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Hi! The statement that the Hellmann-Feynman (HF) theorem only holds "for the exact wave function" is misleading, and the following example actually wrong. The HF theorem holds for any wavefunction that satisfies a variational principle in a functional space that does not depend on λ. Of course, if the variational principle is an approximate one (as it is the case in the Hartree-Fock theory), the resulting derivative is approximate, but in a sense that deserves further qualification: it is in fact the exact derivative of an approximate energy. If the wavefunction does not result from a variational principle (or if it does so in such a way that the functional space depends on λ-for instance when the basis set depends on λ), then further contributions to the derivative (the so called "Pulay forces") have to be considered. The statement that the HF theorem does not hold in Hartree Fock contradicts several decades of quantum chemistry and should be corrected. Stefano Baroni, SISSA, Trieste (Italy)
