Pseudopotential

From Wikipedia, the free encyclopedia

Comparison of a wavefunction in the Coulomb potential of the nucleus (blue) to the one in the pseudopotential (red). The real and the pseudo wavefunction and potentials match above a certain cutoff radius r_c.

In quantum mechanics, the pseudopotential approximation is an attempt to replace the complicated effects of the motion of the core (i.e. non-valence) electrons of an atom and its nucleus with an effective potential, or pseudopotential, so that the Schrödinger equation contains a modified effective potential term instead of e.g. the Coulombic potential term for core electrons normally found in the Schrödinger equation. The pseudopotential approximation was first introduced by Hans Hellmann in the 1930s. By construction of this pseudopotential, the valence wavefunction generated is also guaranteed to be orthogonal to all the core states.

[edit] Motivation

1. Reduction of basis set size
2. Reduction of number of electrons
3. Inclusion of relativistic and other effects

[edit] Approximations

1. one-electron picture
2. frozen-core approximation
3. small-core appr. assumes that there is no significant overlap between core and valence WF. So the exchange correlation potential( see DFT) is: E_xc(n_core + n_valence) = E_xc(n_core) + E_xc(n_valence); If this is not true, the non-linear core corrections technique (Louie et al., 1982) is used.

[edit] Types

Two kinds of PPs are used, Norm-conserving PP and Ultrasoft PP.

[edit] Norm-conserving PP

Norm-conserving PP: Outside of a cutoff-radius, the pseudo-wavefunctions are identical to the real all-electron WF.
e.g. BHS-PP, Bachelet,Hamann,Schlüter (Hamann et al., 1982)

[edit] Literature

Hans Hellmann in the Journal of Chemical Physics 3 61 (1935) and Journal of Chemical Physics 4 (1936), Harrison (1966), Brust (1968), Stoneham (1975), Heine (1970), Pickett (1989),..

see also: Density functional theory

This quantum mechanics-related article is a stub. You can help Wikipedia by expanding it.