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A free-electron theory of conjugated molecules

II. A Derived Algebraic Scheme

Published online by Cambridge University Press:  24 October 2008

J. Stanley Griffith
J. Stanley Griffith
Affiliation:
Department of Theoretical ChemistryUniversity of Cambridge*
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Abstract

The values of a free-electron eigenfunotion at the carbon nuclei of a conjugated hydrocarbon are found to satisfy a system of algebraic equations. These equations are similar in form to those obtained in the method known as the linear combination of atomic orbitale but only coincide with them for linear polyenes and benzene. The symmetry, degeneracy and energy of the eigenvectors of these free-electron equations correspond exactly to those of the free-electron wave functions found by the usual methods. From this correspondence, a theorem is deduced about the free-electron charge density in alternant hydrocarbons.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 49 , Issue 4 , October 1953 , pp. 650 - 658
Copyright
Copyright © Cambridge Philosophical Society 1953

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References

REFERENCES

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