LOCATING FRAGMENTS OF ORDER IN COMPLEX SPECTRA: THE EXTENDED AUTOCORRELATION FUNCTION
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Date
1993
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Ohio State University
Abstract
Many experimental techniques, including stimulated emission pumping, dispersed fluorescence, and others, provide large quantities of high-quality spectral data for highly vibrationally excited polyatomic molecules. Understanding how to extrapolate the hard-won detailed information on Hamiltonian models from lower energy ranges to these much more complex regions requires the development of more rapid methods of analysis and assignment which provide both ensemble average and state-specific information. Faced with the strongly hierarchical polyatomic molecular dynamics in which interactions occur with matrix elements which range from thousands of wavenumbers to tens of kilohertz, existing methods such as the Fourier transform or level-statistics are very difficult to interpret. Nonetheless, this hierarchy of couplings leaves traces in the spectrum of the remaining approximately conserved quantities, and of the energy ranges (or delocalization widths) over which basis states for the mostly-broken quantum numbers are distributed. The extended autocorrelation function (XAC) is designed to detect and locate those remnants of order. It allows complex patterns parameterized in a multi-dimensional way to be located in a spectrum in the presence of interfering data. We describe the motivation for this method, and illustrate its application to synthetic systems, and to $C_{2}H_{2}$ dispersed fluorescence data. A second method which provides additional hierarchical information, parsimonious trees, is described with the XAC $elsewhere^{1}$.
Description
$^{1.}$ Stephen L Coy, David Chasman, and Robert W. Field, to be published in Molecular Dynamics and Spectroscopy by Stimulated Emission Pumping, H.-L Dai and R. W. Field, eds.
Author Institution: Department of Chemistry, MIT
Author Institution: Department of Chemistry, MIT