Analysis of an algebraic model for the chromophore vibrations of CF3CHFI

Abstract

We extract the dynamics implicit in an algebraic fitted model Hamiltonian for the hydrogen chromophore's vibrational motion in the molecule CF 3 CHF I. The original model has 4 degrees of freedom, three positions and one representing interbond couplings. A conserved polyad allows the reduction to 3 degrees of freedom. For most quantum states we can identify the underlying motion that when quantized gives the said state. Most of the classifications, identifications and assignments are done by visual inspection of the already available wave function semiclassically transformed from the number representation to a representation on the reduced dimension toroidal configuration space corresponding to the classical action and angle variables. The concentration of the wave function density to lower dimensional subsets centered on idealized simple lower dimensional organizing structures and the behavior of the phase along such organizing centers already reveals the atomic motion. Extremely little computational work is needed.

Assignment and Extraction of Dynamics of a Small Molecule with a Complex Vibrational Spectrum: Thiophosgene

“…The semiclassical analysis was developed in previous studies of complex vibrations for such molecules as acetylene, 13,14 CHBrClF, 21 N 2 O, 22 DCO, 23 CDBrClF, 24 and CF 3 CHFI. 25 The analysis allows inspection of the density and phases of its eigenfunctions previously calculated in the Hamiltonian derivation process but now transformed to a reduced dimension semiclassical action-angle representation. This reveals extremely simple albeit unfamiliar topologies that give quantum numbers by simply counting nodes and phase advances.…”

Demixing and Cleaning of Wave Functions by Projection, Application to the Assignment of Molecular Vibrations

“…As shown in ref , the polyad 5 of CF 3 CHFI has also another class of states that shows strong coupling of the stretch with the modes a and f. This other class of states does not have the approximate symmetry described in the present subsection. This demonstrates two properties of the system that are worth being emphasized very clearly.…”

“…Later we will analyze some eigenstates belonging to the eigenvalue 5 of P . This is the same polyad as the one investigated in ref , therefore we can compare results.…”

“…The experience from ref shows that at the lower end of the polyad 5 the eigenstates of the complete Hamiltonian are almost pure eigenstates of n s = a s † a s . This indicates that all the various Fermi resonances of the Hamiltonian have little effect; they are the only ones that could cause a mixing of basis states with different quantum numbers n s .…”

Decoding the Dynamical Information Embedded in Highly Excited Vibrational Eigenstates: State Space and Phase Space Viewpoints

“…Second, the complicated interleaving of high and low values of IPRs in both systems reflects the interleaved sequences of states uncovered by Jung et al in their work. 7,8 The IPR analysis cannot give any more information regarding the dynamical assignment. In particular there is no possibility of extracting a set of approximate quantum numbers from the IPR data alone.…”