Elimination of the linearization error and improved basis-set convergence within the FLAPW method

We analyze in detail the error that arises from the linearization in linearized augmented-plane-wave (LAPW) basis functions around predetermined energies $E_l$ and show that it can lead to undesirable dependences of the calculated results on method-inherent parameters such as energy parameters $E_l$ and muffin-tin sphere radii. To overcome these dependences, we evaluate approaches that eliminate the linearization error systematically by adding local orbitals (LOs) to the basis set. We consider two kinds of LOs: (i) constructed from solutions $u_l(r,E)$ to the scalar-relativistic approximation of the radial Dirac equation with $E>E_l$ and (ii) constructed from second energy derivatives $\partial^2 u_l(r,E) / \partial E^2$ at $E=E_l$. We find that the latter eliminates the error most efficiently and yields the density functional answer to many electronic and materials properties with very high precision. Finally, we demonstrate that the so constructed LAPW+LO basis shows a more favorable convergence behavior than the conventional LAPW basis due to a better decoupling of muffin-tin and interstitial regions, similarly to the related APW+lo approach, which requires an extra set of LOs to reach the same total energy, though.Comment: 12 pages, 15 figure

Phonons from Density-Functional Perturbation Theory using the All-Electron Full-Potential Linearized Augmented Plane-Wave Method FLEUR

Phonons are quantized vibrations of a crystal lattice that play a crucial role in understanding many properties of solids. Density functional theory (DFT) provides a state-of-the-art computational approach to lattice vibrations from first-principles. We present a successful software implementation for calculating phonons in the harmonic approximation, employing density-functional perturbation theory (DFPT) within the framework of the full-potential linearized augmented plane-wave (FLAPW) method as implemented in the electronic structure package FLEUR. The implementation, which involves the Sternheimer equation for the linear response of the wave function, charge density, and potential with respect to infinitesimal atomic displacements, as well as the setup of the dynamical matrix, is presented and the specifics due to the muffin-tin sphere centered LAPW basis-set and the all-electron nature are discussed. As a test, we calculate the phonon dispersion of several solids including an insulator, a semiconductor as well as several metals. The latter are comprised of magnetic, simple, and transition metals. The results are validated on the basis of phonon dispersions calculated using the finite displacement approach in conjunction with the FLEUR code and the phonopy package, as well as by some experimental results. An excellent agreement is obtained.Comment: 44 pages, 6 figure

How to verify the precision of density-functional-theory implementations via reproducible and universal workflows

In the past decades many density-functional theory methods and codes adopting periodic boundary conditions have been developed and are now extensively used in condensed matter physics and materials science research. Only in 2016, however, their precision (i.e., to which extent properties computed with different codes agree among each other) was systematically assessed on elemental crystals: a first crucial step to evaluate the reliability of such computations. We discuss here general recommendations for verification studies aiming at further testing precision and transferability of density-functional-theory computational approaches and codes. We illustrate such recommendations using a greatly expanded protocol covering the whole periodic table from Z=1 to 96 and characterizing 10 prototypical cubic compounds for each element: 4 unaries and 6 oxides, spanning a wide range of coordination numbers and oxidation states. The primary outcome is a reference dataset of 960 equations of state cross-checked between two all-electron codes, then used to verify and improve nine pseudopotential-based approaches. Such effort is facilitated by deploying AiiDA common workflows that perform automatic input parameter selection, provide identical input/output interfaces across codes, and ensure full reproducibility. Finally, we discuss the extent to which the current results for total energies can be reused for different goals (e.g., obtaining formation energies).Comment: Main text: 23 pages, 4 figures. Supplementary: 68 page

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 kindand 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) effciency.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)2 PW) 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