Analytic perturbative classification and assignment of eigenstates of algebraic vibrational Hamiltonians

Demixing and cleaning of wave functions by projection, application to the assignment of molecular vibrations

It is shown how the projection of a quantum mechanical state into an appropriate subspace of the Hilbert space can be useful for the classification and the assignment of states. The projection cleans the wave function and decomposes mixtures caused by near-accidental degeneracy. The idea is applied to vibrational states of the molecule CF(3)CHFI obtained from an algebraic Hamiltonian.

The Fock space method of vibrational analysis

A reformulation of a semiclassical theory that presently seems uniquely capable of interpreting generic complex multiresonant vibrational spectra is presented. Once given the spectroscopic Hamiltonian which reveals the set of possible resonant couplings and its eigenstates, the new and old formulations both yield without any further computation level by level dynamical assignments for the spectra. Computing a simple trajectory in phase space reveals the motions that when quantized yield the assigned levels. The reformulation introduces two new projected representations of the wave functions. The first is in action space and the second in angle space. The projected representations often allow the reduced angle space, where nodal searches are made, to be of lower dimension than formally occurred. In addition the action representation is a similarly lower dimension lattice representation whose discreteness and regularity allow higher reduced dimensions to be studied. The lattice representation is used to produce a significantly more complete and detailed assignment of the thiophosgene spectrum than previously published.