Efficient implementation of theGWapproximation within the all-electron FLAPW method

Abstract

We present an implementation of the GW approximation for the electronic self-energy within the full-potential linearized augmented-plane-wave (FLAPW) method. The algorithm uses an allelectron mixed product basis for the representation of response matrices and related quantities. This basis is derived from the FLAPW basis and is exact for wave-function products. The correlation part of the self-energy is calculated on the imaginary frequency axis with a subsequent analytic continuation to the real axis. As an alternative we can perform the frequency convolution of the Green function G and the dynamically screened Coulomb interaction W explicitly by a contour integration. The singularity of the bare and screened interaction potentials gives rise to a numerically important self-energy contribution, which we treat analytically to achieve good convergence with respect to the k-point sampling. As numerical realizations of the GW approximation typically suffer from the high computational expense required for the evaluation of the nonlocal and frequencydependent self-energy, we demonstrate how the algorithm can be made very efficient by exploiting spatial and time-reversal symmetry as well as by applying an optimization of the mixed product basis that retains only the numerically important contributions of the electron-electron interaction. This optimization step reduces the basis size without compromising the accuracy and accelerates the code considerably. Furthermore, we demonstrate that one can employ an extrapolar approximation for high-lying states to reduce the number of empty states that must be taken into account explicitly in the construction of the polarization function and the self-energy. We show convergence tests, CPU timings, and results for prototype semiconductors and insulators as well as ferromagnetic nickel.

HSE hybrid functional within the FLAPW method and its application to GdN

“…In this way, the MPB is on the same level of accuracy as the all-electron LAPW basis for the wave functions. It was shown 41,54 that G max and L max can be well below their mathematically determined exact limit, i.e., 2G max and 2l max , and even below G max and l max , which makes the MPB a very efficient basis. Further details about the MPB can be found elsewhere.…”

Local exact exchange potentials within the all-electron FLAPW method and a comparison with pseudopotential results

“…The OEP equation is formulated utilizing the mixed product basis (MPB), [42][43][44] which has been adjusted for the present purpose: it is augmented with the atomic EXX potential, the constant function is eliminated, and the basis functions are made continuous all over the space. In this basis, the OEP equation becomes an algebraic equation, which is solved for the local EXX potential with standard numerical tools.…”

“…(13) are defined in terms of wavefunction products, the basis should be constructed foremost of products of LAPW basis functions. In recent publications we have already used such a mixed product basis (MPB), which was first proposed by Kotani and van Schilfgaarde, 41 to implement hybrid functionals 42 and the GW approximation 43 as well as to calculate EELS spectra. 44 However, we introduce a slightly modified version for the present purpose: (1) as the potential is strictly periodic, the MPB may be restricted to k = 0; (2) we add the atomic EXX potential as a basis function; and (3) we make the functions M I (r) continuous over the whole space.…”

Role of surface passivation in the formation of Dirac states at polar surfaces of topological crystalline insulators: The case of SnTe(111)

“…The manybody corrections were found within the one-shot GW approach as realized by the SPEX code [25]. The spin-orbit interaction was included into the GW calculations already at the DFT level [26].…”

“…The Fermi level was placed in the middle of the band gap. In the GW calculations, the dielectric matrix was evaluated within the random-phase approximation and represented with the use of the mixed product basis [25,30], where we chose an angular momentum cutoff in the muffin-tin spheres of 4 and a linear momentum cutoff of 3.5 bohr −1 . The GW quasiparticle spectrum presented in this paper was obtained with number of bands N b = 700 (occupied and unoccupied bands within the energy window of 350 eV centered at the Fermi level) and a less dense k-point mesh (5 × 5 × 5) than in the GGA calculations.…”