Pseudopotentials and physical ions

The eigenvalues of a bare norm-conserving ionic pseudopotential, derived from a full-core atom within the local-density-functional theory, agree rather accurately with the measured excitation energies of a single valence electron in the field of the ion for a good portion (about 1/4) of the Periodic Table. Such a remarkable property rests on a chain of approximate equalitities that are intrinsic to the pseudopotential construction, and holds to a good approximation for many atoms, with the exception of first-row transition metals, rare earths, and a few heavier elements. This explains a number of recent numerical findings and provides arguments and limits for the interpretation of many ionic pseudopotentials, constructed from single-particle theories, as true physical ions, and thus for their safe use in the context of modern quantum simulations for valence electrons.