Pseudopotential

The pseudopotential formalism in quantum mechanics is an approach to approximate the computationally intensive near-core (non- valence ) electrons of an atom or ion and the nucleus by an effective potential. This approach is possible because the core electrons hardly contribute to chemical bonds. However, valence electrons are orthogonal to all the core electrons, resulting in a strong Oszilation near the core and therefore to a high computational effort. In addition, close to the core electrons have high energy, which means a short wavelength, which must be calculated with a high spatial resolution. Careful selection of an empirical potential can estimate the effort for solving the Schrödinger equation reduce massively. The wave function of the valence electrons is then orthogonal to all core states.

The pseudopotential was first introduced in 1934 by Hans Hellmann. The method was widely used in band structure calculations in solid state physics, where James C. Phillips in the late 1950s was a pioneer (later with Marvin Cohen, Volker Heine and others).

Approximations

Species

There are two classes of pseudo- potentials ( PP): Standard - conserving PP and Ultra Soft PP.

Norm - conserving ( standard -preserving ) PP: Outside a certain radius ( cutoff radius), the PP wave functions are identical to the real (all- electron ) WF. eg BHS- PP, Bachelet, Hamann, Schlüter ( Hamann et al., 1982)

Ultrasoft PP were introduced by David Vanderbilt [ Phys. Rev. B 41.7892, (1990 ) ] and have the advantage that the wave functions still " smooth ", ie for the same accuracy, a significantly lower number of plane waves to describe need, and thus the computation time is even lower. A disadvantage of these potentials is that the atomic orbitals no longer form an orthonormal system.

Both types of pseudo- potentials are "non- local", which means that the potential function of the angular momentum quantum number.