Cited by 917Machine Learning in Materials ScienceAdvanced Chemical Physics StudiesHigh-pressure geophysics and materials

Precision and efficiency in solid-state pseudopotential calculations

Open access
Prandini, Gianluca, Marrazzo, Antimo, Castelli, Ivano E., Mounet, Nicolas, Marzari, Nicola·2018·npj Computational Materials

Abstract

Despite the enormous success and popularity of density-functional theory, systematic verification and validation studies are still limited in number and scope. Here, we propose a protocol to test publicly available pseudopotential libraries, based on several independent criteria including verification against all-electron equations of state and plane-wave convergence tests for phonon frequencies, band structure, cohesive energy and pressure. Adopting these criteria we obtain curated pseudopotential libraries (named SSSP or standard solid-state pseudopotential libraries), that we target for high-throughput materials screening (“SSSP efficiency”) and high-precision materials modelling (“SSSP precision”). This latter scores highest among open-source pseudopotential libraries available in the Δ-factor test of equations of states of elemental solids.

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Written from the paper’s full text.

TL;DR

The paper introduces the SSSP testing protocol, combining Δ-factor verification against all-electron equations of state with plane-wave convergence tests for phonons, cohesive energies, pressure, and band structures, to select optimal pseudopotentials for 85 elements. It releases SSSP efficiency and SSSP precision libraries, with the precision library scoring highest among open-source pseudopotential libraries in the Δ-factor test of elemental solids.

Key findings

  • The SSSP protocol selects two libraries for 85 elements: SSSP efficiency and SSSP precision (version 1.1), with average suggested wavefunction cutoffs of 44 Ry and 56 Ry, respectively.
  • Average Δ-factors are 0.44 meV for SSSP efficiency and 0.33 meV for SSSP precision, excluding the 15 rare-earth nitrides.
  • Pseudopotential precision is property-dependent: for sodium, all tested equations of state have Δ-factors below 0.3 meV, yet one pseudopotential shows band-structure differences up to η10 = 65 meV.
  • Ghost states in conduction bands up to 10 eV above the Fermi level were detected in listed pseudopotentials; none were found in the valence bands.

Methods

  • More than 50,000 DFT and DFPT calculations were performed with Quantum ESPRESSO’s PWscf and Phonon codes, automated through AiiDA, using the PBE functional and testing up to eight publicly available NC, US, and PAW pseudopotential libraries for 85 elements.
  • The Δ-factor was computed from Birch-Murnaghan fits to energy-versus-volume data at 7 equidistant points around the reference equilibrium volume, using WIEN2k all-electron reference results; convergence tests used a reference wavefunction cutoff of 200 Ry, a 6×6×6 Monkhorst-Pack k-grid (10×10×10 for oxygen and lanthanides), and duals of 4 for NC, 8 for US/PAW, and 12 for selected Fe and Mn cases.
  • Selection criteria included, for SSSP efficiency, phonon convergence within 2% (or 2 cm⁻¹ if ωmax < 100 cm⁻¹), cohesive energy within 2 meV/atom, pressure within 1% δVpress, η10 within 10 meV, max η10 within 20 meV, and Δ-factor below 1 meV/atom when possible; SSSP precision used stricter thresholds and systematically chose the smallest Δ-factor.

Limitations

  • The study is restricted to the PBE functional because it is the only functional with a verified set of all-electron reference results for solids, so the Δ-factor verification cannot currently be performed for other functionals.
  • Transferability tests to PBEsol and PZ showed similar convergence patterns when pseudopotentials were generated with the same atomic parameters, but consistent tests for nonlocal functionals such as SCAN or HSE were not possible because no pseudopotential libraries for those functionals exist.
  • The authors state that in difficult cases the SSSP selection criteria were used as general guidelines rather than strict rules, with pseudopotentials chosen by human inspection and compromises made, for example for very soft noble-gas solids where stress and phonon convergence can be noisy.
  • The paper explicitly performs verification against all-electron PBE results, not validation against experiment, and it adopts the Δ-factor rather than the Δ′-factor despite noting that Δ′ is more strongly correlated with equilibrium-volume differences, because more Δ-factor reference data are available.

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Integrity signals

Registry

Crossref · 10.1038/s41524-018-0127-2

Cites

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Statistics

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Claims the paper makes

0 of 54 cited sources checked · 0 supported · 0 flagged

  • Findingown data
    § SSSP testing protocol · p. 2

    For N, O, F and Hf, all the PSP libraries above perform less well in the Δ-factor test.

    “For a few selected elements, i.e. N, O, F and Hf, in which all the PSP libraries above perform less well in the ∆-factor test we also consider the recent NC Pseudo Dojo library [21] and, only for N, our own set (called THEOS) of US PSPs.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [21] Hybertsen, M. S. & Louie, S. G. Electron correlation in semiconductors and insulators: band gaps and quasiparticle energies. Phys. Rev. B 34, 5390–5413 (1986). source

      Not checked in the free run.

  • Findingcitation
    § SSSP testing protocol · p. 2

    The Δ-factor is scattered along a wide range of slopes corresponding to different bulk modulus B0 values: small (large) bulk moduli correspond to small (large) slopes.

    “Instead the ∆-factor is scattered along a wide range of slopes that correspond to different values of the bulk modulus B 0 : small (large) bulk moduli correspond to small (large) slopes.”
    Quote in the paperSubstantial claim
  • Findingown data
    § Precision and efficiency in solid-state pseudopotential calculations · p. 1

    The SSSP precision library scores highest among open-source pseudopotential libraries available in the Δ-factor test of equations of state of elemental solids.

    “This latter scores highest among open-source pseudopotential libraries available in the ∆-factor test of equations of states of elemental solids.”
    Quote in the paperSubstantial claim
  • Findingown data
    § SSSP testing protocol · p. 2

    The Δ′-factor is very strongly correlated with differences in equilibrium volume δV0 obtained from equations of state.

    “In Fig. 1 it is shown how the ∆ ′ -factor is indeed very strongly correlated with the differences in equilibrium volume, δV 0 , obtained from the equations of state”
    Quote in the paperNot a substantial claim
  • Findingown data
    § SSSP testing protocol · p. 3

    For each element, all quantities tested in the SSSP testing protocol typically converge well before 200 Ry for at least one PSP, with radon being the only exception.

    “We choose 200 Ry as the reference wavefunction cutoff because, for each element, all the quantities tested in the SSSP testing protocol typically convergence well before that value for at least one PSP (with radon being the only exception, as discussed in the Supplementary Figure 1).”
    Quote in the paperSubstantial claim
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    Findingreasoning
    § Precision and efficiency in solid-state pseudopotential calculations · p. 1

    Adopting the SSSP criteria, the authors obtained curated pseudopotential libraries (SSSP) targeted for high-throughput materials screening (SSSP efficiency) and high-precision materials modelling (SSSP precision).

    “Adopting these criteria we obtain curated pseudopotential libraries (named SSSP or standard solid-state pseudopotential libraries), that we target for highthroughput materials screening ('SSSP efficiency') and high-precision materials modelling ('SSSP precision').”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Findingown data
    § INTRODUCTION · p. 1

    The authors introduce a PSP testing protocol based on extensive DFT and DFPT calculations of elemental solids and select the optimal PSP for 85 elements of the periodic table.

    “Here, we introduce a PSP testing protocol based on extensive DFT and density-functional perturbation theory (DFPT) calculations of elemental solids, and select the optimal PSP for 85 elements of the periodic table.”
    Quote in the paperSubstantial claim
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    Findingnone given
    § SSSP testing protocol · p. 3

    The elemental fluorine structure has convergence issues.

    “with the exception of fluorine for which the SiF 4 structure is used because of convergence issues of the elemental fluorine structure”
    Quote in the paperSubstantial claim
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    Findingreasoning
    § SSSP selection criteria · p. 5

    For some elements, no PSP satisfies all selection criteria at a reasonable wavefunction cutoff, or convergence patterns show outlier data points or oscillations.

    “For example it can happen that the selection criteria are not all together satisfied at a reasonable wavefunction cutoff for any of the PSPs of a given element or that the convergence patterns show outlier data points or oscillations.”
    Quote in the paperSubstantial claim
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    Findingnone given
    § SSSP testing protocol · p. 3

    Manganese, iron, cobalt, hafnium and oxygen show particularly high wavefunction cutoffs.

    “the convergence patterns at duals equal to 12 and 16 are also checked for selected elements that show a particularly high wavefunction cutoff, namely manganese, iron, cobalt, hafnium and oxygen”
    Quote in the paperNot a substantial claim
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    Findingown data
    § Correlations among tested quantities · p. 6

    Correlations between equation of state and pressure, cohesive energy, highest phonon frequency, and valence band structure are very weak, suggesting PSP precision is property dependent.

    “Fig. 5 shows how for all such properties correlation is very weak, suggesting that the precision of a PSP is property dependent.”
    Quote in the paperSubstantial claim
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    Findingown data
    § Correlations among tested quantities · p. 6

    There is no strong correlation between pairs of tested quantities entering the selection criteria; similarity between PSPs is strongly property dependent.

    “From our results we conclude that there is no strong correlation between pairs of tested quantities entering our selection criteria, hence the similarity between PSPs is strongly property dependent.”
    Quote in the paperSubstantial claim
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    Findingcitation
    § SSSP libraries · p. 7

    The SSSP efficiency and SSSP precision have small average Δ-factors of 0.44 meV and 0.33 meV, respectively, excluding the 15 rare-earth nitrides.

    “The SSSP efficiency and SSSP precision have small average ∆-factors of 0.44 meV and 0.33 meV, respectively (where the average is performed over all elements tested excluding the 15 rare-earth nitrides, following the recipe of Ref. [6]).”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [6] Hamann, D., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497 (1979). source

      Not checked in the free run.

  • May combine two claims.

    Findingown data
    § Correlations among tested quantities · p. 6

    For sodium, all considered PSPs produce very similar equations of state (Δ-factors <0.3 meV), but one PSP's band structure shows substantial differences up to η10 = 65 meV.

    “We notice that, even if all the sodium PSPs we considered produce very similar equations of states-with ∆-factors always smaller than 0 . 3 meV-the band structure of a particular PSP shows instead substantial differences up to η 10 = 65 meV.”
    Quote in the paperSubstantial claim
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    Findingown data
    § FIGURES · p. 12

    The ∆′-factor is strongly correlated with the difference in equilibrium volume δV0, while the ∆-factor is scattered along a wide range of slopes corresponding to different values of the bulk modulus B0.

    “While the ∆ ′ -factor is strongly correlated with δV 0 , the ∆-factor is instead scattered along a wide range of slopes that correspond to different values of the bulk modulus B 0 .”
    Quote in the paperSubstantial claim
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    Findingown data
    § FIGURES · p. 14

    No strong correlations among the tested quantities (equations of state, pressure, cohesive energy, highest phonon frequency, valence band structure) are observed, but the ∆′-factor is more correlated to δVpress than the ∆-factor.

    “No strong correlations among the quantities tested are observed but we note that the ∆ ′ -factor is more correlated to δV press than the ∆-factor.”
    Quote in the paperNot a substantial claim
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    Findingown data
    § FIGURES · p. 14

    For sodium, all equations of state are very similar among each other, but the 031US band structure shows some discrepancies with respect to other PSPs.

    “Although all equations of state are very similar among each other, the 031US band structure shows some discrepancies with respect to other PSPs.”
    Quote in the paperNot a substantial claim
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    Findingown data
    § FIGURES · p. 13

    The valence bands of FCC Pb are almost identical across several pseudopotential libraries, while differences appear in the conduction bands: SG15 bands deviate from the other bands around 7-10 eV over the Fermi level, and a flat ghost state in the GBRV bands is clearly visible at around 8 eV.

    “The valence bands are almost identical to each other, while some differences appear in the conduction bands: the SG15 bands deviate from the other bands around 7-10 eV over the Fermi level and a flat ghost state in the GBRV bands is clearly visible at around 8 eV.”
    Quote in the paperSubstantial claim
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    Findingnone given
    § TABLES · p. 18

    The latest release of the SG15 library (SG15-1.1) has no ghost states.

    “The latest release of the SG15 library (SG15-1.1) has no ghost states.”
    Quote in the paperNot a substantial claim
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    Study design and conductcitation
    § INTRODUCTION · p. 1

    The SSSP testing protocol is made of a verification part based on the Δ-factor and a performance-oriented part based on plane-wave convergence tests for phonon frequencies, band structures, cohesive energies and stress tensors.

    “Our protocol, named SSSP (standard solid-state pseudopotential) testing protocol, is made of a verification part, based on the ∆ -factor (i.e. the difference between allelectron and PSP equations of state) [6, 7], and an extensive performance-oriented part based on plane-wave convergence tests for phonon frequencies, band structures, cohesive energies and stress tensors.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [6] Hamann, D., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497 (1979). source

      Not checked in the free run.

    • cites [7] Vanderbilt, D. Soft self-consistent pseudopotentials in a generalized eigenvalue formalism. Phys. Rev. B 41, 7892–7895 (1990). source

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Study design and conductnone given
    § Precision and efficiency in solid-state pseudopotential calculations · p. 1

    The authors propose a protocol to test publicly available pseudopotential libraries based on several independent criteria including verification against all-electron equations of state and plane-wave convergence tests for phonon frequencies, band structure, cohesive energy and pressure.

    “Here, we propose a protocol to test publicly available pseudopotential libraries, based on several independent criteria including verification against all-electron equations of state and plane-wave convergence tests for phonon frequencies, band structure, cohesive energy and pressure.”
    Quote in the paperSubstantial claim
  • May combine two claims.

    Premisecitation
    § SSSP testing protocol · p. 2

    Very soft materials, such as noble-gas solids, are generally associated with small Δ-factor values even for significant volume differences, while very hard materials show large Δ-factor values for small volume differences.

    “Indeed, very soft materials, as for example the noble-gas solids, are generally associated with small values of the ∆-factor, even for significant volume differences. On the other hand for very hard materials the opposite situation occurs, i.e. small volume differences give rise to large values of the ∆-factor.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [23] Reining, L. The GW approximation: content, successes and limitations. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 8, e1344 (2018).

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    Study design and conductown data
    § INTRODUCTION · p. 1

    The PSP testing was performed in an automated fashion within the AiiDA infrastructure for reproducible computational science.

    “We consider up to eight (depending on the element) publicly available PSP libraries for the PBE functional [8] and test them with the PWscf and Phonon codes of the Quantum ESPRESSO (QE) distribution [9] in an automated fashion within the framework of the AiiDA [10] infrastructure for reproducible computational science.”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [8] Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994). source

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    • cites [9] Kucukbenli, E. et al. Projector augmented-wave and all-electron calculations across the periodic table: a comparison of structural and energetic properties. Preprint at arXiv:1404.3015 (2014).

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    • cites [10] Dal Corso, A. Pseudopotentials periodic table: from H to Pu. Comput. Mater. Sci. 95, 337–350 (2014). source

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    Premisereasoning
    § INTRODUCTION · p. 1

    A softer, smoother PSP allows faster calculations because the basis set is decreased and minimization or iterative approaches can become more efficient or better pre-conditioned with a smaller basis.

    “a softer, smoother PSP will allow straightforwardly faster calculations, both because the basis set is decreased as the computational cost scales with the square of the basis size, and because the minimization or iterative approaches can become more efficient or better pre-conditioned with a smaller basis.”
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    Premisecitation
    § INTRODUCTION · p. 1

    Only in 2016 a multi-group effort established a baseline in the calculations of the equations of state of elemental crystals.

    “Only in 2016 a multi-group effort was able to establish a baseline in the calculations of the equations of state of elemental crystals [6].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [6] Hamann, D., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497 (1979). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § SSSP testing protocol · p. 2

    All tested PSP libraries are based on the PBE GGA exchange-correlation functional and include norm-conserving, ultrasoft, and projector-augmented wave pseudization approaches.

    “All the tested PSP libraries are based on the generalized gradient approximation (GGA) for the exchangecorrelation functional of Perdew, Burke and Ernzerhof (PBE) [8] and they include the three main pseudization approaches [12]: norm-conserving (NC) [13], ultrasoft (US) [14] and projector-augmented wave (PAW) [15].”
    Quote in the paperNot a substantial claim0 of 3 sources checked
    • cites [8] Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994). source

      Not checked in the free run.

    • cites [12] Garrity, K. F., Bennett, J. W., Rabe, K. M. & Vanderbilt, D. Pseudopotentials for high-throughput DFT calculations. Comput. Mater. Sci. 81, 446–452 (2014). source

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    • cites [13] Schlipf, M. & Gygi, F. Optimization algorithm for the generation of ONCV pseudopotentials. Comput. Phys. Commun. 196, 36–44 (2015). source

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    Premisecitation
    § SSSP testing protocol · p. 2

    The protocol introduced by Lejaeghere et al. in 2014 was recently exploited to compare 15 different DFT codes, including all-electron and PSP codes, to verify reproducibility of PBE equations of state of elemental crystals across methods and implementations.

    “This protocol was recently exploited to compare 15 different DFT codes, including both all-electron and PSP codes, in order to verify the reproducibility of the PBE equations of state of elemental crystals across different methods and implementations [6].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [6] Hamann, D., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497 (1979). source

      Not checked in the free run.

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    Premisenone given
    § SSSP testing protocol · p. 3

    In PAW and US formalisms, wavefunctions are designed to be slowly varying in real space (soft), requiring substantially fewer plane-waves than NC pseudo-wavefunctions.

    “In the PAW and US formalisms, wavefunctions are designed to be slowly varying in real space (i.e. to be soft) requiring substantially fewer plane-waves to be represented with respect to NC pseudo-wavefunctions.”
    Quote in the paperSubstantial claim
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    Premisenone given
    § SSSP testing protocol · p. 2

    Two compared equations of state can be considered indistinguishable if the Δ-factor is smaller than 1 meV/atom (valid for most elemental solids except very soft materials) or if the Δ′-factor is smaller than 3 meV/atom, which corresponds to a variation in equilibrium volume of less than 0.5% for all elemental solids.

    “Broadly speaking two compared equations of state can be considered undistinguishable if the ∆-factor is smaller than 1 meV/atom (valid for most of the elemental solids but with the notable exception of very soft materials) or if the ∆ ′ -factor is smaller than 3 meV/atom, where the latter corresponds to a variation in the equilibrium volume of less than 0.5% for all elemental solids (see Fig. 1).”
    Quote in the paperSubstantial claim
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    Premisecitation
    § SSSP testing protocol · p. 4

    The majority of excited-state calculations are based on many-body perturbation theory (e.g., G0W0, self-consistent GW, BSE, DMFT) and are performed on top of a DFT calculation, which provides the starting point.

    “The majority of excited-states calculations are based on many-body perturbation theory (MBPT), e.g. G 0 W 0 and self-consistent GW [31-33], the Bethe-Salpeter equation (BSE) [34], or dynamical mean field theory (DMFT) [35], and are performed on-top of a DFT calculation, which provides the starting point for both self-consistent and one-shot approaches.”
    Quote in the paperSubstantial claim0 of 5 sources checked
    • cites [31] Prodan, E. & Kohn, W. Nearsightedness of electronic matter. Proc. Natl Acad. Sci. USA 102, 11635–11638 (2005). source

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    • cites [32] Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I. & Vanderbilt, D. Maximally localized Wannier functions: theory and applications. Rev. Mod. Phys. 84, 1419–1475 (2012). source

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    • cites [33] Gonze, X., Stumpf, R. & Scheffler, M. Analysis of separable potentials. Phys. Rev. B 44, 8503–8513 (1991). source

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    • cites [34] Perdew, J. P. et al. Restoring the density-gradient expansion for exchange in solids and surfaces. Phys. Rev. Lett. 100, 136406 (2008). source

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    • cites [35] Perdew, J. P. & Zunger, A. Self-interaction correction to density-functional approximations for many-electron systems. Phys. Rev. B 23, 5048–5079 (1981). source

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    Premisenone given
    § SSSP testing protocol · p. 3

    By considering phonon frequencies at the border of the Brillouin zone, one has access to information related to both acoustic and optical modes.

    “While the ∆-factor test is related to the structural and elastic properties of the system, by considering phonon frequencies at the border of the Brillouin zone we have access to information related to both acoustic and optical modes.”
    Quote in the paperSubstantial claim
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    Premisecitation
    § SSSP testing protocol · p. 2

    The reference all-electron equations of state used are WIEN2k results from Ref. [6], except for rare-earth nitrides which use WIEN2k results from Ref. [18].

    “The reference all-electron results of the equation of states chosen in this work are the ones of the WIEN2k code [24] reported in Ref. [6], with the exception of the rare-earth nitrides for which we use the WIEN2k results reported in Ref. [18].”
    Quote in the paperSubstantial claim0 of 3 sources checked
    • cites [6] Hamann, D., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497 (1979). source

      Not checked in the free run.

    • cites [18] Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976). source

      Not checked in the free run.

    • cites [24] Strinati, G. Application of the Green’s functions method to the study of the optical properties of semiconductors. Riv. Nuovo Cim. 11, 1–86 (1988). source

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    Premisecitation
    § SSSP testing protocol · p. 4

    A uniform k-point mesh is more appropriate from the point of view of electron's nearsightedness: if energy eigenvalues are known on a sufficiently fine uniform mesh, an exact real-space representation of the Hamiltonian in a Wannier function basis is possible and can be interpolated to an arbitrary fine mesh.

    “A uniform mesh is also more appropriate from the point of view of electron's nearsightedness [41]: if the energy eigenvalues are known on a sufficiently fine uniform k -points mesh, it is possible to get an exact real-space representation of the Hamiltonian in a Wannier function basis [42] and then interpolate to an arbitrary fine mesh.”
    Quote in the paperSubstantial claim0 of 2 sources checked
    • cites [41] Prandini, G., Marrazzo, A., Castelli, I. E., Mounet, N. & Marzari, N. A Standard Solid State Pseudopotentials (SSSP) library optimized for precision and efficiency (Version 1.1, data download). Materials Cloud Archive (2018); https://archive.materialscloud.org/2018.0001/v3.

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    • cites [42]

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    Premisecitation
    § SSSP testing protocol · p. 3

    In all PSP frameworks, a plane-wave representation of the charge density requires a cutoff Eρ higher than the wavefunction cutoff Ec.

    “In all PSP frameworks, a plane-wave representation of the charge density requires a cutoff, E ρ , higher than the wavefunction cutoff, E c [28].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [28] Setyawan, W. & Curtarolo, S. High-throughput electronic band structure calculations: challenges and tools. Comput. Mater. Sci. 49, 299–312 (2010). source

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    Premisecitation
    § SSSP testing protocol · p. 4

    Choosing a high-symmetry path for band structure comparison could result in an unsatisfactory arbitrary choice, as different standardization recipes exist and interesting features may occur far from high-symmetry lines.

    “Choosing a high-symmetry path could result in an unsatisfactory arbitrary choice, as different recipes for the standardization of paths have been introduced in the recent literature [37, 38] and interesting features of the band structure may occur far from the high-symmetry lines (such as Weyl points) [39, 40].”
    Quote in the paperSubstantial claim0 of 4 sources checked
    • cites [37] Heyd, J., Scuseria, G. E. & Ernzerhof, M. Hybrid functionals based on a screened Coulomb potential. J. Chem. Phys. 118, 8207–8215 (2003). source

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    • cites [38] Mounet, N. et al. Two-dimensional materials from high-throughput computational exfoliation of experimentally known compounds. Nat. Nanotechnol. 13, 246–252 (2018). source

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    • cites [39] Lebedev, D. et al. Highly active and stable iridium pyrochlores for oxygen evolution reaction. Chem. Mater. 29, 5182–5191 (2017). source

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    • cites [40] Wilkinson, M. D. et al. The FAIR Guiding Principles for scientific data management and stewardship. Sci. Data 3, 160018 (2016). source

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    Study design and conductnone given
    § SSSP selection criteria · p. 5

    For SSSP efficiency, the selection criteria are: Δ-factor below 1 meV/atom when possible; phonon δ ̄ω converged within 2% (or 2 cm-1 if highest phonon frequency <100 cm-1); cohesive energy δEcoh within 2 meV/atom; pressure δVpress within 1%; band structure η10 within 10 meV and max η10 within 20 meV.

    “For SSSP efficiency, when possible we select PSPs with a rather small ∆-factor (below 1 meV/atom). The phonons δ ¯ ω should be converged within 2% (or within 2 cm -1 if the highest phonon frequency is smaller than 100 cm -1 ), the cohesive energy δE coh within 2 meV/atom, the pressure within 1% for δV press (i.e. 0.33% on the lattice parameter of a cubic crystal) and the band structure within 10 m”
    Quote in the paperSubstantial claim
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    Study design and conductnone given
    § SSSP selection criteria · p. 5

    For SSSP precision, the criteria are slightly stricter than for SSSP efficiency, and the PSP with the smallest Δ-factor is systematically chosen.

    “For the SSSP precision, the criteria are slightly stricter (see Table 2) and we systematically opt for the PSP with the smallest ∆-factor.”
    Quote in the paperSubstantial claim
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    Premisereasoning
    § SSSP testing protocol · p. 4

    Converting pressure convergence into an equivalent volume allows a stiffness-agnostic and material-independent convergence criterion.

    “Rather than checking convergence directly on the pressure itself (the magnitude of which depends strongly on the stiffness of the material) we evaluate it through its conversion into an equivalent volume. This allows the definition of a stiffness-agnostic and hence material's independent convergence criterion.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim. May combine two claims.

    Premisereasoning
    § SSSP testing protocol · p. 3

    The charge density ρ is the fundamental quantity in DFT; the physics and energy functional determine its spatial variation and thus the cutoff Eρ, independently of the PSP scheme.

    “However the charge density ρ is the fundamental quantity in DFT. The physics of the problem and the energy functional determine the spatial variation of ρ and thus the cutoff E ρ , independently of the PSP scheme that is adopted.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim.

    Study design and conductnone given
    § SSSP selection criteria · p. 5

    The main idea behind the SSSP precision library is to provide PSPs closest to all-electron calculations in terms of Δ-factor at the reference cutoff, without much consideration of computational cost and wavefunction cutoffs.

    “The main idea behind the SSSP precision library is to provide the PSPs that are the closest to all-electron calculations in terms of ∆-factor computed at the reference wavefunction cutoff E ref c , without much consideration on the computational cost and the wavefunction cutoffs actually needed to converge all relevant quantities.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based). May combine two claims.

    Premisenone given
    § SSSP testing protocol · p. 3

    PAW and US PSPs require relatively high duals, and a dual of 8 is usually reasonable to efficiently achieve good precision.

    “Fundamentally, that is why PAW and US PSPs require relatively high duals, where according to common knowledge a choice of a dual of 8 is usually reasonable to efficiently achieve good precision.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim. May combine two claims.

    Study design and conductreasoning
    § SSSP selection criteria · p. 5

    The SSSP efficiency library is designed for practical applications that should remain affordable, so PSPs are chosen such that wavefunction cutoffs are as low as possible while keeping precision reasonable.

    “On the other hand, the SSSP efficiency library is designed for practical applications that should remain affordable, and therefore PSPs are chosen such that wavefunction cutoffs are as low as possible while keeping the precision reasonable.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S2 (checkable), S4 (based).

    Premisenone given
    § SSSP testing protocol · p. 4

    A precision of a few cm-1 is often the reasonable target for a DFPT calculation.

    “since a precision of a few cm -1 is often the reasonable target for a DFPT calculation.”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Study design and conductnone given
    § SSSP libraries · p. 7

    The SSSP protocol incorporates a verification part based on the ∆-factor and an efficiency part based on plane-wave cutoff convergence tests for phonon frequencies, cohesive energies, pressures, and band structures.

    “We incorporate in the SSSP protocol a verification part, based on the ∆-factor, and an efficiency part, based on the plane-wave cutoff convergence tests for phonon frequencies, cohesive energies, pressures, and band structures.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim.

    Interpretationnone given
    § SSSP libraries · p. 7

    The paper proposes an extensive testing protocol for PSPs to investigate precision and performance of several NC, US and PAW PSP libraries that are publicly available.

    “In summary, we propose an extensive testing protocol for PSPs to investigate precision and performance of several NC, US and PAW PSP libraries that are publicly available.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim.

    Interpretationown data
    § SSSP libraries · p. 7

    A user can quickly select the optimal PSP and wavefunction cutoff tailored for a specific application by looking at the paper's plots and data, such as the condensed plot for palladium in Fig. 2.

    “By a look at our plots and data, see for instance the condensed plot for palladium shown in Fig. 2, a user can quickly select the optimal PSP and wavefunction cutoff tailored for the specific application.”
    Quote in the paperSubstantial claim
  • Classified as probably not a substantial claim.

    Premisenone given
    § Ghost states · p. 5

    Different PSPs are often generated with different combinations of semi-core states in the valence band.

    “However different PSPs are often generated with different combinations of semi-core states in the valence band.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationnone given
    § Ghost states · p. 5

    Ghost states above the Fermi level could be a possible source of problems for excited-state properties (e.g., GW or BSE).

    “Nonetheless they could be a possible source of problems for applications related to excited-state properties (e.g. in MBPT calculations such as GW or BSE).”
    Quote in the paperNot a substantial claim
  • May combine two claims.

    Study design and conductcitation
    § Exchange-correlation functionals · p. 6

    The study is restricted to the PBE functional because it is among the most popular in the electronic structure community and the only functional for which a verified set of reference all-electron results for solids exists.

    “Our study on the precision and efficiency of PSPs is restricted to the PBE functional as it is among the most popular ones in the electronic structure community and the only functional for which a verified set of reference all-electron results for solids exists [6].”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [6] Hamann, D., Schlüter, M. & Chiang, C. Norm-conserving pseudopotentials. Phys. Rev. Lett. 43, 1494–1497 (1979). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § Ghost states · p. 5

    Standard DFT calculations for ground-state properties are unaffected by ghost states above the Fermi level.

    “However, it is worth noting that standard DFT calculations for ground-state properties are unaffected by ghost states above the Fermi level.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Premisecitation
    § SSSP libraries · p. 7

    The SSSP libraries have already proven to be a reliable tool for a number of computational studies, e.g., enabling high-throughput computational exfoliation of two-dimensional materials and supporting a combined experimental and theoretical study of catalysts for oxygen evolution reaction.

    “The SSSP libraries have already proven to be a reliable tool for a number of computational studies: for instance the beta version (called version 0.7) of the SSSP libraries have enabled the high-throughput computational exfoliation of two-dimensional materials [49] and have supported the combined experimental and theoretical study of catalysts for oxygen evolution reaction [50].”
    Quote in the paperNot a substantial claim0 of 2 sources checked
    • cites [49]

      Not checked in the free run.

    • cites [50]

      Not checked in the free run.

  • Classified as probably not a substantial claim.

    Interpretationreasoning
    § SSSP selection criteria · p. 5

    In difficult cases, compromise choices are necessary that can sacrifice or increase some thresholds to keep computational cost reasonable.

    “In these cases it is therefore necessary to make compromise choices that can sacrifice or increase some of the thresholds imposed by the SSSP selection criteria, if no other possibilities are available or in order to keep the computational cost reasonable.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S2 (checkable).

    Interpretationreasoning
    § SSSP libraries · p. 7

    There is a need for a verification standard in the computational solid-state community.

    “Our work shows how the assessment of both precision and efficiency of pseudopotentials is strongly property-dependent and requires a multi-dimensional quality gauge, pointing to the need of a verification standard in the computational solid-state community.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim. May combine two claims.

    Premisecitation
    § METHODS · p. 7

    AiiDA is an open-source Python infrastructure for computational science specifically designed to track the provenance of data and calculations and to allow users to implement workflows that can run complex sequences of calculations.

    “This is the reason why we used AiiDA [10], an open-source Python infrastructure for computational science, that is specifically designed to track the provenance of data and calculations and that allow the user to implement workflows that can run complex sequences of calculations.”
    Quote in the paperSubstantial claim0 of 1 sources checked
    • cites [10] Dal Corso, A. Pseudopotentials periodic table: from H to Pu. Comput. Mater. Sci. 95, 337–350 (2014). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductnone given
    § METHODS · p. 8

    The SsspWorkflow is built on top of the PwWorkflow, a lower-level workflow that handles all the QE simulations and can restart calculations in case of standard QE errors or if the user-specified wall time is too small.

    “The SsspWorkflow is built on top of the PwWorkflow, a very robust lower-level workflow in charge of handling all the QE simulations and that can restart calculations in case of standard QE errors or, for example, if the user-specified wall time is too small.”
    Quote in the paperNot a substantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

    Study design and conductcitation
    § DATA AVAILABILITY · p. 8

    All the data produced in this work is freely available on the Materials Cloud online platform, where the user can interactively browse the results and explore the data provenance.

    “All the data produced in this work is freely available on the Materials Cloud online platform [11], where the user can interactively browse the results and explore the data provenance.”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [11] Topsakal, M. & Wentzcovitch, R. Accurate projected augmented wave (PAW) datasets for rare-earth elements (RE = La–Lu). Comput. Mater. Sci. 95, 263–270 (2014). source

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Interpretationreasoning
    § METHODS · p. 7

    AiiDA is particularly suited for high-throughput studies, such as the deployment of the SSSP testing protocol, where a large number of simulations are involved.

    “It is therefore particularly suited for high-throughput studies, such as the deployment of the SSSP testing protocol, where a large number of simulations are involved.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim.

    Interpretationown data
    § SSSP libraries · p. 7

    The paper provides a systematic survey of PSP quality across multiple physical properties and multiple libraries and techniques (NC, US and PAW).

    “Building on the invaluable work behind all the PSP libraries we considered, we provide a systematic survey of PSP quality across multiple physical properties and multiple libraries and techniques (NC, US and PAW).”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductcitation
    § METHODS · p. 7

    All calculations needed for this work (more than 50,000 DFT and DFPT calculations) were performed with the goal to ensure reproducibility of all the data obtained, compliant with the FAIR guiding principles for data management.

    “All the calculations needed for this work (more than 50'000 DFT and DFPT calculations) were performed with the goal to ensure reproducibility of all the data obtained, compliant with the FAIR guiding principles for data management [51].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [51]

      Not checked in the free run.

  • Probably not a substantial claim: may not pass S3 (load-bearing), S4 (based).

    Premisenone given
    § FIGURES · p. 15

    PBEsol and PZ PSPs are generated with the same atomic parameters of the original PBE pseudopotential from the GBRV-1.4 PSP library.

    “PBEsol and PZ PSPs are generated with the same atomic parameters of the original PBE pseudopotential from the GBRV-1.4 PSP library.”
    Quote in the paperNot a substantial claim
  • Classified as probably not a substantial claim.

    Study design and conductnone given
    § METHODS · p. 8

    The complete SSSP testing protocol is implemented as an AiiDA workflow called SsspWorkflow that can run all the convergence tests and the ∆-factor verification test.

    “The complete SSSP testing protocol is implemented as an AiiDA workflow, called SsspWorkflow, that can run all the convergence tests and the ∆-factor verification test.”
    Quote in the paperSubstantial claim
  • Probably not a substantial claim: may not pass S3 (load-bearing).

    Study design and conductcitation
    § DATA AVAILABILITY · p. 8

    The full database with all the data can be downloaded.

    “The full database with all the data can also be downloaded [52].”
    Quote in the paperNot a substantial claim0 of 1 sources checked
    • cites [52]

      Not checked in the free run.

57 of 57
  • The paper relies on this without support.

    The Δ-factor is the only verification test present in the literature to assess the precision of DFT calculations of solids.

    “Up to now, the ∆-factor is the only verification test present in the literature to assess the precision of DFT calculations of solids.”
  • The paper relies on this without support.

    No PSP libraries for complex nonlocal functionals such as SCAN or HSE exist as of today.

    “as of today, no PSP libraries for these kind of functionals exist.”
2 of 2

Self-check

Percentages, sums and reported differences re-computed from the paper’s own numbers.

Each contradiction between two passages listed here was confirmed by an independent check.

  • Cobalt also has a suggested dual of 12

    Minor

    The text names only iron and manganese as exceptions requiring a dual of 12, but Table 4 assigns a dual of 12 to cobalt in the SSSP precision library.

1 of 1

Cites

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Authors
Prandini, G., Marrazzo, A., Castelli, I. E., Mounet, N., & Marzari, N.
Affiliations
École Polytechnique Fédérale de Lausanne (CH)
Corresponding author
Marzari, Nicola
Venue
npj Computational Materials
Published
2018-12-06
Volume
4
Issue
1
ISSN
2057-3960 (ISSN-L)
OpenAlex
W2808484747
Cited by
917
References
41
Citations by year
2026: 163 · 2025: 197 · 2024: 160 · 2023: 133 · 2022: 81 · 2021: 75 · 2020: 62 · 2019: 42 · 2018: 4
FWCI
17.04
Type
journal article
Language
en
Open access
Locations
  • npj Computational Materials (publishedVersion, cc-by)
  • arXiv (Cornell University) (submittedVersion)
  • ArTS Archivio della ricerca di Trieste (University of Trieste https://www.units.it/) (submittedVersion, cc-by)
  • SDL (submittedVersion, cc-by)
  • DOAJ (DOAJ: Directory of Open Access Journals) (submittedVersion)
  • Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
  • Technical University of Denmark, DTU Orbit (Technical University of Denmark, DTU) (submittedVersion, other-oa)
  • arXiv (Cornell University) (cc-by)
Funders
This work has been supported by NCCR MARVEL, computing time has been provided by the Swiss National Supercomputing Centre (CSCS) and by PRACE.
Topics
  • Physical Sciences › Materials Science › Materials Chemistry › Machine Learning in Materials Science
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Earth and Planetary Sciences › Geophysics › High-pressure geophysics and materials
Keywords
verification and validation, equation of state, phonon frequencies, cohesive energy, electronic band structure, high-throughput materials screening, open source software, density functional theory

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