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The norm-conserving pseudopotential approach provides an effective and
reliable means for performing calculations on complex molecular, liquid and
solid state systems using plane wave basis sets.
In this approach only the chemically active valence electrons are dealt
with explicitely. The inert core electrons are eliminated within the frozen-core approximation,
being considered together with the nuclei as rigid non-polarizable ion cores.
In turn, all electrostatic and quantum-mechanical
interactions of the valence electrons with the cores, as the nuclear Coulomb attraction
screened by the core electrons, Pauli repulsion and exchange and correlation
between core and valence electrons, are accounted for by angular momentum
dependent pseudopotentials. These reproduce the true potential and valence
orbitals outside a chosen core region but remain much weaker and smoother inside.
The valence electrons are described by smooth pseudo orbitals which play the same role as the
true orbitals, but avoid the nodal structure near the nuclei that keeps the core
and valence states orthogonal in an all-electron framework.
The respective Pauli repulsion largely cancels the attractive parts of
the true potential in the core region, and is built into the therefore rather
weak pseudopotential. This pseudoization of the valence wavefunctions along with
the removal of the core states eminently facilitates a numerically accurate solution
of the Kohn-Sham equations and the Poisson equation, and enables the use
of plane waves as an expedient basis set in electronic structure calculations.
By virtue of the norm-conservation property and when constructed carefully
pseudopotentials present a rather marginal approximation, and indeed allow for an
adequate description of the valence electrons over the entire
chemically relevant range of systems.
Next: Why Pseudopotentials ?
Up: Calculating the Electronic Structure
Previous: Localized Orbitals, Wannier Functions
Contents
Index
Costas Bekas
2008-07-04