The Fock space method of vibrational analysis

Abstract

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.

On the nature of highly vibrationally excited states of thiophosgene#

“…The various sequences observed here are consistent [12] with the previous results of Jung and Taylor. This can be established by looking at appropriate slices of the semiclassical three-dimensional angle space representations of the eiegnstates.…”

“…For instance, looking at the phase of the semiclassical state in the ψ 1 = 0 plane will immediately reveal the (v 2 , v 3 ) quantum numbers. Similarly, keeping track of the phase advance along the ψ 1 direction in the ψ 3 = 0 or ψ 2 = 0 plane will yield µ as the excitation quantum number [12,13].…”

“…In the first approach [11][12][13] the quantum states |α for a given (K, L, M ) are expressed in the semiclassical angle…”

“…Nevertheless, as will be seen below, even this reduced system presents a stiff challenge with regards to the dynamical assignments of the highly excited eigenstates. The IVR dynamics in SCCl 2 has been the subject of several recent experimental [7][8][9] and theoretical [10][11][12] studies. In an early detailed study, Strickler and Gruebele established [7] that the IVR state space (zeroth-order quantum number space) has an effective dimensionality of three as opposed to the theoretically possible six.…”

“…1 established [11] that several distinct eigenstate classes exist in the spectrally complicated region 7000−9000 cm −1 (∼ 210 − 270 THz). More recently [12], Jung and Taylor dynamically assigned the states and came up with a detailed semiclassical classification scheme for the eigenstates.…”