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The |L = 0, S = 0〉 state of the N = 4 dot was the only one that did not agree, for reasons that we do not understand Since the DMC energy was the lower one for this state, the discrepancy cannot be due to the fixed-node error
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for an example where the energy obtained need not be an upper bound
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See W.M.C. Foulkes, R.Q. Hood, R.J. Needs, Phys. Rev. B 60, 4558 (1999) for an example where the energy obtained need not be an upper bound
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edited by J.M. Seminario Elsevier, Amsterdam
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The HF approximation gives oscillations that are a bit too large for atomic densities as well. See, e.g., C. Filippi, X. Gonze, C.J. Umrigar, Recent Developments and Applications of Density Functional Theory, edited by J.M. Seminario (Elsevier, Amsterdam, 1996)
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