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.

Assignment and extracting dynamics from experimentally and theoretically obtained spectroscopic hamiltonians in the complex spectral and classically chaotic regions.

An analysis of existing algebraic multiresonance spectroscopic Hamiltonians, derived by fitting to experimental data or from classical canonical or quantum Van Vleck perturbation theory, allows without any significant further classical or quantum calculation the assignment of quantum numbers and motions to states observed in spectra that were previously thought to be irregular or just unassignable. In such cases, inspection of the amplitude and phase of eigenfunctions previously calculated in the Hamiltonians derivation process but now transformed to a reduced dimension semiclassical action-angle representation reveals extremely simple albeit unfamiliar topologies that give quantum numbers by simply counting nodes and phase advances. The topology allows these simple wave functions to be sorted into dynamically different excitation ladders or classes of states which are associated with different regions of phase space.

Assignment and extraction of dynamics of a small molecule with a complex vibrational spectrum: thiophosgene.

The dispersed fluorescence spectrum of the ground electronic state of thiophosgene, SCCl2, is analyzed in a very complex region of vibrational excitation, 7000-9000 cm(-1). The final result is that most of the inferred excited vibrational levels are assigned in terms of approximate constants of the motion. Furthermore, each level is associated with a rung on a ladder of quantum states on the basis of common reduced dimension fundamental motions.

New signal processing method for the faster observation of natural-abundance 15N NMR spectra and its application to N5+.

The new harmonic inversion noise reduction method was applied to (15)N natural-abundance NMR spectroscopy and N(5)SbF(6). This method is superior to conventional Fourier transform methods for processing FIDs and permits the detection of natural abundance (15)N NMR signals with significantly reduced numbers of scans and improved sensitivity. In addition to the confirmation of the previously reported chemical shifts for N(5)(+), the one bond coupling between N(beta) and N(gamma) could be observed for the first time.

An application of error reduction and harmonic inversion schemes to the semiclassical calculation of molecular vibrational energy levels.

A singular value decomposition based harmonic inversion signal processing scheme is applied to the semiclassical initial value representation (IVR) calculation of molecular vibrational states. Relative to usual IVR procedure of Fourier analysis of a signal made from the Monte Carlo evaluation of the phase space integral in which many trajectories are needed, the new procedure obtains acceptable results with many fewer trajectories. Calculations are carried out for vibrational energy levels of H2O to illustrate the overall procedure.

Classical, semiclassical, and quantum investigations of the four-sphere scattering system.

A genuinely three-dimensional system, viz. the hyperbolic four-sphere scattering system, is investigated with classical, semiclassical, and quantum mechanical methods at various center-to-center separations of the spheres. The efficiency and scaling properties of the computations are discussed by comparisons to the two-dimensional three-disk system.