there is an inberent ambiguity in the value determined for $\rho$. These and other matters concerning the methylamine spectrum will be discussed.