The Hooke model for the two‐electron atom replaces the electron–nuclear interaction by a harmonic oscillator potential, but retains the Coulomb repulsion of the electrons. The first‐order perturbation equation for the electron repulsion is solved analytically, and the exact first‐, second‐, and third‐order perturbation energies are obtained. A similar perturbation treatment is carried out for the Hartree–Fock equation and other variational approximations. The expansion of the correlation energy is compared with that for heliumlike atoms and found to be similar.
REFERENCES
1.
J. O. Hirschfelder, W. B. Brown, and S. T. Epstein in Advances in Quantum Chemistry, edited by P.‐O. Löwdin (Academic, New York, 1964), Vol. 1, p. 256.
2.
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Reference 1, p. 270.
8.
More details are presented in R. J. White and W. B. Brown, Wisc. Theoret. Chem. Inst. Tech. Rept. WIS‐TCI‐116 (1965).
9.
Reference 1, p. 271.
10.
11.
12.
L. Lewin, Dilogarithms and Associated Functions (Macdonald, London, 1958).
13.
14.
W. B. Brown (unpublished work).
An account of the two‐electron delta model atom is given in an appendix to
R. J.
White
and F. H.
Stillinger
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52
, 5800
(1970
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W. Gröbner and N. Hofreiter, Integraltafel (Springer, Vienna, 1966).
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© 1970 American Institute of Physics.
1970
American Institute of Physics
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