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Notes on the molecular orbital treatment of linearly coupled systems

Published online by Cambridge University Press:  24 October 2008

C. A. Coulson  and
G. S. Rushbrooke
C. A. Coulson
Affiliation:
Physical Chemistry LaboratoryOxford (Now at King's College, London)
G. S. Rushbrooke
Affiliation:
Chemistry LaboratoryLeeds
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Extract

It is well known (1) that for an unsaturated hydrocarbon of the type CnHn+2 (where n is the number of carbon atoms in the linear chain), the theory of molecular orbitals applied to calculate the binding energy of the mobile π-electrons leads to the secular determinant, of continuant type,

where β is the resonance integral between adjacent carbon centres and x stands for the quantity generally written E0 − E, E being the energy of a mobile electron, which we seek to calculate. The equation for the allowed energies E is, of course, simply Pn = 0.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 44 , Issue 2 , April 1948 , pp. 272 - 279
Copyright
Copyright © Cambridge Philosophical Society 1948

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References

REFERENCES

(1)Lennard-Jones, J. E. and Coulson, C. A.Trans. Faraday Soc. 35 (1939), 811.CrossRefGoogle Scholar
(2)Coulson, C. A.Proc. Roy. Soc. A, 164 (1938), 383.Google Scholar
(3)Mott, N. F. and Jones, H.Theory of metals and alloys (Oxford University Press, 1936).Google Scholar
(4)Goodwin, E. T.Proc. Cambridge Phil. Soc. 35 (1939), 205.CrossRefGoogle Scholar
(5)Lennard-Jones, J. E.Proc. Roy. Soc. A, 158 (1937), 280.Google Scholar
(6)Bradburn, M., Coulson, C. A. and Rushbrooke, G. S.Proc. Roy. Soc. Edinb. A (in the Press).Google Scholar