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Four different types of perturbation theories for the exchange forces between two atoms are applied to the lowest gerade and ungerade state of a simple one-dimensional model. It is shown that the second-order energy in one of the expansions (the Eisenschitz–London, van der Avoird, or Hirschfelder HAV expansion) exhibits undesirable behavior in the limit corresponding to large internuclear distances.
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Phillip R. Certain (1968) studied this question.
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