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Some solutions in the graph theory of alternant benzenoids
Author(s) -
Hall George G.
Publication year - 1993
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560450204
Subject(s) - eigenvalues and eigenvectors , molecule , simple (philosophy) , transcendental equation , series (stratigraphy) , exact solutions in general relativity , transcendental number , mathematics , physics , quantum mechanics , mathematical analysis , numerical analysis , paleontology , philosophy , epistemology , biology
A new formulation of the eigenvector equations for certain polymeric molecules is given. The electronic bands for the infinite molecules are deduced. For the finite molecules, the use of ghost molecules allows an exact specialization of the infinite to the finite eigenvector equations. The complete solution of the equations depends on the solution of a simple transcendental equation. Approximate solutions of this equation are given that bracket the accurate solutions so that, for molecules with many repeated moieties, the approximations become good. The general theory is illustrated by applications to the chrysene series and to the polyphenyls. © 1993 John Wiley & Sons, Inc.