A theoretical foundation for the pseudopotential concept has been provided by switching from the Hartree-Fock framework to the $G1$ framework. The new method allows ab initio determinations of the potential and removes many of the serious theoretical difficulties which have plagued the pseudopotential approach. The potential from ab initio calculations on the Li atom using the new approach is reported, along with the Fourier transform of the potential. There are still practical difficulties in solving the equations for the pseudopotentials of large atoms.
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William A. Goddard (1968) studied this question.
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