GEOMETRICAL FOUNDATION OF THE HUCKEL-MOBIUS CONCEPT AND ITS APPLICATION TO CYCLIC, TWISTED LINEAR AND HELICAL MOLECULAR SYSTEMS
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Publisher:Ohio State University
Definitions of Huckel and Mobius systems are clarified using the cyclic group formalism and screw symmetry operation. It is shown that the Mobius ring system has half-integral pseudo-angular momentum similar to that of spin space, and that all applications of Mobius system to chemical reactions have been based on truncated single-circle Mobius rings which have unique beginning and end. This concept is illustrated by application to the [1,7] antarafacial hydrogen shift. Definition of a Hukel versus Mobius ring system for in-plane and out-of-plane $\pi, \delta and \phi$ orbitals as well as the appropriate relative angle of twists are given. Using the concept of the compatibility of the twist (screw) angle and rotation around a ring, we also derive the proper phase coherence and energy correlation between a parent cyclic molecule and its dissociated linear fragments. The concept of parentage in diabatic fragmentation is discussed. For finite, open, helical chain molecules exact periodic boundary conditions based on the compatibility of twist angle and numbers of turns in a helical ring parent molecule is applied to derive their analytic wave functions.
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