Calculation of Raman intensities for the ring-puckering vibrations of trimethylene oxide and cyclobutane. The importance of electrical anharmonicity

Abstract

Raman intensities are calculated for the ring-puckering vibration of trimethylene oxide (TMO) and cyclobutane using an anisotropic atom–point dipole interaction model to calculate the elements of the molecular polarizability tensor. Three different models for the ring-puckering motion are examined: (i) a model in which the methylene groups are held rigid to the molecular frame as the ring puckers, (ii) a dynamical model in which the methylene groups rock (TMO and cyclobutane) and wag (TMO) as the ring puckers, and (iii) a second rigid model in which all of the polarizability of the molecule is localized on the atoms of the ring skeleton. All three models for the ring-puckering motion predict unusually large second-order terms in the expansion of the polarizability tensor elements in the ring puckering coordinate [‖∂2amn/∂Z2)0‖≳0]. These terms result in intense Dv = 2 overtone transitions. The calculated relative intensities of the members of the Dv = 2 overtone progression are in good agreement with those observed for both molecules. The calculations also predict that for TMO the intensities of the Dv = 2 overtones are comparable to the Dv = 1 fundamentals. This result when evaluated in terms of the expected differences in the band shapes of the two types of transitions readily accounts for the predominance of the overtone transitions in the Raman spectrum of TMO.