Phonons from Density-Functional Perturbation Theory using the All-Electron Full-Potential Linearized Augmented Plane-Wave Method FLEUR
Christian-Roman Gerhorst, Alexander Neukirchen, Daniel A. Klüppelberg, Gustav Bihlmayer, Markus Betzinger, Gregor Michalicek, Daniel Wortmann, Stefan Blügel
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.
Convergence in self-consistent-field cycles can be a major computational bottleneck of density-functional theory calculations. We propose a Resta-like preconditioning method for full-potential all-electron calculations in the linearized augmented planewave (LAPW) method to smoothly converge to self-consistency. We implemented this preconditioner in the exciting code and apply it to the two semiconducting systems of MoS$_2$ slabs and P-rich GaP(100) surfaces as well as the metallic system Au(111), containing a sufficiently large amount of vacuum. Our calculations demonstrate that the implemente…
We present an implementaion of interface between the full-potential linearized augmented plane wave package Wien2k and the wannier90 code for the construction of maximally localized Wannier functions. The FORTRAN code and a documentation is made available and results are discussed for SrVO$_3$, Sr$_2$IrO$_4$ (including spin-orbit coupling), LaFeAsO, and FeSb$_2$.
The Kohn-Sham orbital kinetic energy density $τ_σ(\vec{r}) = \sum_{i} w_{iσ} \big|\nabla ψ_{iσ}(\vec{r}) \big|^2$ is one fundamental quantity for constructing meta-generalized gradient approximations (meta-GGA) for use by density functional theory. We present a computational scheme of $τ_σ(\vec{r})$ for full-potential linearized augmented plane wave method. Our scheme is highly accurate and efficient and easy to implement to existing computer code. To illustrate its performance, we construct the Becke-Johnson meta-GGA exchange potentials for Be, Ne, Mg, Ar, Ca, Zn, Kr, Cd atoms which are in ve…
X-ray absorption and its dependence on the polarization of light is a powerful tool to investigate the orbital and spin moments of magnetic materials and their orientation relative to crystalline axes. Here, we present a program for the calculation of dichroic spectra from first principles. We have implemented the calculation of x-ray absorption spectra for left and right circularly polarized light into the Wien2k code. In this package, spin-density functional theory is applied in an all-electron scheme that allows to describe both core and valence electrons on the same footing. The matrix ele…
We devise a mixing algorithm for full-potential (FP) all-electron calculations in the linearized augmented planewave (LAPW) method. Pulay's direct inversion in the iterative subspace is complemented with the Kerker preconditioner and further improvements to achieve smooth convergence, avoiding charge sloshing and noise in the exchange-correlation potential. As the Kerker preconditioner was originally designed for the planewave basis, we have adapted it to the FP-LAPW method and implemented in the exciting code. Applications to the $2\times 2$ Au(111) surface with a vacancy and to the Pd(111) s…
In order to increase the accuracy of the linearized augmented plane wave method (LAPW) we present a new approach where the plane wave basis function is augmented by two different atomic radial components constructed at two different linearization energies corresponding to two different electron bands (or energy windows). We demonstrate that this case can be reduced to the standard treatment within the LAPW paradigm where the usual basis set is enriched by the basis functions of the tight binding type, which go to zero with zero derivative at the sphere boundary. We show that the task is closel…
We provide accurate projected augmented wave (PAW) datasets for rare-earth (RE) elements with some suggested Hubbard U values allowing efficient plane-wave calculations. Solid state tests of generated datasets were performed on rare-earth nitrides. Through density of state (DOS) and equation of state (EoS) comparisons, generated datasets were shown to yield excellent results comparable to highly accurate all-electron full-potential linearized augmented plane-wave plus local orbital (FLAPW+LO) calculations. Hubbard U values for trivalent RE ions are determined according to hybrid functional cal…
The $GW$ approach of many-body perturbation theory (MBPT) has become a common tool for calculating the electronic structure of materials. However, with increasing number of published results, discrepancies between the values obtained by different methods and codes become more and more apparent. For a test set of small- and wide-gap semiconductors, we demonstrate how to reach the numerically \emph{best} electronic structure within the framework of the full-potential linearized augmented planewave (FLAPW) method. We first evaluate the impact of local orbitals in the Kohn-Sham eigenvalue spectrum…
In the Projector Augmented Wave (PAW) method, a local potential, basis functions, and projector functions form an All-Electron (AE) basis for valence wave functions in the application of Density Functional Theory (DFT). The construction of these potentials, basis functions and projector functions for each element can be complex, and several codes capable of utilizing the PAW method have been otherwise prevented from its use by the lack of PAW basis sets for all atoms. We have developed a procedure that improves the ease and efficiency of construction of PAW basis sets. An evolutionary algorith…
Implementation and application of a DFT$+U$$+V$ approach within the all-electron FLAPW method
Peter Grünberg Institut, Forschungszentrum Jülich and JARA（彼得·格林伯格研究所，于利希研究中心和JARA）；Institute for Theoretical Physics, RWTH Aachen University（亚琛工业大学理论物理研究所）
We have developed an efficient computational scheme utilizing the real-space finite-difference formalism and the projector augmented-wave (PAW) method to perform precise first-principles electronic-structure simulations based on the density functional theory for systems containing transition metals with a modest computational effort. By combining the advantages of the time-saving double-grid technique and the Fourier filtering procedure for the projectors of pseudopotentials, we can overcome the egg box effect in the computations even for first-row elements and transition metals, which is a pr…
Total and partial density of states, frequency dependent complex refractive index including extinction coefficient, optical conductivity and transmission of MgxZn1-xO (0 \leq x \leq 1) in rocksalt and wurtzite phases are calculated using full potential linearized augmented plane wave (FP-LAPW) method. The real part of refractive index decreases while the extinction coefficient, optical conductivity and transmission for rocksalt phase increases with the increase in Mg concentration. In wurtzite phase, ordinary and extraordinary indices decreases while extinction coefficient, optical conductivit…
The method based on fast Fourier transforms proposed by G. Román-Pérez and J. M. Soler [Phys. Rev. Lett. 103, 096102 (2009)], which allows for a computationally fast implementation of the nonlocal van der Waals (vdW) functionals, has significantly contributed to making the vdW functionals popular in solid-state physics. However, the Román-Pérez-Soler method relies on a plane-wave expansion of the electron density; therefore it can not be applied readily to all-electron densities for which an unaffordable number of plane waves would be required for an accurate expansion. In this work, we presen…
Linearized augmented planewaves combined with local-orbitals (LAPW+lo) are arguably the most precise basis set to represent Kohn-Sham states. When employed within real-time time-dependent density functional theory (RT-TDDFT), they promise ultimate precision achievable for exploring the evolution of electronic excitations. In this work, we present an implementation of RT-TDDFT in the full-potential LAPW+lo code exciting. We benchmark our results against those obtained by linear-response TDDFT with exciting and by RT-TDDFT calculations with the Octopus code, finding a satisfactory level of agree…
Using the full potential linearized augmented plane wave plus local orbitals method we determine ab-initio the lattice parameters of tetragonally distorted Co2TiSn in the L21 structure. The tetragonal lattice parameter c is determined as a function of the lattice parameter a by energy minimization. The change in total energy is found to be only a few $k_B T$ with respect to room temperature. The spin polarizations as well as the magnetizations are stable against small lattice distortions. It is shown, that the volume is not constant upon distortion and that the volume change is related with si…
The electronic structures of tetragonally distorted half-Heuselr compound LaPtBi in the C1b structure are investigated in the framework of density functional theory using the full potential linearized augmented plane with local spin density approximation method. The calculation results show that both the band structures and the Fermi level can be tuned by using either compressive or tensile in-plane strain. A large bulk band gap of 0.3 eV can be induced through the application of a compressive in-pane strain in LaPtBi with the assumption of a relaxed volume of the unit cell. Our results could …
We report APW+${lo}$ (augmented plane wave plus local orbital) density functional theory (DFT) calculations of molecule systems using the domain specific SIRIUS multi-functional DFT package. Compared to other packages the additional APW and FLAPW task and data parallelism and the additional eigensystem solver provided by the SIRIUS package can be exploited for performance gains in in the ground state Kohn-Sham calculation. This is in contrast with the use of SIRIUS as a library backend to some other APW+${lo}$ or FLAPW (full-potential linearized AWP) code. We benchmark the code and demonstrate…
As a second part of a previous paper, here the calculated electronic band structure of ideal Pt(100) and Pt(110) surfaces, studied using density functional theory and the empirical tight-binding method, is presented. A detailed discussion of the surface- and resonance--states is given. It is shown that the calculated surface- and resonance--states of ideal Pt(100) surfaces agree very well with the available experimental data. For Pt(110), some of the surface- and resonance-states are characteristic of the low degree of symmetry of the surface and are identified as being independent of surface …
We describe the software package SPEX, which allows first-principles calculations of quasiparticle and collective electronic excitations in solids using techniques from many-body perturbation theory. The implementation is based on the full-potential linearized augmented-plane-wave (FLAPW) method, which treats core and valence electrons on an equal footing and can be applied to a wide range of materials, including transition metals and rare earths. After a discussion of essential features that contribute to the high numerical efficiency of the code, we present illustrative results for quasipart…
The exact-exchange (EXX) potential, which is obtained by solving the optimized-effective potential (OEP) equation, is compared to various approximate semilocal exchange potentials for a set of selected solids (C, Si, BN, MgO, Cu$_{2}$O, and NiO). This is done in the framework of the linearized augmented plane-wave method, which allows for a very accurate all-electron solution of electronic structure problems in solids. In order to assess the ability of the semilocal potentials to approximate the EXX-OEP, we considered the EXX total energy, electronic structure, electric-field gradient, and mag…
We present results of extensive theoretical studies of Co$_2$FeAl$_{1-x}$Si$_x$ Heusler alloys, which have been performed in the framework of density functional theory employing the all-electron full-potential linearized augmented plane-wave scheme. It is shown that the Si-rich alloys are more resistive to structural disorder and as a consequence Si stabilizes the $L2_1$ structure. Si alloying changes position of the Fermi level, pushing it into the gap of the minority spin-band. It is also shown that the hyperfine field on Co nuclei increases with the Si concentration, and this increase origi…
To address ultimate precision in density-functional-theory calculations we employ the full-potential linearized augmented planewave + local-orbital (LAPW+lo) method and justify its usage as a benchmark method. LAPW+lo and two completely unrelated numerical approaches, multi-resolution analysis (MRA) and linear combination of atomic orbitals, yield total energies of atoms with a mean deviation of 0.9~μHa and 0.2~μHa, respectively. Spectacular agreement with the MRA is reached also for total and atomization energies of the G2-1 set consisting of 55 molecules. With the example of $α$-iron we demo…
Correlation effects play an important role in the electronic structure of half-metallic (HM) magnets. In particular, they give rise to non-quasiparticle states above (or below) the Fermi energy at finite temperatures that reduce the spin polarization and, as a consequence, the efficiency of spintronics devices. Employing the constrained random-phase approximation (cRPA) within the full-potential linearized augmented-plane-wave (FLAPW) method using maximally localized Wannier functions, we calculate the strength of the effective on-site Coulomb interaction (Hubbard $U$ and Hund exchange $J$) be…
In this paper, we report the implementation of first-principles calculations of topological invariants Z2 within the full-potential linearized augmented plane-wave (FP-LAPW) formalism. In systems with both time-reversal and spatial inversion symmetry (centrosymmetric), one can use the parity analysis of Bloch functions at time-reversal invariant momenta to determine the Z2 invariants. In systems without spatial inversion symmetry (noncentrosymmetric), however, a more complex and systematic method in terms of the Berry gauge potential and the Berry curvature is required to identify the band top…
