dc.creator Chiu, Ying-Nan en_US dc.date.accessioned 2007-08-31T14:10:04Z dc.date.available 2007-08-31T14:10:04Z dc.date.issued 1982 en_US dc.identifier 1982-WE-3 en_US dc.identifier.uri http://hdl.handle.net/1811/29103 dc.description.abstract Linear combination of vibrational wave functions centered at the periodic potential minima is used to approximate the torsional wavefunction normally obtained by Floquet's Theorem in Mathieu function form. The Huckel type $\Sigma_{k} Exp^{(2\pi 1\Lambda K}/n)\phi_{k}$ and Mubius type $\Sigma_{k} Exp[^{\pi 1(2A+1)k}/n]\phi_{k}$ combinations are shown to have the correct pseudo-angular momentum upon rotation of one or both parts of the coaxial (torsional) rotor. Therefore, they may be correlated to wave functions with free internal rotation. The combination of Huckel and Mobius energy levels then forms the cluster of properly alternating non-degenerate levels for the high-barrier case. For example, in $X_{2}Y_{6}$, the cluster is AEEA and for $X_{2}Y_{10}$ the cluster is AEEEEA. The even vibrational wavefunctions in general forms a Huckel energy system and Mobius when the system has 3 (such as $X_{2}Y_{6}$), 5,7 fold symmetry. This treatment is compared with spin double group and spectroscopic double group of Hougen and Bunker. It is suggested that the ratio of splitting between different vibrational levels might be roughly estimated by the ratio of Frank-Condon overlap integrals for displaced oscillators. en_US dc.format.extent 102359 bytes dc.format.mimetype image/jpeg dc.language.iso English en_US dc.publisher Ohio State University en_US dc.title APPLICATION OF HUCKEL-MOBIUS CONCEPT TO TORSIONAL VIBRATION AND INTERNAL ROTATION-COMPARISON OF MOBIUS, SPIN DOUBLE GROUP AND SPECTROSCOPIC DOUBLE GROUP METHOD en_US dc.type article en_US
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