Assignment and Extracting Dynamics from Experimentally and Theoretically Obtained Spectroscopic Hamiltonians in the Complex Spectral and Classically Chaotic Regions

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• 作者：Christof Jung ; Howard S. Taylor
• 刊名：Journal of Physical Chemistry A
• 出版年：2007
• 出版时间：April 26, 2007
• 年：2007
• 卷：111
• 期：16
• 页码：3047 - 3068
• 全文大小：761K
• 年卷期：v.111,no.16(April 26, 2007)
• ISSN：1520-5215

文摘

An analysis of existing algebraic multiresonance spectroscopic Hamiltonians, derived by fitting to experimentaldata or from classical canonical or quantum Van Vleck perturbation theory, allows without any significantfurther classical or quantum calculation the assignment of quantum numbers and motions to states observedin spectra that were previously thought to be irregular or just unassignable. In such cases, inspection of theamplitude and phase of eigenfunctions previously calculated in the Hamiltonians derivation process but nowtransformed to a reduced dimension semiclassical action-angle representation reveals extremely simple albeitunfamiliar topologies that give quantum numbers by simply counting nodes and phase advances. The topologyallows these simple wave functions to be sorted into dynamically different excitation ladders or classes ofstates which are associated with different regions of phase space. The rungs of these ladders or the states inthe classes intersperse in energy causing the spectral complexity. No experimental procedure allows suchsorting. The success of the work stems from (1) the qualitative insights of nonlinear dynamics, (2) the conversionof the quantum problem in full dimension to a semiclassical one in reduced dimension by use of a canonicaltransform that takes advantage of the polyad and other constants of the motion, and (3) the judicious choiceof the reduced angle variables to reflect rational ratio resonance frequency conditions. This leads to localizationof those semiclassical wave functions, which are affected by the particular resonance. In reverse, the localizedappearance of the reduced dimension wave function reveals which resonances govern it and makes sortingvisually simple. The success of the work also stems from (4) the revealing use of plots of phase advances aswell as the usual densities of the eigenstates for sorting and assignment purposes. Even in classically chaoticregions, organizing trajectories, which correspond to averages over regional phase space structures that neednot be computed, can easily be drawn as the structure about which eigenfunction localization takes place.The organizing trajectories when transformed back to the full dimensional configuration space reveal theinternal molecular motions. The complexity of the usual quantum stationary and propagated wave functionsand associated classical trajectories forbids most often such assignments and sorting. This procedure bringsthe ability to interpret complex vibrational spectra to a degree previously thought possible only for lowerexcitations. The new methodology replaces and extends the computationally more difficult parts of a procedureused by the authors that was applied successfully to several molecules during the past few years. The newmethodology is applied to DCO, CHBrClF, and the bending of acetylene.