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Single-centre expansions for the hydrogen molecular ion. II

Published online by Cambridge University Press:  24 October 2008

M. Cohen
M. Cohen
Affiliation:
Department of Applied MathematicsThe Queen's University of Belfast
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Extract

In an earlier paper (Cohen and Coulson(3), referred to hereafter as I), it was shown that satisfactory energy eigenvalues and eigenfunctions for various even σ-states of may be obtained using a single-centre expansion, provided that the radial functions are properly determined. In particular, the ground-state energy at the equilibrium internuclear separation of 2 a.u. was found to be within 0·25% of the exact value (Bates, Ledsham and Stewart (2)), and the eigenfunction reproduced all the characteristics of the exact wave-function. The method has now been extended to the odd σ-states, as well as to the two lowest π-states (2pπu, 3dπg), and the results are in good agreement with the calculations of Bates et al.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 58 , Issue 1 , January 1962 , pp. 130 - 135
Copyright
Copyright © Cambridge Philosophical Society 1962

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References

REFERENCES

(1)Adams, J. C.Collected scientific papers, vol. II (Cambridge, 1900).Google Scholar
(2)Bates, D. R., Kathleen, Ledsham and Stewart, A. L.Philos. Trans. Roy. Soc. London, Ser. A, 246 (1953), 215.Google Scholar
(3)Cohen, M. and Coulson, C. A.Proc. Cambridge Philos. Soc. 57 (1961), 96.CrossRefGoogle Scholar
(4)Edmonds, A. R.Angular momentum in quantum mechanics (Princeton, 1957).CrossRefGoogle Scholar
(5)Simon, A.Numerical table of the Clebsch–Gordon coefficients (Oak Ridge National Labora-tory, ORNL-1718, 1954).Google Scholar