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THE RELIABILITY OF THE HELLMANN-FEYNMAN THEOREM FOR APPROXIMATE CHARGE DENSITIES
HARVARD UNIV CAMBRIDGE MASS MALLINCKRODT LAB
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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 the correct force. For spherical atoms in an external field, the contribution of the continuum states to the electronic screening of the field is very large, 54 for H and about 72 for He. From this case also one can evolve general considerations concerning the use of effective nuclear charges in electrostatic force calculations. In the general case it is shown that for a system submitted to a given perturbation the wave function correct to order n, or the corresponding charge density, yields the force correct to order n and to order n only. This result leads to a brief comparison of the HellmannFeynman procedure and the variational meth d. Author
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