Serially Improved GTOs for Molecular Applications (SIGMA): basis sets from monovalent ions

Guillermo Ramirez; Ignacio Ema; Jose Manuel Garcia-de-la-Vega; Rafael Lopez

REVIEW 2 major objections 4 minor 17 references

Serially Improved GTOs for Molecular Applications (SIGMA): basis sets from monovalent ions

T0 review · 2 major / 4 minor · reviewed 2026-07-13 · grok-4.5

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Pith's one-line read Ionic basis sets iσXZ1 describe alkali-halide clusters accurately and stay numerically stable up to 792 NaCl units.

desk verdict Solid, usable ion-specific SIGMA bases plus compact RI-J auxiliaries that actually run on (NaCl)792 without linear-dependence drama. read the letter →

arxiv 2607.09238 v1 pith:D7S2GW7M submitted 2026-07-10 physics.chem-ph physics.comp-ph

Ignacio Ema , Guillermo Ramirez , Rafael Lopez , Jose Manuel Garcia-de-la-Vega This is my paper · ORCID

classification physics.chem-phphysics.comp-ph

keywords ionicbasissetsSIGMAalkali-halideclustersresolution-of-the-identityGaussian-typeorbitalsnear-lineardependencemolecularelectrostaticpotential

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

This paper introduces a family of Gaussian basis sets, iσXZ1, built specifically for monovalent cations and anions rather than neutral atoms. The sets are more compact than standard Dunning-style bases yet often give lower correlation energies, and they pair with new Coulomb auxiliary sets for efficient resolution-of-the-identity calculations. On alkali-halide clusters the bases recover band gaps, lattice energies and bond lengths that approach experiment as cluster size and basis quality grow, while remaining free of near-linear-dependency problems even for (NaCl)792. Because electron correlation is small in these highly ionic systems, a density-functional method already gives reliable structures and energies, making the combination practical for very large ionic aggregates. The same compactness also makes the molecular electrostatic potential expand rapidly when the density is partitioned into nearly spherical atomic contributions.

What carries the argument

The iσXZ1 basis sets: monovalent-ion-specific contracted Gaussians that place one extra primitive in each polarization shell and whose diffuse exponents are chosen to avoid linear dependence in extended ionic environments.

What would settle it

A high-level correlated single-point calculation (for example RI-MP2 or CCSD) on a medium-sized non-NaCl cluster such as (LiH)24 or (KF)90 that yields lattice energies or band gaps differing substantially from the RI-PBE values reported with the same iσXZ1 bases.

Watch

Extended reading notes

Core claim

A new family of ionic Gaussian basis sets, iσXZ1, together with matching Coulomb auxiliary sets, furnishes accurate structural, energetic and electronic properties for alkali-halide clusters while remaining free of near-linear dependencies even for systems containing hundreds of formula units.

Load-bearing premise

The paper assumes that electron-correlation effects stay small enough in all the alkali-halide systems studied that density-functional results validated on NaCl can be trusted for the other cation-anion combinations without further checks.

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Signed reviews

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Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

This is a methods paper that delivers what it claims: compact contracted Gaussian sets (iσDZ1/TZ1/QZ1) for H−, Li+, F−, Na+, Cl−, K+ plus matching Coulomb auxiliaries (iσAuxJ), engineered for monovalent ionic clusters. The new pieces are the ion-specific contractions (extra primitive in each polarization shell) and the DAM self-repulsion fitting that produces the auxiliaries. Everything else is careful numerical work.

What they do well is the evidence. Table 2 shows lower CISD energies with fewer contracted functions than the corresponding Dunning aXZ/cXZ/pwcXZ sets. Tables 3–7 track band gaps, lattice energies and nearest-neighbor distances for (MX)n up to n=792; the numbers move systematically toward experiment with both cardinality and cluster size. The Appendix tables (A2–A10) demonstrate that iσAuxJ recovers non-RI HF/PBE energies to ~10−6 Eh or better while staying far smaller than autoAux. The (NaCl)792 single-point with ~50k basis / 96k auxiliary functions is a real stress test of linear-dependence robustness, and they report clean convergence. The DAM multipole expansion of the MESP also converges faster than with Dunning sets, which is consistent with the near-spherical ion picture.

Soft spots are real but limited. After Table 3 they assert that correlation is small enough that RI-PBE results transfer to the other (MX)n series; they never re-check that with MP2 or a hybrid for LiH/KH etc. That is a domain-specific assumption, not a hidden flaw, but it is the weakest link. The main-basis optimization protocol is only sketched by reference to earlier SIGMA papers; a reader who wants to regenerate the exponents will need those. Chemical scope is deliberately narrow (alkali hydrides/halides). None of this breaks the central claim.

Math and data look clean; citations are appropriate (Dunning, Koga numerical atoms, their own SIGMA series, DAM). Free parameters are the usual basis exponents and the 10−10 self-repulsion threshold—standard for this genre. No circularity: they test against external atomic energies, experiment, and non-RI references.

This is for people who actually run large ionic clusters or salt models and need compact, stable bases. It deserves a serious referee. I would accept it for peer review and would cite the sets if I needed monovalent-ion calculations in the next year.

Referee Report

2 major / 4 minor

Summary. The manuscript introduces the iσXZ1 family of contracted Gaussian basis sets (DZ1/TZ1/QZ1) for the monovalent ions H−, Li+, F−, Na+, Cl− and K+, together with matching Coulomb auxiliary sets iσAuxJ. The sets are constructed to reflect the distinct electronic structure of cations versus anions and are shown, via HF/CISD atomic energies, RI-HF/PBE/MP2 calculations on (NaCl)n clusters up to n=792, and RI-PBE calculations on a broader set of (MX)n alkali-halide clusters, to deliver structural, energetic and electronic properties that systematically approach experiment while remaining free of near-linear-dependence problems. An additional DAM analysis of the molecular electrostatic potential is used to illustrate rapid multipole convergence.

Significance. If the numerical performance holds under independent re-implementation, the work supplies a compact, robust and immediately usable alternative to conventional Dunning-style sets for large-scale calculations on ionic materials and clusters. Strengths that raise the contribution above a routine basis-set paper include (i) the explicit demonstration of numerical stability for a 50 688-function (NaCl)792 calculation, (ii) the carefully validated, self-repulsion-optimized iσAuxJ auxiliaries that outperform autoAux at smaller size, (iii) the systematic size- and cardinality-convergence tables against experimental lattice energies, gaps and distances, and (iv) the DAM multipole analysis that quantifies the near-spherical character of the ions. These features make the sets practically valuable for the ionic systems for which they are designed.

major comments (2)

[text after Table 3] After Table 3 the authors assert that electron-correlation effects remain small for all (MX)n systems (M = Li/Na/K, X = H/F/Cl) and therefore report only RI-PBE results in Tables 5–7. The assertion is plausible for highly ionic species and is supported by the HF/PBE/MP2 comparison for NaCl, yet no analogous multi-method check is provided for even one other stoichiometry (e.g., LiF or KH). A short additional validation (HF versus PBE lattice energies or gaps for two or three representative clusters) would remove the sole load-bearing transferability assumption.
[Introduction / Table 1] The generation protocol for the iσXZ1 primitive exponents and contraction coefficients is never stated; only the final composition (Table 1) and the resulting atomic energies (Table 2) are given. In contrast, the Appendix supplies a complete, reproducible optimization procedure for the auxiliary sets. Because the central claim rests on the quality of these primary bases, a concise description of how the serial-improvement procedure of the earlier SIGMA papers was adapted for the ionic electronic structure (or an explicit pointer to the precise algorithmic steps) is required for independent verification.

minor comments (4)

[Appendix Tables A2–A10] Numerous typographical inconsistencies appear in the Appendix tables (e.g., “isDZ1” for iσDZ1, incorrect ion labels such as “Li+” in the NaF header of Table A7, and occasional reference energies that do not match the non-RI values quoted in the same table). These should be corrected for clarity.
[Table 6] In Table 6 several contracted-function counts look anomalous (e.g., LiF iσTZ1 listed as 8280/7650). These appear to be transcription errors and should be reconciled with the compositions of Table 1.
[Figure 1] Figure 1 caption and the surrounding text would benefit from an explicit statement of the isosurface value (0.001 a.u.) and of the color scale used for the MESP maps so that the visual comparison is fully self-contained.
[Tables 5–7] The experimental references for the bulk NaCl gap, lattice energy and lattice constant are given, but analogous citations for the other MX solids discussed in Tables 5–7 are missing; adding them would strengthen the convergence claims.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity; iσXZ1 performance claims rest on external numerical, experimental, and non-RI benchmarks rather than self-referential definitions or fits.

full rationale

The paper constructs ionic basis sets iσXZ1 (extending prior SIGMA work) and auxiliary iσAuxJ sets, then validates them against independent references: numerical atomic HF/CISD energies (Koga et al.), experimental bulk gaps/lattice energies/distances, Dunning caXZ comparisons (Tables 1–2), and non-RI HF/PBE total energies for clusters (Appendix Tables A2–A10). Auxiliary optimization minimizes self-repulsion of DAM density fragments from diatomic HF densities, then separately checks recovery of molecular energies to ~10^{-6} Eh; the fit objective is not the reported molecular properties, so predictions are not forced by construction. Self-citations to the authors’ SIGMA series and DAM partition are present for context and methodology but are not load-bearing for the central accuracy/robustness claims, which stand on the external benchmarks and size-scaling tests up to (NaCl)792. The explicit transferability assumption for RI-PBE (post-Table 3) is a domain limitation, not a circular reduction. No self-definitional loops, fitted-as-prediction tautologies, uniqueness theorems, or renamed known results appear in the derivation chain.

Assumptions & free parameters 3 free parameters · 4 assumptions · 2 invented entities

The central claim rests on standard electronic-structure methods plus the authors’ prior SIGMA construction philosophy and the DAM density partition. Free parameters are the Gaussian exponents and contraction coefficients of the new sets (and of the auxiliaries). No new physical entities are postulated; the ‘invented’ objects are the basis-set definitions themselves.

free parameters (3)

iσXZ1 primitive exponents and contraction coefficients
The main product of the paper; values are optimized (by the SIGMA serial-improvement procedure referenced but not re-derived here) and then frozen for all subsequent molecular tests.
iσAuxJ Gaussian exponents and coefficients per angular momentum
Fitted by minimizing the DAM-fragment self-repulsion residual (Eqs. 9–12) to ~10−10 relative error; shared across the three diatomics of each ion.
lmax truncation threshold 10−10 for auxiliary expansion
Ad-hoc numerical cutoff that determines which angular-momentum shells enter iσAuxJ (Appendix).

assumptions (4)

domain assumption HF, DFT (PBE) and MP2 with Gaussian bases are adequate for structural and energetic properties of highly ionic alkali-halide clusters.
Used throughout Tables 3–7; PBE is then taken as representative for all MX systems.
domain assumption The DAM atoms-in-molecules density partition (Fernández Rico et al.) correctly separates molecular density into atomic fragments for both MESP analysis and auxiliary-set fitting.
Invoked for Figure 1 and for the entire Appendix optimization of iσAuxJ.
ad hoc to paper Electron-correlation effects remain small for all (MX)n systems considered, so RI-PBE conclusions transfer from NaCl to Li/Na/K hydrides and halides.
Stated after Table 3; thereafter only RI-PBE results are reported for the broader set.
domain assumption Standard resolution-of-the-identity Coulomb approximation with a fitted auxiliary basis is sufficiently accurate when self-repulsion residuals are ~10−10.
Underpins all RI timings and energy comparisons in Tables 3–7 and A2–A10.

invented entities (2)

iσXZ1 ionic basis-set family (DZ1/TZ1/QZ1) independent evidence
purpose: Provide compact, ion-specific contracted Gaussian bases for monovalent cations and anions.
New basis-set definitions; independent evidence is the numerical performance tables against experiment and Dunning sets.
iσAuxJ Coulomb auxiliary basis sets independent evidence
purpose: Enable accurate RI-J calculations for the same ions with far fewer auxiliaries than autoAux.
New auxiliary definitions; validated against non-RI reference energies in Appendix tables.

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Pith. "Pith review of Serially Improved GTOs for Molecular Applications (SIGMA): basis sets from monovalent ions." pith.science (2026). https://pith.science/paper/D7S2GW7M

@misc{pith2026260709238,
  author       = {Pith},
  title        = {Pith review of: Serially Improved GTOs for Molecular Applications (SIGMA): basis sets from monovalent ions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/D7S2GW7M}},
  note         = {Machine review of arXiv:2607.09238}
}

read the original abstract

A new family of ionic basis sets, denoted i{\sigma}XZ1, is presented for molecular calculations on systems containing monovalent ions. The basis sets extend the SIGMA family by explicitly accounting for the different electronic structure of cations and anions. Auxiliary basis sets for resolution-of-the-identity calculations are also developed for the Coulomb term. The performance of the proposed basis sets is assessed for alkali-halide clusters. Compared with conventional basis sets, i{\sigma}XZ1 provides an accurate description of structural, energetic, and electronic properties while showing remarkable robustness against near-linear dependencies, allowing stable calculations on systems containing up to 792 NaCl units. These features make the i{\sigma}XZ1 family a reliable and efficient alternative for large-scale calculations on ionic systems.

Figures

Figures reproduced from arXiv: 2607.09238 by the authors.

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Works this paper leans on

17 extracted references · 7 canonical work pages

[1]

Ema , author G

author author I. Ema , author G. Ram\' rez , author R. L\'opez ,\ and\ author J. M. \ Garc\' a de la Vega ,\ title title Serially improved GTOs for molecular applications (SIGMA): Basis sets from H to Ne , \ @noop journal journal J. Chem. Phys. \ volume 158 ,\ pages 244112 ( year 2023 ) NoStop

2023
[2]

Ema , author G

author author I. Ema , author G. Ram\' rez , author R. L\'opez ,\ and\ author J. M. \ Garc\' a de la Vega ,\ title title Serially improved gaussian-type orbitals for molecular calculations containing third-row atoms , \ https://doi.org/10.1103/PhysRevA.111.022801 journal journal Phys. Rev. A \ volume 111 ,\ pages 022801 ( year 2025 a ) NoStop

work page doi:10.1103/physreva.111.022801 2025
[3]

Ema , author J

author author I. Ema , author J. San-Fabián , author G. Ramírez , author R. López ,\ and\ author J. M. \ García de la Vega ,\ title title Reduced Serially Improved GTOs for Molecular Applications from H to Ar: Efficient Diffuse Functions in Augmented Basis Sets , \ https://doi.org/10.1021/acs.jpca.5c05079 journal journal J. Phys. Chem. A \ volume 129 ,\ p...

work page doi:10.1021/acs.jpca.5c05079 2025
[4]

author author R. A. \ Kendall , author T. H. \ Dunning Jr ,\ and\ author R. J. \ Harrison ,\ title title Electron affinities of the first-row atoms revisited. systematic basis sets and wave functions , \ @noop journal journal J. Chem. Phys. \ volume 96 ,\ pages 6796--6806 ( year 1992 ) NoStop

1992
[5]

author author D. E. \ Woon \ and\ author J. Dunning , Thom H. ,\ title title Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon , \ https://doi.org/10.1063/1.464303 journal journal J. Chem. Phys. \ volume 98 ,\ pages 1358--1371 ( year 1993 ) NoStop

doi:10.1063/1.464303 1993
[6]

author author B. P. \ Prascher , author D. E. \ Woon , author K. A. \ Peterson , author T. H. \ Dunning ,\ and\ author A. K. \ Wilson ,\ title title Gaussian Basis Sets for Use in Correlated Molecular Calculations. VII. Valence, Core-Valence, and Scalar Relativistic Basis Sets for Li, Be, Na, and Mg , \ https://doi.org/10.1007/s00214-010-0764-0 journal jo...

work page doi:10.1007/s00214-010-0764-0 2011
[7]

author author J. G. \ Hill \ and\ author K. A. \ Peterson ,\ title title Gaussian basis sets for use in correlated molecular calculations. xi. pseudopotential-based and all-electron relativistic basis sets for alkali metal (k--fr) and alkaline earth (ca--ra) elements , \ https://doi.org/10.1063/1.5010587 journal journal J. Chem. Phys. \ volume 147 ,\ page...

doi:10.1063/1.5010587 2017
[8]

Lehtola ,\ title title Curing basis set overcompleteness with pivoted Cholesky decompositions , \ https://doi.org/10.1063/1.5139948 journal journal J

author author S. Lehtola ,\ title title Curing basis set overcompleteness with pivoted Cholesky decompositions , \ https://doi.org/10.1063/1.5139948 journal journal J. Chem. Phys. \ volume 151 ,\ pages 241102 ( year 2019 ) NoStop

work page doi:10.1063/1.5139948 2019

Show all 17 references

[9]

Fern\'andez Rico , author R

author author J. Fern\'andez Rico , author R. L \'o pez , author I. Ema ,\ and\ author G. Ram \'i rez ,\ title title Electrostatic potentials and fields from density expansions of deformed atoms in molecules , \ @noop journal journal J. Comput. Chem. \ volume 25 ,\ pages 1347-...

2004
[10]

Fern \'a ndez Rico , author R

author author J. Fern \'a ndez Rico , author R. L \'o pez , author I. Ema , author G. Ram \'i rez ,\ and\ author E. Lude \ n a ,\ title title Analytical method for the representation of atoms-in-molecules densities , \ @noop journal journal J. Comput. Chem. \ volume 25 ,\ page...

2004
[11]

author author I. S. \ Gradshteyn \ and\ author I. M. \ Ryzhik ,\ @noop title Table of Integrals, Series and Products ,\ edition 4th \ ed.\ ( publisher Academic Press ,\ address New York ,\ year 1980 ) NoStop

1980
[12]

author author A. W. \ Alherz \ and\ author B. A. \ Alayyoub ,\ title title Evaluation of surface and bulk properties of alkali halides: A first-principles study on (100) and (110) facets , \ https://doi.org/10.1021/acsomega.5c06914 journal journal ACS Omega \ volume 10 ,\ page...

2025 doi
[13]

Koga , author S

author author T. Koga , author S. Watanabe , author K. Kanayama , author R. Yasuda ,\ and\ author A. J. \ Thakkar ,\ title title Improved Roothaan-Hartree-Fock wave functions for atoms and ions with N 54 , \ https://doi.org/10.1063/1.470488 journal journal J. Chem. Phys. \ vol...

1995 doi
[14]

author author D. M. \ Roessler \ and\ author W. C. \ Walker ,\ title title Electronic spectrum and ultraviolet optical properties of crystalline NaCl , \ https://doi.org/10.1103/PhysRev.159.733 journal journal Phys. Rev. \ volume 159 ,\ pages 733--738 ( year 1967 ) NoStop

1967 doi
[15]

author author National Institute of Standards and Technology ,\ https://webbook.nist.gov/cgi/cbook.cgi?ID=C7647145 title Nist chemistry webbook, srd 69: Sodium chloride ( NaCl ) , \ ( year 2026 ),\ note accessed: 2026-06-17 NoStop

2026
[16]

author author J. E. \ Nickels , author M. A. \ Fineman ,\ and\ author W. E. \ Wallace ,\ title title Lattice constant of sodium chloride , \ @noop journal journal J. Phys. Chem. \ volume 53 ,\ pages 625--628 ( year 1949 ) NoStop

1949
[17]

Neese ,\ title title Software update: the ORCA program system, version 6.0 , \ https://doi.org/10.1002/wcms.70019 journal journal WIRES Comput

author author F. Neese ,\ title title Software update: the ORCA program system, version 6.0 , \ https://doi.org/10.1002/wcms.70019 journal journal WIRES Comput. Molec. Sci. \ volume 15 ,\ pages e70019 ( year 2025 ) NoStop

2025 doi

Pith tools

Reviewed July 13, 2026 · model on record in the stance chip above.

[1] [1]

Ema , author G

author author I. Ema , author G. Ram\' rez , author R. L\'opez ,\ and\ author J. M. \ Garc\' a de la Vega ,\ title title Serially improved GTOs for molecular applications (SIGMA): Basis sets from H to Ne , \ @noop journal journal J. Chem. Phys. \ volume 158 ,\ pages 244112 ( year 2023 ) NoStop

2023

[2] [2]

Ema , author G

author author I. Ema , author G. Ram\' rez , author R. L\'opez ,\ and\ author J. M. \ Garc\' a de la Vega ,\ title title Serially improved gaussian-type orbitals for molecular calculations containing third-row atoms , \ https://doi.org/10.1103/PhysRevA.111.022801 journal journal Phys. Rev. A \ volume 111 ,\ pages 022801 ( year 2025 a ) NoStop

work page doi:10.1103/physreva.111.022801 2025

[3] [3]

Ema , author J

author author I. Ema , author J. San-Fabián , author G. Ramírez , author R. López ,\ and\ author J. M. \ García de la Vega ,\ title title Reduced Serially Improved GTOs for Molecular Applications from H to Ar: Efficient Diffuse Functions in Augmented Basis Sets , \ https://doi.org/10.1021/acs.jpca.5c05079 journal journal J. Phys. Chem. A \ volume 129 ,\ p...

work page doi:10.1021/acs.jpca.5c05079 2025

[4] [4]

author author R. A. \ Kendall , author T. H. \ Dunning Jr ,\ and\ author R. J. \ Harrison ,\ title title Electron affinities of the first-row atoms revisited. systematic basis sets and wave functions , \ @noop journal journal J. Chem. Phys. \ volume 96 ,\ pages 6796--6806 ( year 1992 ) NoStop

1992

[5] [5]

author author D. E. \ Woon \ and\ author J. Dunning , Thom H. ,\ title title Gaussian basis sets for use in correlated molecular calculations. III. The atoms aluminum through argon , \ https://doi.org/10.1063/1.464303 journal journal J. Chem. Phys. \ volume 98 ,\ pages 1358--1371 ( year 1993 ) NoStop

doi:10.1063/1.464303 1993

[6] [6]

author author B. P. \ Prascher , author D. E. \ Woon , author K. A. \ Peterson , author T. H. \ Dunning ,\ and\ author A. K. \ Wilson ,\ title title Gaussian Basis Sets for Use in Correlated Molecular Calculations. VII. Valence, Core-Valence, and Scalar Relativistic Basis Sets for Li, Be, Na, and Mg , \ https://doi.org/10.1007/s00214-010-0764-0 journal jo...

work page doi:10.1007/s00214-010-0764-0 2011

[7] [7]

author author J. G. \ Hill \ and\ author K. A. \ Peterson ,\ title title Gaussian basis sets for use in correlated molecular calculations. xi. pseudopotential-based and all-electron relativistic basis sets for alkali metal (k--fr) and alkaline earth (ca--ra) elements , \ https://doi.org/10.1063/1.5010587 journal journal J. Chem. Phys. \ volume 147 ,\ page...

doi:10.1063/1.5010587 2017

[8] [8]

Lehtola ,\ title title Curing basis set overcompleteness with pivoted Cholesky decompositions , \ https://doi.org/10.1063/1.5139948 journal journal J

author author S. Lehtola ,\ title title Curing basis set overcompleteness with pivoted Cholesky decompositions , \ https://doi.org/10.1063/1.5139948 journal journal J. Chem. Phys. \ volume 151 ,\ pages 241102 ( year 2019 ) NoStop

work page doi:10.1063/1.5139948 2019