Extending the precision and efficiency of the all-electron full-potential linearized augmented plane-wave density-functional theory method

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.