The Pseudopotential Approximation in Electronic Structure Theory

Abstract

A short review is presented on one of the most successful theories for electronic structure calculations, the pseudopotential approximation, originally introduced by Hans G. A. Hellmann in 1934. Recent developments in relativistic quantum theory allow for the accurate adjustment of pseudopotential parameters to valence spectra, producing results for properties of atoms, molecules, and the solid-state in excellent agreement with more accurate all-electron results if a small-core definition is used. Thus the relativistic pseudopotential approximation is now the most widely applied method for systems containing heavy elements.

Relativistic Pseudopotentials and Their Applications

“…This operator keeps the valence electrons out of the core and in the valence space, i.e., it is repulsive in the short-range and attractive in the long-range [6]. The main task for the PP development is now to find an analytical form, i.e., a suitable parametrization, forV I PP , which is able to compensate for all errors introduced by the simplification of the original Hamiltonian and at the same time easily applicable [19].…”

“…The analytical form applied for PPs nowadays is the semilocal ansatz (local in the coordinate r, but nonlocal in spherical angle coordinates θ and φ [6]), which goes back to Abarenkov and Heine working in the field of solid states [29,30] and was introduced a few years later to quantum chemistry by Schwarz [31] as well as Kahn and Goddard [32]. In this ansatz besides the r-dependency of the PP also a l-dependency, i.e., a dependency on the angular momentum quantum number l, is taken into account.…”

“…has been taken in the adjustment, the error produced by the ECP approximation is almost always smaller than the error due to the ab initio electron correlation or density functional procedure [6].…”

“…For further reading the minireview on the PP approximation by Schwerdtfeger [6], the rigorous recent review on relativistic PPs by Dolg and Cao [19], and the relatively complete list of older reviews given in the latter are recommended.…”

Two-extremum electrostatic potential of metal-lattice plasma and the work function of an electron

“…In metals theory based on valence electrons, different pseudopotential approximations are employed to compensate the ion core Coulomb potential [1][2][3][4][5][6]. One of such approaches together with density-functional theory [7] based approximations and perturbation methods, for treating the electron interactions in different states of matter and elements, is the pseudopotential plane wave method, apart from other or mixed methods.…”