A spherical atom is a uniform external field and the long-range interaction of 2 molecules are examples illustrating the unreliability of the Hellmann-Feynman theorem when applied to systems described by approximate wave functions or charge densities. However in the 1st case a wave function correct to 1st order in the perturbing field, and in the 2nd case a wave function correct to 2nd order in the mutual interaction, will yield ...
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