Random matrix treatment of intramolecular vibrational redistribution. I. Methodology and anharmonic interactions in 1-butyne

A random matrix methodology is presented which is capable of modeling sparse through intermediate case intramolecular vibrational redistribution (IVR). A class of random Hamiltonian ensembles, called the Gaussian Poisson ensembles, is defined. These ensembles deviate from the Gaussian orthogonal ensemble (GOE) in a way that allows particular molecular spectra to be modeled, yet they can retain the desirable GOE statistical properties. The principal assumption tested by this work is that the vibrational identity of the bath states in both the calculation and in 1-butyne is sufficiently scrambled that a statistical treatment is justified. Comparison to the experimental eigenstate-resolved infrared spectra of 1-butyne is accomplished by means of four measures of IVR: the dilution factor, the interaction width, the counted level density, and the effective level density. Corrections to each of the four measures for limited experimental signal-to-noise are presented. A fit to the dilution factor and interaction width yielded the root-mean-square matrix elements for anharmonic coupling of the bright state to the bath. The values obtained, 0.010 and 0.014 cm-1, respectively, for the ν1 and ν16 bands of 1-butyne, are in close agreement with those obtained by direct deconvolution of the spectra