Pure Sequence Vibrational Spectra of Small Polyatomic Molecules
Authors: Field Robert W. , Coy Stephen L. , Solina Stephani Ann B. 
Published: July 2007

Highly excited (0&lt;E&lt;4 eV) vibrational levels in the electronic ground state of small, gas phase, polyatomic molecules can be examined by a variety of Franck-Condon controlled laser spectroscopic schemes: one-laser (Dispersed Fluorescence: DF), two-laser (Stimulated Emission Pumping: SEP) and three-laser (IR-SEP). The DF spectra contain patterns of vibrational level spacings and transition intensities that can provide a basis for assigning nonrigorous quantum numbers to individual eigenstates or feature states (which consist of clusters of unresolved eigenstates) or refining a superpolyad fit model. The SEP spectra contain a quantity (∼103) of features sufficient to invite application of a variety of statistical measures. Rigorously pure sequences (same total symmetry, same J) can be constructed. The &gt; 103: 1 dynamic range of these spectra combined with the ability to vary systematically the electronically excited rovibronic level from which these spectra emanate, can produce nearly complete pure sequences. Low resolution spectra correspond to early time, localized dynamics. Such spectra often contain fully resolved Franck-Condon bright feature states, each of which can be unambiguously assigned to a set of normal mode vibrational quantum numbers. Sometimes, such assignments can only be secured by high resolution detective work. Viewed at higher resolution, feature states often split up, revealing several layers of underlying structure. The hierarchy of splittings in the frequency domain corresponds to sequential spreading of the initially localized excitation in the time domain. Elaborate but traditional multi-resonance superpolyad effective Hamiltonian (ℌeff) matrix fit models can describe the coarse structure in the spectrum and the early time intramolecular dynamics. Since the superpolyad model is based on matrix elements of a relatively small number of anharmonic coupling terms (e.g., k122Q1Q22) evaluated in a normal mode, harmonic oscillator, product basis set, the superpolyad model is readily scaled to higher energy. The superpolyad model provides an accurate and refinable model for early time sequential Intramolecular Vibrational Redistribution (IVR) processes. Upon scaling to higher energy, the model provides testable predictions as the early time dynamics becomes more rapid and more complex. The most informative, reliable, and robust statistical measures applicable to polyatomic molecule vibrational spectra are those based on the well characterized initial localization and its early time dynamics, as described by a superpolyad ℌeff model. Superpolyad models describe how the remnants of regular dynamics are encoded in the spectrum at both high and low resolution. The models predict characteristic patterns of frequency separations and relative intensities which will be approximately replicated many times in the spectrum. The Extended Autocorrelation (XAC) pattern recognition method allows these patterns to be detected and located in the spectrum. Another scheme is based on the appearance in the spectrum of fine permutation splittings superimposed on a much coarser manifold of vibrational levels. These identical atom permutation splittings become resolvable when a molecule begins to tunnel between different chemically bonded networks on a time scale comparable to the inverse of the spectral resolution (1/δν). A third technique, tree-based hierarchical analysis (e.g., parsimonious trees) can reveal, without an a priori specified model, a hierarchy of coupling matrix elements (or delocalization rates). Spectroscopic detective work can identify the approximately conserved quantities that are destroyed by each of the hierarchical couplings. Because of the wide variety of approximately conserved quantities and coupling mechanisms responsible for the sequential destruction of these quantities, it is likely that the usual statistical measures developed by “quantum chaologists” for locating a system on the Poisson (regular, localized) ↔GOE (chaotic, delocalized) continuum, are too inflexible and reductionistic to yield useful insights into polyatomic molecule rotation-vibration dynamics. We believe that the important question is not whether molecules ever achieve the “bag of atoms limit”, but how they approach this limit. How fast does the initially localized excitation decay? Where does the energy go? What are the mechanisms that cause the energy to flow?