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Register a new userHybrid functionals within the all-electron FLAPW method: implementation and applications of PBE0
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We present an efficient implementation of the PBE0 hybrid functional within the full-potential linearized augmented-plane-wave (FLAPW) method. The Hartree-Fock exchange term, which is a central ingredient of hybrid functionals, gives rise to a computationally expensive nonlocal potential in the one-particle Schroedinger equation. The matrix elements of this exchange potential are calculated with the help of an auxiliary basis that is constructed from products of FLAPW basis functions. By representing the Coulomb interaction in this basis the nonlocal exchange term becomes a Brillouin-zone (BZ) sum over vector-matrix-vector products. We show that the Coulomb matrix can be made sparse by a suitable unitary transformation of the auxiliary basis, which accelerates the computation of the vector-matrix-vector products considerably. Additionally, we exploit spatial and time-reversal symmetry to identify the nonvanishing exchange matrix elements in advance and to restrict the k summations for the nonlocal potential to an irreducible set of k points. Favorable convergence of the self-consistent-field cycle is achieved by a nested density-only and density-matrix iteration scheme. We discuss the convergence with respect to the parameters of our numerical scheme and show results for a variety of semiconductors and insulators, including oxide materials, where the PBE0 hybrid functional improves the band gaps and the description of localized states in comparison with the PBE functional. Furthermore, we find that in contrast to conventional local exchange-correlation functionals ferromagnetic EuO is correctly predicted to be a semiconductor.
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We present a general numerical approach to construct local Kohn-Sham potentials from orbital-dependent functionals within the all-electron full-potential linearized augmented-plane-wave (FLAPW) method, in which core and valence electrons are treated on an equal footing. As a practical example, we present a treatment of the orbital-dependent exact-exchange (EXX) energy and potential. A formulation in terms of a mixed product basis, which is constructed from products of LAPW basis functions, enables a solution of the optimized-effective-potential (OEP) equation with standard numerical algebraic tools and without shape approximations for the resulting potential. We find that the mixed product and LAPW basis sets must be properly balanced to obtain smooth and converged EXX potentials without spurious oscillations. The construction and convergence of the exchange potential is analyzed in detail for diamond. Our all-electron results for C, Si, SiC, Ge, GaAs semiconductors as well as Ne and Ar noble-gas solids are in very favorable agreement with plane-wave pseudopotential calculations. This confirms the adequacy of the pseudopotential approximation in the context of the EXX-OEP formalism and clarifies a previous contradiction between FLAPW and pseudopotential results.
The method based on fast Fourier transforms proposed by G. Roman-Perez 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 Roman-Perez-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 present the results for the lattice constant and binding energy of solids that were obtained by applying a smoothing procedure to the all-electron density calculated with the linearized augmented plane-wave method. The smoothing procedure has the advantages of being very simple to implement, basis-set independent, and allowing the calculation of the potential. It is also shown that the results agree very well with those from the literature that were obtained with the projector augmented wave method.
We report on the implementation of the Wannier Functions (WFs) formalism within the full-potential linearized augmented plane wave method (FLAPW), suitable for bulk, film and one-dimensional geometries. The details of the implementation, as well as results for the metallic SrVO3, ferroelectric BaTiO3 grown on SrTiO3, covalently bonded graphene and a one-dimensional Pt-chain are given. We discuss the effect of spin-orbit coupling on the Wannier Functions for the cases of SrVO3 and platinum. The dependency of the WFs on the choice of the localized trial orbitals as well as the difference between the maximally localized and first-guess WFs are discussed. Our results on SrVO3 and BaTiO3, e.g. the ferroelectric polarization of BaTiO3, are compared to results published elsewhere and found to be in excellent agreement.
Within density-functional theory, perturbation theory~(PT) is the state-of-the-art formalism for assessing the response to homogeneous electric fields and the associated material properties, e.g., polarizabilities, dielectric constants, and Raman intensities. Here we derive a real-space formulation of PT and present an implementation within the all-electron, numeric atom-centered orbitals electronic structure code FHI-aims that allows for massively-parallel calculations. As demonstrated by extensive validation, this allows the rapid computation of accurate response properties of molecules and solids. As an application showcase, we present harmonic and anharmonic Raman spectra, the latter obtained by combining hundreds of thousands of PT calculations with textit{ab initio} molecular dynamics. By using the PBE exchange-correlation functional with many-body van der Waals corrections, we obtain spectra in good agreement with experiment especially with respect to lineshapes for the isolated paracetamol molecule and two polymorphs of the paracetamol crystal.
We have implemented the so called GW approximation (GWA) based on an all-electron full-potential Projector Augmented Wave (PAW) method. For the screening of the Coulomb interaction W we tested three different plasmon-pole dielectric function models, and showed that the accuracy of the quasiparticle energies is not sensitive to the the details of these models. We have then applied this new method to compute the quasiparticle band structure of some small, medium and large-band-gap semiconductors: Si, GaAs, AlAs, InP, SiMg$_2$, C and (insulator) LiCl. A special attention was devoted to the convergence of the self-energy with respect to both the {bf k}-points in the Brillouin zone and to the number of reciprocal space $bf G$-vectors. The most important result is that although the all-electron GWA improves considerably the quasiparticle band structure of semiconductors, it does not always provide the correct energy band gaps as originally claimed by GWA pseudopotential type of calculations. We argue that the decoupling between the valence and core electrons is a problem, and is some what hidden in a pseudopotential type of approach.
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