Geometrical-Classical Limit of Algebraic Hamiltonians for Molecular Vibrotational Spectra

摘要

A classical limit, which is amenable to a geometrical interpretation, is discussed for the vibron model of molecular vibrotational spectra. Both diatomic and triatomic molecules are considered. An example of a coupling between the two stretching modes of a linear triatomic is examined in detail. Examination of the algebraic hamiltonian in terms of classical variables provides additional insight on the nature of the coupling and their geometrical significance. Work is in progress on other types of couplings in the U(2) x U(2) case and on the extension of the present results to U(4) x U(4). In the latter case, even after elimination of the constants of the motion related to the 0(4) symmetry, the phase space is four-dimensional. The resulting classical trajectories need not then be simple. Additional effects are also expected due to the role of the bending vibration. (Reprint)