A Perturbation Approach to Predict the Infrared Spectra of Small Molecular Clusters Applied to Methanol
Udo Buck and Burkhard Schmidt
A method for predicting splittings and shifts of bands in infrared spectra of small clusters of polyatomic molecules is presented. Based on an approach of early publications of Buckingham, the influence of the intermolecular forces on the vibrational energy levels of the constituent molecules is calculated using perturbation theory to second order. In order to describe the interaction of identical molecules, this ansatz is extended to also cover degenerate systems. In first order, a coupling of the vibrational modes of the interacting molecules occurs which leads to delocalized vibrations of all the molecules in the cluster. The second order correction of the vibrational excitation frequencies are found to be dominated by the intramolecular couplings of the normal modes due to the cubic anharmonicity of the force field. The procedures developed here are applied for the interpretation of vibrational photodissociation spectra of small methanol clusters in the region of the fundamental excitation frequency of the OH stretching mode (ν1, 3681.5 cm-1), the CH3 rocking mode (ν7, 1074.5 cm-1), and the CO stretching mode (ν8, 1033.5 cm-1). Using semiempirical models for the intermolecular potential functions, splittings and positions of the experimental bands can well be explained. The nonequivalent positions of the two molecules in the linear dimer structure give rise to two different absorption frequencies for each of the three modes of the donor and the acceptor molecule, respectively. The trimer and tetramer spectrum with only one absorption band are in agreement with the existence of symmetric planar ring structures (C3h and C4h) for these species. The pentamer spectrum which also consists of one band is explained by the occurrence of three closely spaced frequencies of an asymmetric ring. The double peak structure in the hexamer spectra can be attributed to a distorted ring structure of S6 symmetry, while the occurrence of other energetically near-degenerate isomers can be ruled out by means of their spectra.