Erratum: Band convergence and linearization error correction of all-electron<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>G</mml:mi><mml:mi>W</mml:mi></mml:mrow></mml:math>calculations: The extreme case of zinc oxide [Phys. Rev. B10.1103/PhysRevB.83.081101<b>83</b>, 081101(R) (2011)]

Friedrich, Christoph; Müller, Mathias C. T. D.; Blügel, Stefan

doi:10.1103/physrevb.84.039906

Cited by 67 publications

(86 citation statements)

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“…It is well known, and zinc oxide is a prominent example of it, 72,73 that, similarly to the KS response function in EXX-OEP, GW calculations usually converge badly with respect to the basis set and the number of unoccupied states.…”

Section: Discussionmentioning

confidence: 99%

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

et al. 2012

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The optimized-effective-potential method is a special technique to construct local Kohn-Sham potentials from general orbital-dependent energy functionals. In a recent publication [M. Betzinger, C. Friedrich, S. Blügel, A. Görling, Phys. Rev. B 83, 045105 (2011)] we showed that uneconomically large basis sets were required to obtain a smooth local potential without spurious oscillations within the full-potential linearized augmented-planewave method. This could be attributed to the slow convergence behavior of the density response function. In this paper, we derive an incomplete-basis-set correction for the response, which consists of two terms: (1) a correction that is formally similar to the Pulay correction in atomic-force calculations and (2) a numerically more important basis response term originating from the potential dependence of the basis functions. The basis response term is constructed from the solutions of radial Sternheimer equations in the muffin-tin spheres. With these corrections the local potential converges at much smaller basis sets, at much fewer states, and its construction becomes numerically very stable. We analyze the improvements for rock-salt ScN and report results for BN, AlN, and GaN, as well as the perovskites CaTiO 3 , SrTiO 3 , and BaTiO 3 . The incomplete-basis-set correction can be applied to other electronic-structure methods with potential-dependent basis sets and opens the perspective to investigate a broad spectrum of problems in theoretical solid-state physics that involve response functions.

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Section: Discussionmentioning

confidence: 99%

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

et al. 2012

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“…We trimmed the SC/40 database by deleting seven of the semiconductors for which there are no experimental values for either the lattice constant, the bandgap, or both and three semiconductors for which we had serious difficulties in obtaining converged self-consistent field solutions, even using a very high number of k points. This leaves 30 semiconductors, to which we added ZnO data 32,33 because of its importance in applications, [34][35][36][37][38] and strong theoretical interest, [39][40][41][42][43] for a total of 31 semiconductors. We then created two databases, SLC34 with 34 semiconductor lattice constants and SBG31 with 31 semiconductor bandgaps.…”

Section: Test Set and Computational Detailsmentioning

confidence: 99%

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

Peverati¹,

Truhlar²

2012

The Journal of Chemical Physics

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The recently developed SOGGA11 and M11-L density functionals have been tested for the prediction of bandgaps and lattice constants by comparing to databases containing 31 bandgaps and 34 lattice constants. To make a comparative assessment we also test several other density functionals against the same databases; in particular, we test the local spin density approximation, PBE, PBEsol, SOGGA, TPSS, revTPSS, and M06-L local density functionals and the HSE screened-exchange hybrid nonlocal density functional; and for a subset of 13 lattice constants we also compare the mean errors to those of the AM05 and WC local density functionals and the HISS and HSEsol nonlocal density functionals. The tests show that, of the ten functionals tested against all 65 data, the SOGGA, PBEsol, and HSE functionals are the most accurate for lattice constants, whereas the HSE, M11-L, and M06-L density functionals are the most accurate for bandgaps. However, the SOGGA11 density functional is the most accurate generalized gradient approximation for bandgaps.

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“…Indeed, the truncation error of the quasiparticle band gap in solids appears to exhibit the same exponent. 34 If confirmed, this would enable practical direct extrapolation schemes with an appropriate fitting function, implying enormous potential benefits for computationally expensive ab initio calculations. Furthermore, if some way was known to determine the relevant prefactor based on general characteristics of the material in question, then even an a posteriori correction without the ambiguities of numerical fitting procedures would be possible.…”

Section: Discussionmentioning

confidence: 99%

“…The leading term is proportional to E −1 cut but of small absolute magnitude, because the renormalization factors (27) (32), (34), and (35). In the latter case, only the term proportional to E −3/2 cut is included.…”

Section: Asymptotic Convergencementioning

confidence: 99%

“…33 However, a similarly slow convergence was again observed in an all-electron calculation for zinc oxide that not only avoided plasmon-pole models but also the additional pseudopotential approximation. 34 Parallel to these developments, different approaches were proposed to circumvent or at least alleviate the convergence problem. These include the replacement of all high-lying empty states by plane waves, 35 the extrapolar method, 31 in which merely a small number of unoccupied states are treated explicitly and a common energy denominator is assigned to the remainder, so that the closure relation can be applied, the Lanczos-chain algorithm, 36 as well as the effective-energy technique 37 and methods based on the self-consistent Sternheimer equation, 38 which are formally exact despite only involving occupied states.…”

Section: Introductionmentioning

confidence: 99%

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Analytic evaluation of the electronic self-energy in theGWapproximation for two electrons on a sphere

Schindlmayr

2013

Phys. Rev. B

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The GW approximation for the electronic self-energy is an important tool for the quantitative prediction of excited states in solids, but its mathematical exploration is hampered by the fact that it must, in general, be evaluated numerically even for very simple systems. In this paper I describe a nontrivial model consisting of two electrons on the surface of a sphere, interacting with the normal long-range Coulomb potential, and show that the GW self-energy, in the absence of self-consistency, can in fact be derived completely analytically in this case. The resulting expression is subsequently used to analyze the convergence of the energy gap between the highest occupied and the lowest unoccupied quasiparticle orbital with respect to the total number of states included in the spectral summations. The asymptotic formula for the truncation error obtained in this way, whose dominant contribution is proportional to the cutoff energy to the power −3/2, may be adapted to extrapolate energy gaps in other systems.

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Erratum: Band convergence and linearization error correction of all-electronGWcalculations: The extreme case of zinc oxide [Phys. Rev. B10.1103/PhysRevB.83.08110183, 081101(R) (2011)]

Cited by 67 publications

References 0 publications

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

Precise response functions in all-electron methods: Application to the optimized-effective-potential approach

Performance of the M11-L density functional for bandgaps and lattice constants of unary and binary semiconductors

Analytic evaluation of the electronic self-energy in theGWapproximation for two electrons on a sphere

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