Some Remarks on the Use of the Variational Principle for the Second-Order Energy

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Abstract
It is shown that the second-order energy correction calculated by means of the Hylleraas variation principle with an approximate zero-order function need bear no special relationship to the true value. In particular, there may be considerable deviation from the true value even if the approximate zero-order wavefunction is nearly exact, unless one requires that the trial function be orthogonal to the approximate zero-order function.

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