Abstract
This article points out a new aspect of approximate calculations of molecular potential curves. Two curves that cross in an exact solution of the electronic wave equation may avoid each other when an approximate method is used. This is in direct contradiction to the usual interpretation of the von Neumann-Wigner non-crossing rule. Examples of this behavior are shown in one-electron systems. The question is, to what extent are calculated avoidances real, and to what extent are they artifacts of incomplete calculations? We suggest that this question is unanswered at present and mention possible molecules for critical theoretical investigations.
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