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REVIEW 3 major objections 4 minor 51 references

Highly accurate local basis sets for large-scale DFT calculations in CONQUEST

T0 review · 3 major / 4 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Conquest's default local basis sets reproduce plane-wave bulk moduli to below 1% and lattice constants to within 0.1%.

desk verdict Useful Conquest basis-set benchmark, but the 'better than 1%' conclusion is contradicted by the paper's own tables and needs correcting. read the letter →

arxiv 1908.02707 v1 pith:YNKURTEO submitted 2019-08-07 cond-mat.mtrl-sci

David R. Bowler , Jack S. Baker , Jack T. L. Poulton , Shereif Y. Mujahed , Jianbo Lin , Sushma Yadav , Zamaan Raza , Tsuyoshi Miyazaki This is my paper · ORCID
classification cond-mat.mtrl-sci PACS 71.15.Mb
keywords densityfunctionaltheorylarge-scaleDFTpseudo-atomicorbitalslocalbasissetsConquestplane-wavebenchmarkbasis-setconvergencebulkmodulus
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper sets out to show that the Conquest large-scale density functional theory (DFT) code can use default, unoptimised pseudo-atomic orbital basis sets that reproduce fully converged plane-wave results for a wide range of solids. The authors construct basis sets of increasing size from confinement energy shifts of 2 eV, 0.2 eV and 0.02 eV (or from common radii averaged across angular momenta), and compare SZP, DZP and TZTP basis sets against plane-wave calculations that use the same pseudopotentials, functionals and grids. They report that the large TZTP basis sets match the plane-wave reference to better than 1% in bulk modulus and often within 0.1% in lattice constant, while the medium DZP sets are nearly as accurate except in weakly bonded systems such as ice. This matters because it offers a route to near-plane-wave accuracy in calculations on thousands of atoms, where plane-wave methods scale poorly.

What carries the argument

The central object is the pseudo-atomic orbital (PAO): a numerical radial function tabulated on a fine radial mesh, multiplied by spherical harmonics, and confined to a finite radius so matrices stay sparse. The machinery is the rule for choosing those radii. The equal-energy rule fixes confinement by energy shifts spaced by factors of ten above the atomic eigenvalue (2 eV, 0.2 eV, 0.02 eV), giving increasingly diffuse radial functions; the equal-radii variant averages the radii over angular momenta for each shift. These rules turn the notoriously unsystematic question of basis set size into a small, reproducible ladder of SZP, DZP, and TZTP basis sets. The accuracy claim rests on this ladder: larger rungs add variational flexibility by spanning a wider range of radii, and the tests show that the TZTP rung is effectively converged against the plane-wave limit.

What would settle it

Recompute one of the test cases, say Ge or MgSiO3, with the same pseudopotentials but twice the plane-wave cutoff and a denser k-point mesh; if the plane-wave bulk modulus or lattice constant shifts by more than about 1%, then part of the difference attributed to the basis sets is actually reference error, and the headline accuracy claims would need to be re-expressed relative to the true converged value.

Watch

Extended reading notes

Core claim

The central claim is that a small set of parameter-free construction rules for pseudo-atomic orbitals yields basis sets whose structural predictions essentially coincide with converged plane-wave DFT when the same pseudopotentials and exchange-correlation functionals are used. Two constructions are compared: equal energy, where each radial function's confinement radius comes from a fixed energy shift (2 eV, 0.2 eV and 0.02 eV for one, two and three radial functions), and equal radii, where all angular momenta share the mean of the radii found at those energies. Across elemental semiconductors, simple and perovskite oxides, metallic bcc iron, ice XI and hexagonal boron nitride, TZTP basis sets keep bulk modulus errors below 1% and lattice constants or volumes within about 0.1% of plane-wave values. The paper also shows that a DZP basis with perturbative polarisation is nearly as accurate for most covalently or ionically bonded systems, but that phase-stability comparisons such as quartz versus stishovite need an extra polarisation function (DZDP) or a TZTP set to get the correct energy ordering.

Load-bearing premise

The load-bearing premise is that the plane-wave reference calculations are fully converged at the reported cutoffs (40–60 Ha) and k-point meshes; the paper gives these settings but does not report convergence tests, so unreferenced error in the reference would reduce the claimed basis-set accuracy.

Editorial extensions

If this is right

  • Users of Conquest can run large-scale DFT with default TZTP basis sets and expect bulk moduli and lattice constants within about 1% and 0.1% of converged plane-wave results, without per-system optimisation.
  • For most covalent and ionic solids, the DZP basis is nearly as accurate and is roughly 5–10 times faster than TZTP because of the smaller matrix size.
  • The equal-radii construction gives slightly better accuracy overall and smaller support-function radii, so it should be the preferred default on efficiency grounds.
  • When comparing relative stability of different coordination environments, at least DZDP or TZTP is needed; the paper finds DZP can give the wrong ordering for quartz versus stishovite.
  • The results support the broader claim that local-orbital DFT codes can be as accurate as converged plane-wave codes when both use the same pseudopotentials.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • This suggests the same 1%-accuracy threshold could carry over to derived properties such as forces, phonons, and defect formation energies, but the paper does not test those; a targeted comparison would be needed.
  • The equal-energy and equal-radii recipes are generic enough that they could be adopted by other pseudo-atomic-orbital codes, offering a common benchmark ladder for basis-set convergence.
  • Because all tests use the same pseudopotentials, the reported errors isolate basis-set truncation; combining these basis sets with other pseudopotential libraries may shift absolute numbers, but the relative ladder should remain predictive.
  • A practical test of the claim would be running a >1,000-atom system, such as a screw dislocation or dilute dopant, with TZTP and comparing forces against plane-wave calculations on the same cell; if forces agree to the same tight tolerance, the accuracy extends beyond the fitted structural parameters.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper describes a scheme for generating pseudo-atomic orbital (PAO) basis sets for the large-scale DFT code CONQUEST, based on confinement energy shifts of 2, 0.2, and 0.02 eV, with equal-energy and equal-radii variants. It defines SZP, DZP, and TZTP basis sets and tests them against plane-wave calculations with the same pseudopotentials and functionals for elemental semiconductors (C, Si, Ge), oxides (SiO2 polymorphs, MgO), perovskites (SrTiO3, PbTiO3, MgSiO3), bcc Fe, ice XI, and hexagonal BN. The central claim, stated in the Conclusion, is that the large TZTP basis sets reproduce plane-wave results to better than 1% in bulk modulus and often within 0.1% of the lattice constant. The body text is more cautious, reporting that results are 'typically' accurate to these levels for elemental semiconductors and explicitly flagging outliers for SrTiO3 and MgSiO3.

Significance. If the central claim held, this would be a valuable practical result: it would show that default, unsystematized PAO basis sets in CONQUEST can approach plane-wave accuracy across diverse bonding types, strengthening the case for local-orbital large-scale DFT. The paper has genuine strengths: tests use identical pseudopotentials and functionals for both codes; the basis-set construction is transparent and reproducible from the described PAO generation code; and the authors candidly report the SiO2 phase-ordering failure and the SrTiO3 and MgSiO3 bulk-modulus outliers. However, the headline quantitative claim is contradicted by the paper's own tables, and the plane-wave reference is not demonstrated to be converged, so the accuracy assessment is not yet reliable as stated.

major comments (3)
  1. [Section 5 (Conclusions) vs Tables 1-4] The Conclusion states that TZTP basis sets reproduce plane-wave results 'to better than 1% in bulk modulus and often within 0.1% of the lattice constant.' This is not supported by the paper's own data. Taking the PW column as reference: Ge TZTP(R) gives B0 = 64.99 GPa versus 67.47 GPa (3.7% error); SrTiO3 TZTP(R) gives 169.9 versus 186.4 GPa (8.9%); MgSiO3 TZTP(R) gives 253.2 versus 235.7 GPa (7.4%); Fe TZTP(R) gives 276.5 versus 271.4 GPa (1.9%). Lattice constants also exceed 0.1% for C (3.562 vs 3.558 Å), Si (5.437 vs 5.431 Å), and Ge (5.690 vs 5.676 Å). The equal-energy TZTP(E) variant still exceeds the 1% bulk-modulus bound for Si (91.79 vs 93.28 GPa, 1.6%) and MgSiO3 (246.1 vs 235.7 GPa, 4.4%). Because the body text correctly hedges with 'typically' and explicitly notes the SrTiO3 and MgSiO3 outliers, this is an internal inconsistency that must be fixed by revising the Conclusion to an accurate quantitative summary.
  2. [Section 4, first paragraph and Tables 1-6] The abstract and Section 4 call the plane-wave results 'fully converged,' but no convergence tests are reported for the stated plane-wave cutoffs (40-60 Ha) or Monkhorst-Pack meshes. Since the paper's accuracy claim is a difference from this reference, any residual reference error enters directly into the reported bulk-modulus and lattice-constant differences. Please report convergence tests of the reference values with respect to cutoff and k-point sampling, or explicitly qualify the claims as relative to the chosen, possibly unconverged reference.
  3. [Section 4, first paragraph] The procedure used to extract V0 and B0 from the energy-volume curves is not described. The paper does not state the equation-of-state form (e.g., Birch-Murnaghan), the number of volumes, or the fitting range. This detail matters at the claimed 1% level because bulk moduli are second derivatives of fitted curves and are sensitive to fitting choices. Please add a brief description of the fitting procedure for Tables 1-6.
minor comments (4)
  1. [Section 4, paragraph on MgSiO3] The text says MgSiO3 bulk-modulus errors are 'nearly 5%,' but Table 3 shows 7.4% for TZTP(R) and 4.4% for TZTP(E); please reconcile the wording with the tabulated values.
  2. [References] Several author names contain corrupted special characters (e.g., 'Blchl', 'Khler', 'Bjrkman'); these should be corrected.
  3. [Section 4, opening paragraph] The code name 'PWSCF' appears; the standard spelling is 'PWscf'.
  4. [Table 6 caption] The caption says 'minimum energies' for the BN table; please clarify whether this is the interaction energy per atom at the optimal interlayer distance and state the counterpoise-correction convention used.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: basis sets are generated from isolated-atom confined calculations with fixed empirical energy shifts, and accuracy is judged against independent plane-wave benchmarks using the same pseudopotentials.

full rationale

The paper's central claim is that its default pseudo-atomic orbital (PAO) basis sets, when used in Conquest, reproduce converged plane-wave results for a range of solids. The derivation chain does not introduce the benchmark results as inputs. The basis sets are defined by the paper in Section 3: radial functions are generated from confined isolated-atom calculations using energy shifts of 2 eV, 0.2 eV and 0.02 eV, chosen empirically but not fitted to the solids studied in Section 4. The paper states: 'We have found, empirically, that energy shifts of 2 eV and 0.02 eV fulfil these criteria well' and then defines the basis sizes (SZ, SZP, DZP, TZTP) from these fixed shifts. No parameter appearing in the reported accuracy comparison is tuned to the target lattice constants or bulk moduli of C, Si, Ge, SiO2, MgO, SrTiO3, PbTiO3, MgSiO3, Fe, ice XI or BN. The comparison itself is made against independent PWSCF/Quantum ESPRESSO calculations that read the same pseudopotentials, as stated: 'For this purpose we use the PWSCF code from the QuantumEspresso suite, which reads the same pseudopotentials as Conquest and allows a direct comparison.' This is an external benchmark rather than a restatement of an input. The paper's self-citations are to previous Conquest methodology papers and are used as implementation references, not as a load-bearing uniqueness theorem or ansatz justification for the present accuracy claim. The reader's noted concern that the plane-wave references may not be fully converged at the stated cutoffs is a convergence-testing limitation, not circularity: an unconverged reference would make the comparison inaccurate, but it would not make the claim true by construction. Similarly, the skeptic's observation that the Conclusion states 'better than 1% in bulk modulus and often within 0.1% of the lattice constant' while some table entries exceed these bounds is an internal consistency issue about the strength of the claim, not a circularity. No step in the paper reduces a prediction to a fitted input, a self-definition, or a renamed known result. The derivation is self-contained with respect to the benchmark data, so no circular step is present.

Assumptions & free parameters 1 free parameters · 3 assumptions · 0 invented entities

The central results rest on standard PAO assumptions plus an unverified convergence premise; no new physical entities are introduced.

free parameters (1)
  • Confinement energy shift ladder = 2 eV, 0.2 eV, 0.02 eV
    Chosen empirically ('We have found, empirically, that energy shifts of 2 eV and 0.02 eV fulfil these criteria well', Section 3). Not fitted to the benchmark solids, but hand-selected values on which the transferability claim depends.
assumptions (3)
  • domain assumption Confined-atom pseudo-atomic orbitals provide a variational basis for Kohn-Sham eigenstates in solids.
    Standard assumption of PAO-based DFT codes; invoked throughout Section 3 when defining radial functions from confinement energies.
  • domain assumption The Quantum Espresso plane-wave calculations at the stated cutoffs and k-point meshes are fully converged.
    The paper states cutoffs in table captions but does not show convergence tests; the comparison assumes PW results are exact within the chosen functional/pseudopotential. Section 4.
  • domain assumption Using the same pseudopotentials and functionals in both codes isolates basis-set error.
    The paper states 'comparing to fully converged plane wave results using the same pseudopotentials and grids' (Abstract); this assumes no implementation differences beyond basis set.

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Cite this review

Pith. "Pith review of Highly accurate local basis sets for large-scale DFT calculations in CONQUEST." pith.science (2026). https://pith.science/paper/YNKURTEO

@misc{pith2026190802707,
  author       = {Pith},
  title        = {Pith review of: Highly accurate local basis sets for large-scale DFT calculations in CONQUEST},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YNKURTEO}},
  note         = {Machine review of arXiv:1908.02707}
}
read the original abstract

Given the widespread use of density functional theory (DFT), there is an increasing need for the ability to model large systems (beyond 1,000 atoms). We present a brief overview of the large-scale DFT code Conquest, which is capable of modelling such large systems, and discuss approaches to the generation of consistent, well-converged pseudo-atomic basis sets which will allow such large scale calculations. We present tests of these basis sets for a variety of materials, comparing to fully converged plane wave results using the same pseudopotentials and grids.

Figures

Figures reproduced from arXiv: 1908.02707 by the authors.

Figure 1
Figure 1. Binding energy curves for bulk Ge calculated with plane waves, and the three equal radii PAO basis sets. Parameters as in the caption to [PITH_FULL_IMAGE:figures/full_fig_p007_1.png] view at source ↗

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