Source-linked AI summary
Precision and efficiency in solid-state pseudopotential calculations
Gianluca Prandini, Antimo Marrazzo, Ivano E. Castelli, Nicolas Mounet, Nicola Marzari
TL;DR
Systematic verification of pseudopotentials remains limited, and different properties can demand different choices. This paper develops a multi-criteria testing protocol and produces two curated SSSP libraries for 85 elements, supporting efficiency and precision-oriented calculations.
Problem
Systematic pseudopotential verification remains limited, while similar results for one property may conceal discrepancies for another.
Method
The SSSP protocol combines all-electron equation-of-state verification with plane-wave convergence tests for phonons, band structures, cohesive energies, and stresses.
Results
The study identifies two curated SSSP libraries, efficiency and precision, containing tested pseudopotentials for 85 elements.
Takeaways & Limitations
The libraries and accompanying verification database facilitate selecting pseudopotentials and wavefunction cutoffs for materials calculations.
Takeaways & Limitations
The precision and efficiency study is restricted to the PBE functional because verified all-electron solid references are available only for PBE.
Abstract
from arXiv · showhide
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.
INTRODUCTION · RESULTS · SSSP testing protocol
The paper introduces the SSSP testing protocol to verify pseudopotential precision against all-electron equations of state and evaluate plane-wave convergence across several material properties. It applies these criteria to select optimal pseudopotentials and curate libraries for efficiency- and precision-oriented solid-state calculations.
- INTRODUCTION: Softer, smoother pseudopotentials improve computational performance by reducing basis-set size and potentially improving iterative minimization.The computational cost scales with the square of the basis size.
- INTRODUCTION: The SSSP protocol selects optimal pseudopotentials for 85 elements using verification and performance-oriented tests.Verification uses the Δ-factor, while performance testing uses plane-wave convergence calculations.
- RESULTS: The paper compares pseudopotentials across multiple properties because agreement and convergence for one property may not predict performance for another.It presents two optimal pseudopotential libraries selected according to the SSSP testing protocol.
- SSSP testing protocol: The study investigates the precision and performance of pseudopotential libraries available for Quantum ESPRESSO.Quantum ESPRESSO uses plane waves and pseudopotentials for DFT electronic-structure calculations.
- SSSP testing protocol: The Δ-factor measures the integrated difference between pseudopotential and reference all-electron equations of state.The protocol follows the method introduced by Lejaeghere and colleagues for comparing elemental-crystal equations of state.
- SSSP testing protocol: Four quantities are tested for convergence with wavefunction cutoff: zone-border phonon frequencies, cohesive energies, pressure, and band structures.Calculations use ground-state structures of elemental crystals at 0 K, with fluorine treated as an exception.
- SSSP testing protocol: Pressure convergence is assessed through an equivalent relative volume deviation, making the criterion independent of material stiffness.Hydrostatic pressure is converted through the Birch-Murnaghan equation of state rather than evaluated directly by magnitude.
- SSSP testing protocol: Band structures are included because pseudopotential-based DFT calculations provide starting points for many-body excited-state methods.The protocol uses η10 and max η10 to assess valence bands and conduction bands up to 10 eV above the Fermi energy.
DISCUSSION · SSSP selection criteria
The SSSP precision and efficiency libraries are selected for different priorities: closeness to all-electron calculations versus affordable convergence. Selection follows flexible guidelines, with difficult cases handled through human inspection because convergence can be slow or irregular.
- SSSP selection criteria: SSSP precision prioritizes agreement with all-electron calculations using the Δ-factor at the reference wavefunction cutoff Eref.
- SSSP selection criteria: SSSP efficiency prioritizes affordability by choosing low wavefunction cutoffs while maintaining reasonable precision.
- SSSP selection criteria: The precision library typically uses higher wavefunction cutoffs than the efficiency library.
- SSSP selection criteria: The criteria are general guidelines rather than strict rules in a few difficult cases.
- SSSP selection criteria: Pseudopotentials are selected one by one through human inspection rather than by an automatic procedure.
- SSSP selection criteria: This flexible approach is necessary because convergence of some tested quantities can be slow or irregular.
Ghost states
The bands distance η10 is used to compare tested pseudopotential band structures across elemental crystals and can also quantitatively compare them with all-electron references.
- Ghost states: The bands distance η10 compares the band structures of tested pseudopotentials for all considered elemental crystals.Because pseudopotentials may use different semi-core valence states, comparisons include only their common bands, determined by the minimum shared number.
- Ghost states: The bands distance could also support verification studies by quantitatively comparing pseudopotential band structures with reference all-electron band structures.
Correlations among tested quantities
The SSSP criteria show small correlations, supporting the need for multiple independent tests based on different physical properties. Expanding heterogeneous all-electron reference data beyond equations of state could extend verification beyond the Δ-factor for elemental crystals.
- Criteria independence: Small correlations among SSSP criteria indicate that accurate pseudopotential selection requires several independent criteria based on different physical properties.The analysis provides an a posteriori justification for the SSSP testing protocol.
- Reference data: Validated all-electron reference data should include properties beyond equations of state, such as phonons and band structures.The proposed heterogeneous reference set would support broader pseudopotential verification tests.
- Verification scope: Broader reference data could extend pseudopotential verification beyond the Δ-factor for elemental crystals.The passage presents this extension as a potential improvement enabled by additional all-electron references.
Exchange-correlation functionals
The study is restricted to PBE because verified all-electron solid-state references exist only for this functional, enabling the Δ-factor verification test. Convergence patterns transfer across local and semi-local functionals with identical atomic parameters, whereas testing SCAN or HSE is less straightforward.
- Exchange-correlation functionals: The study restricts precision and efficiency tests to PBE, the only functional with verified all-electron reference results for solids.Consequently, the Δ-factor verification test can currently be performed only with PBE.
- Exchange-correlation functionals: Convergence patterns are very similar across local and semi-local functionals when pseudopotentials use the same atomic parameters.The relevant parameters include electronic configuration and cutoff radii, supporting transferability of convergence tests.
- Exchange-correlation functionals: Consistent transferability tests are less straightforward for complex nonlocal functionals such as SCAN and HSE.The passage notes that no pseudopotential libraries for these functionals existed at the time of the study.
SSSP libraries
The paper proposes an extensive SSSP testing protocol combining Δ-factor verification with plane-wave convergence tests, and uses it to identify SSSP efficiency and precision libraries. It also provides verification and convergence data to support application-specific pseudopotential and cutoff selection.
- SSSP libraries: Two optimal libraries, named SSSP efficiency and SSSP precision, are selected according to the protocol’s criteria.Version 1.1 tables report suggested wavefunction cutoffs and duals for each selected pseudopotential.
- Application-specific selection: The resulting database of verification data and convergence tests facilitates pseudopotential and wavefunction-cutoff choices for custom applications.Users can tailor selections to required pseudopotential types and converged quantities, such as for palladium.
- Testing protocol: The SSSP protocol combines Δ-factor verification with plane-wave cutoff convergence tests for phonon frequencies, cohesive energies, pressures, and band structures.It assesses publicly available norm-conserving, ultrasoft, and PAW pseudopotential libraries for precision and performance.
METHODS
The study performed more than 50’000 DFT and DFPT calculations to ensure reproducibility and comply with FAIR guiding principles. AiiDA was used to track provenance and run complex computational workflows for the high-throughput SSSP testing protocol.
- Reproducible computational workflow: More than 50’000 DFT and DFPT calculations were performed to ensure reproducibility of the obtained data.The calculations were designed to comply with the FAIR guiding principles.
- Reproducible computational workflow: AiiDA, an open-source Python infrastructure, was used to manage data and calculations.It is specifically designed to track data and calculation provenance.
- Reproducible computational workflow: AiiDA enabled workflows executing complex sequences of calculations for the high-throughput SSSP testing protocol.The infrastructure is particularly suited to studies involving a large number of simulations.
FUNDING
The work was supported by NCCR MARVEL and H2020 CoE MaX, with computing time from CSCS and PRACE and early seed funding from Sadas Shankar and Intel Corporation.
- The work received support from NCCR MARVEL and H2020 CoE MaX.
- Computing time was provided by CSCS and PRACE under Project IDs 2016153543 and 2016163963.
- Sadas Shankar and Intel Corporation provided early seed funding for validated pseudopotentials for electronic-structure simulations during 2009–11.
DATA AVAILABILITY
All data produced in this work is freely available through the Materials Cloud platform and as a downloadable full database.
- DATA AVAILABILITY: The Materials Cloud platform provides interactive browsing of the results and their data provenance.The complete dataset can also be downloaded.
FIGURES
The figures illustrate the SSSP testing protocol and compare pseudopotentials using equation-of-state, phonon, cohesive-energy, pressure, and band-structure discrepancies. They show that some metrics correlate, while convergence and agreement across properties are not generally interchangeable.
- Metric comparisons: The ∆′-factor strongly correlates with equilibrium-volume differences, whereas the ∆-factor spans slopes associated with different bulk moduli.The comparison covers pairs of pseudopotentials for 85 elemental crystals at Eref c = 200 Ry.
- SSSP protocol: The SSSP protocol monitors cutoff convergence for zone-boundary phonons, cohesive energy, pressure, and band structure against efficiency or precision thresholds.For each pseudopotential, the protocol also reports valence-electron count, Z, and the ∆-factor.
- Band structures: FCC Pb valence bands are nearly identical across libraries, while SG15 conduction bands deviate around 7-10 eV above the Fermi level and GBRV shows a flat ghost state near 8 eV.The differences are summarized by ηv and η10 in meV.
- Elemental comparisons: For sodium at 200 Ry, equations of state are very similar among pseudopotentials, but the 031US band structure differs from the others.The comparison uses the ∆-factor for equations of state and η10 for band structures.
- Metric comparisons: Across the 85 tested elements, no strong correlations appear between equation-of-state discrepancies and pressure, cohesive energy, highest phonon frequency, or valence-band structure.The ∆′-factor is more correlated with δVpress than the ∆-factor.
- Convergence: Convergence of phonon frequencies generally does not imply convergence of cohesive energies when pseudopotential cutoffs are selected under the SSSP efficiency criteria.The figure compares δ¯ω and δEcoh cutoff pairs, with colors indicating how many pseudopotentials share each pair.
TABLES
The tables document the pseudopotential libraries evaluated under the SSSP protocol, the criteria selecting efficiency and precision libraries, ghost-state exclusions, and recommended cutoffs for version 1.1.
- Tested libraries: Table 1 identifies the pseudopotential libraries tested with the SSSP protocol and their short names used in convergence plots.The short names correspond to the labels used in Fig. 2.
- Selection criteria: Table 2 lists the selection criteria for the SSSP efficiency and SSSP precision libraries.The table distinguishes the criteria applied to the two curated library types.
- Ghost-state exclusions: None of the pseudopotentials with ghost states in conduction bands up to 10 eV above the Fermi level is included in the SSSP libraries.The latest SG15 release, SG15-1.1, has no ghost states.
- Version 1.1 recommendations: Tables 4 and 5 report the suggested wavefunction cutoffs in Ry and duals for the SSSP efficiency and precision libraries version 1.1.The recommendations are split across two table parts.