VIRTUAL SYMMETRY
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Date
1961
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Publisher
Ohio State University
Abstract
The H\”uckel theory of alternating hydrocarbons yields a number of accidental $degeneracies^{1}$ which can be explained on the basis of hidden symmetry. By virtual symmetry we mean the symmetry which an asymmetric or partially symmetric system acquires if it is possible to embed it, using symmetry operation, into a larger and more symmetrical system. For example, the accidental three-fold degeneracies of the hexagonally symmetric hydrocarbon coronene can be explained, by embedding the molecule in a two-sheeted Klein bottle gotten by continuing the molecule periodically across its boundaries. Such virtual symmetry, by contributing additional constants of the motion to a Hamiltonian, may be used to improve Hartree-Fock wave functions through projection with respect to a larger symmetry group.
Description
$^{1}$B. and A. Pullman, ""Les Theories Electroniques de la Chimie Organique"", Paris. Masson et Cie, 1952.
Author Institution: RIAS
Author Institution: RIAS