Periodic orbit analysis of molecular vibrational spectra: Spectral patterns and dynamical bifurcations in Fermi resonant systems
Semiclassical periodic orbit theory is used to analyze the quantum density of states for three model molecular vibrational Hamiltonians describing stretch/bend modes with and without 2:1 (Fermi) resonant coupling. Periods of classical periodic orbits as a function of energy are extracted directly from the quantum spectrum using a Gaussian windowed (Gabor) Fourier transform. The quantum (E,τ) plots so obtained provide an informative representation of the level structure. Qualitative similarities and differences between spectra (i.e., resonant vs nonresonant) are immediately apparent; in this sense, the quantum (E,τ) plot is an efficient device for analysis of spectral patterns. At a more detailed level of analysis, we show that, for sufficiently small effective values of ℏ, the quantum (E,τ) plots reflect in full detail the intricate periodic orbit bifurcation structure for Fermi resonant Hamiltonians previously described by Li, Xiao, and Kellman [J. Chem. Phys. 92, 2251 (1990)].