Structure and spectra of molecular clusters
In the present work a procedure to calculate excitation spectra of intramolecular vibrations of small molecular clusters is developed. Starting from the normal mode analysis of the vibrations of polyatomic molecules the influence of the intermolecular potential on the vibrational energy levels is treated with the aid of quantum mechanical perturbation theory. The approach of earlier works of A. D. Buckingham concerning the spectroscopy of chromophores in solution is extended to include the formalism of degenerate perturbation theory. Thereby it follows that in first order a coupling of the vibrational modes of the interacting molecules takes place, while in second order the spectra are dominated by a coupling of the different modes of each molecule depending very sensitively on both the interaction potential and the off-diagonal cubic constants of the anharmonicity of the intramolecular force field. In order to be able also to simulate spectra for finite temperatures, the described procedure is linked to the method of canonical ensemble averaging via the Metropolis algorithm. In this way thermally averaged spectra are obtained, allowing for a direct comparison with experimental results.
The procedure presented here is employed for the interpretation of photodissociation spectra of small methanol clusters in the region of the fundamental excitation frequency of the CO stretching vibration (v8, 1033.5 cm-1). Using semiempirical potential models for the intermolecular interaction the splittings and positions of the experimental spectral lines can well be explained: The two lines in the dimer spectrum shifted to the red and to the blue with respect to the monomer absorption frequency result from the non-equivalent positions of the acceptor and donor molecule in the linear dimer, respectively, the spectra of the trimer and of the tetramer can be explained by the existence of planar symmetric rings. As can be shown with Monte-Carlo-simulations, these are stable up to a temperature of approximately 150 K. The two blue-shifted lines in the hexamer spectrum result from the absorption of a ring-shaped isomer of S6-symmetry, while the occurrence of isomers of different symmetry which lie only slightly higher in energy can be excluded by means of their spectra. The quantitative comparison of simulated and experimental spectra allows the judgement of different potential functions and can be a valuable aid in constructing new model functions of the intermolecular interaction.
Burkhard Schmidt, Ph. D. thesis
University of Göttingen, 1992
Max-Planck-Institut für Strömungsforschung