Calculation of Raman intensities for the ring‐puckering vibrations of 2,5‐dihydropyrrole and trimethyleneimine: Electrical versus mechanical anharmonicity in asymmetric potential wells


Raman intensities are calculated for the ring‐puckering transitions of 2,5‐dihydropyrrole (DHP) and trimethyleneimine (TMI) using an anisotropic atom-point dipole interaction model to evaluate the elements of the molecular polarizability tensor. The calculated relative intensities for the members of the Δv = 1 and Δv = 2 ring‐puckering progressions for DHP are in good agreement with those observed. The calculations predict that the observed Δv = 2 overtones of DHP occur not because of the first‐order allowedness expected for these transitions in the asymmetric double‐minimum potential well which governs the ring‐puckering motion, but rather because of unusually large second‐order terms in the expansions of the polarizability tensor elements in the puckering coordinate [‖(∂2αμν/∂Z2)0‖≫0]. Raman intensities are calculated for the ring‐puckering transitions of TMI using the two different potential functions which have been proposed for the puckering motion. It is found that the intensities calculated for the slightly asymmetric double‐minimum potential V(Z) = (0.922 05×106)Z4-(0.379 44×105)Z2+(0.159 13×105)Z 3 proposed by Carreira and Lord [J. Chem. Phys. 51, 2735 (1969)] cannot be reconciled with experiment. On the other hand, the intensities calculated for the highly asymmetric single‐minimum potential V(Z) = (0.7553×105)Z2-(0.4336×106)Z3+(0.7035×106)Z4 proposed by Robiette et al. [Mol. Phys. 42,1519 (1981)] are in excellent agreement with experiment. Our calculations confirm that the three most intense ring‐puckering transitions observed in the Raman (and far‐infrared) spectrum of TMI are the lowest members of a Δv = 1 rather than a Δv = 2 progression. The calculations further indicate that high‐order electrical terms in the polarizability expansions contribute significantly to the Raman intensities of both the Δv = 1 and Δv = 2 ring‐puckering progressions. Neglect of the electrically anharmonic terms in the intensity calculation for the single‐minimum well results in a significant disparity between calculation and experiment.



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The Journal of Chemical Physics