G. Alan Schick

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

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...

Calculation of molecular polarizabilities using a semiclassical Slater‐type orbital‐point dipole interaction (STOPDI) model

The point dipole interaction model for molecular polarizability proposed by Applequist, Carl, and Fung [J. Am. Chem. Soc. 94, 2952 (1972)] is modified by replacing the point dipole interaction tensor with a descaled distributed charge interaction tensor. Our procedure is based on the descaled tensor algorithm proposed by Thole [Chem. Phys. 59, 341 (1981)] and uses a Slater‐type orbital (STO) function to represent the charge distribution. The resulting STOPDI formalism calculates mean molecular polarizabilities and the components of the molecular polarizabilities with errors comparable to experimental uncertainty. Furthermore, these procedures require only one optimized parameter per atom, the average atomic polarizability. The formalism is invariant to coordinate transformations and avoids the discontinuities and/or false resonances that are characteristic of previous classical and semiclassical formalisms. The STOPDI algorithm requires less parameterization and computation time than the anisotropic atom ...

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...

Calculation of Raman intensities for the ring‐puckering vibrations of cyclopentene and 2,5‐dihydrofuran

Raman intensities are calculated for the ring‐puckering vibrations of cyclopentene and 2,5‐dihydrofuran using an anisotropic atom–point dipole interaction model to calculate the elements of the molecular polarizability tensor. Large second‐order terms are calculated for both molecules in the expansions of the molecular polarizability tensor elements in the ring‐puckering coordinate [‖(∂2αμν/∂Z2)0‖≫0]. These terms result in intense calculated Δv = 2 overtone transitions, in agreement with experimental observations. The calculations predict that the Δv = 2 transitions of cyclopentene are one to two orders of magnitude more intense than the Δv = 1 fundamentals, while the two sets of transitions are comparable in intensity in 2,5‐dihydrofuran. Although the shape of the band contours precludes observation of the Δv = 1 transitions for either molecule, the calculations suggest that the fundamental transitions of cyclopentene would not be observable even if the band shape were amenable to observation.

Calculation of Raman intensities for the torsional vibrations of ethyl halides

Raman intensities are calculated for the torsional vibrations of CH3CH2Cl, CH3CH2Br, CH3CH2I, CH3CHCl2, and CH3CHBr2 using an anisotropic atom‐point dipole interaction model to calculate the elements of the molecular polarizability tensor. The calculated relative intensities for the members of the Δv = 2 torsional overtone progression of each of the ethyl halides are in good agreement with experiment. It is predicted that electrically anharmonic terms contribute substantially to the Raman intensities of these transitions. The Δv = 1 torsional transitions of the five molecules are predicted to be 20–30 times more intense than the overtones (although these transitions are not observed because of broadband contours and interference from other vibrational modes). Electrically anharmonic terms in the polarizability expansions also contribute substantially to the intensity of the fundamentals.

Calculation of Raman intensities for the torsional vibrations of methylcyclopropane and propylene oxide

Raman intensities are calculated for the torsional vibrations of methylcyclopropane and propylene oxide using an anisotropic atom‐point dipole interaction model to calculate the elements of the molecular polarizability tensor. It is predicted that electrical anharmonicity contributes substantially to the intensities of both the Δv = 1 and δv = 2 transitions. The calculated intensity distribution of the Δv = 1 transitions of propylene oxide is in excellent agreement with experiment. The calculated intensities of the fundamental transitions of methylcyclopropane are not in as good agreement with experiment as those of propylene oxide; however, the observed transitions of the former molecule are extremely broad and difficult to measure accurately. The calculations predict that the Δv = 1 transitions of both molecules are substantially more intense than the Δv = 2 overtones. The intensity of the overtones cannot be measured accurately because they are partially obscured by intense in‐dand out‐of‐plane bending...