  We investigate the properties of norm-conserving pseudopotentials (effective
core potentials) generated by inversion of the Hartree-Fock equations. In
particular we investigate the asymptotic behaviour as $\mathbf{r} \to \infty$
and find that such pseudopotentials are non-local over all space, apart from a
few special special cases such H and He. Such extreme non-locality leads to a
lack of transferability and, within periodic boundary conditions, an undefined
total energy. The extreme non-locality must therefore be removed, and we argue
that the best way to accomplish this is a minor relaxation of the
norm-conservation condition. This is implemented, and pseudopotentials for the
atoms H$-$Ar are constructed and tested.
