An efficient method for analyzing the optimal modes of vibration for polyatomic molecules
Aiani, Karen Ellen
Hutchinson, John S.
Doctor of Philosophy
A quantitative analysis of the vibrational spectra of polyatomic molecules in the high energy regime requires a determination of the proper modes that optimally describe the vibrational motions of the nuclei at these energies. Observed vibrational spectra in small polyatomics indicate substantial regularity in the vibrational motion, implying that such a set of "optimal modes"should exist. Experiments have not provided a direct means of characterizing these modes. We present a computationally efficient theoretical method for performing an optimal modes analysis of multi-dimensional vibrational eigenstates. This algorithm consists of direct numerical integration of selected projection coefficients which reveals the extent of zeroth-order character of these eigenstates and is very accurate and significantly less time-intensive than previously employed methods of analysis. Demonstration of this method is presented for the analysis of selected high energy vibrations in hydrogen cyanide, monodeuterioacetylene, and propyne. The propyne analysis demonstrates the quantum mechanical intramolecular vibrational energy redistribution process in addition to the optimal mode analysis.