Extending the precision and efficiency of the all-electron full-potential linearized augmented plane-wave density-functional theory method
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Beschreibung
Density functional theory (DFT) is the most widely-used first-principles theory for
analyzing, describing and predicting the properties of solids based on the fundamental
laws of quantum mechanics. The success of the theory is a consequence of
powerful approximations to the unknown exchange and correlation energy of the
interacting electrons and of sophisticated electronic structure methods that enable
the computation of the density functional equations on a computer. A widely used
electronic structure method is the full-potential linearized augmented plane-wave
(FLAPW) method, that is considered to be one of the most precise methods of its kind
and often referred to as a standard. Challenged by the demand of treating chemically
and structurally increasingly more complex solids, in this thesis this method is revisited
and extended along two different directions: (i) precision and (ii) efficiency.
In the full-potential linearized augmented plane-wave method the space of a solid
is partitioned into nearly touching spheres, centered at each atom, and the remaining
interstitial region between the spheres. The Kohn-Sham orbitals, which are used to
construct the electron density, the essential quantity in DFT, are expanded into a linearized
augmented plane-wave basis, which consists of plane waves in the interstitial
region and angular momentum dependent radial functions in the spheres.
In this thesis it is shown that for certain types of materials, e.g., materials with
very broad electron bands or large band gaps, or materials that allow the usage of
large space-filling spheres, the variational freedom of the basis in the spheres has to
be extended in order to represent the Kohn-Sham orbitals with high precision over a
large energy spread. Two kinds of additional radial functions confined to the spheres,
so-called local orbitals, are evaluated and found to successfully eliminate this error.
A new efficient basis set is developed, named linearized augmented lattice-adapted
plane-wave ((LA)2PW) basis, that enables substantially faster calculations at controlled
precision. The basic idea of this basis is to increase the efficiency of the representation
in the interstitial region by using linear combinations of plane waves,
instead of single plane waves, adapted to the crystal lattice and potential of the solid.
The starting point for this development is an investigation of the basis-set requirements
and the changes of the basis set throughout the iterative self-consistency loop
inherent to density functional theory. The results suggest the construction of a basis
that is given by eigenfunctions of the first iteration. The precision and efficiency
of this basis from early eigenfunctions is evaluated on a test set of materials with
different properties and for a wide spectrum of physical quantities.
Autor*in
Gregor Michalicek
Themen in »Extending the precision and efficiency of the all-electron full-potential linearized augmented plane-wave density-functional theory method«
DFT Density functional theory Plane-wave method