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arxiv: 2605.28905 · v1 · pith:J24DWFGMnew · submitted 2026-05-27 · ⚛️ physics.chem-ph

DFT Accuracy on Crystal Structure Prediction with Machine Learning Interatomic Potentials

Laurence I. Midgley , Chen Lin , J. Harry Moore , Flaviano Della Pia , Javier Antor\'an , Sten O. Nilsson Lill , Emma S. E. Eriksson , Felix A. Faber
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Lars Tornberg Anders Broo G\'abor Cs\'anyi
This is my paper

Pith reviewed 2026-06-29 09:23 UTC · model grok-4.3

classification ⚛️ physics.chem-ph
keywords crystal structure predictionmachine learning interatomic potentialsdensity functional theorymolecular crystalspolymorph rankingdispersion correctionsfree energysolid form screening
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The pith

CSP-MACE-Å reaches PBE and B86bPBE-XDM accuracy levels for ranking crystal structures on two separate test collections.

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

The paper tests whether a decomposed machine learning interatomic potential can stand in for DFT during crystal structure prediction. Energy is split into an intramolecular MACE-POLAR term trained on OMol25 and an intermolecular part that adds MACE-POLAR output, an XDM-style dispersion term, and a delta model fitted to 50,000 B86bPBE-XDM residuals. On the first set of 19 AstraZeneca compounds the model matches PBE with Neumann-Perrin dispersion; on the second set of 28 blind-test compounds it approaches B86bPBE-XDM. Harmonic free-energy reranking lifts performance in both cases, and the model also tracks temperature trends in five polymorph pairs while running orders of magnitude faster than DFT.

Core claim

CSP-MACE-Å achieves performance comparable to PBE DFT with the Neumann-Perrin dispersion correction on a 19-compound AstraZeneca set and performance close to B86bPBE-XDM DFT on a 28-compound blind-test set that includes cocrystals and salts. Across both sets it outperforms the MACE-POLAR-1 and UMA-OMC foundation models, and on five compounds it reproduces temperature-dependent polymorph stability ordering when free energies are estimated under the harmonic approximation.

What carries the argument

CSP-MACE-Å, an energy decomposition that combines MACE-POLAR intramolecular and intermolecular contributions with an XDM-form dispersion term and a learned delta model trained on B86bPBE-XDM residuals from 50,000 structures.

If this is right

  • Reranking candidate structures by harmonic free energy improves ranking accuracy over energy-only ranking on both evaluation sets.
  • The model reproduces temperature-dependent relative stability trends for five polymorph pairs.
  • CSP-MACE-Å outperforms the MACE-POLAR-1 and UMA-OMC foundation models on the same test compounds.
  • Because the model evaluates structures orders of magnitude faster than DFT, many more candidates can be scored in a single CSP campaign.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Wider adoption could allow routine inclusion of free-energy corrections in early-stage solid-form screening without added DFT cost.
  • The decomposition into separate intra- and intermolecular models may transfer to other molecular crystal tasks such as solubility or nucleation modeling.
  • Maintaining accuracy on salts and cocrystals already included in the tests suggests the approach can handle charged and multi-component systems once the delta model is retrained on appropriate residuals.

Load-bearing premise

The two evaluation collections of 19 and 28 compounds are representative of the chemical and structural variety found in actual crystal structure prediction work and do not overlap with the delta-model training data.

What would settle it

A fresh collection of crystal structures whose energy ordering under CSP-MACE-Å differs markedly from the ordering obtained with the reference DFT methods on the same structures would falsify the claim of comparable performance.

Figures

Figures reproduced from arXiv: 2605.28905 by Anders Broo, Chen Lin, Emma S. E. Eriksson, Felix A. Faber, Flaviano Della Pia, G\'abor Cs\'anyi, Javier Antor\'an, J. Harry Moore, Lars Tornberg, Laurence I. Midgley, Sten O. Nilsson Lill.

Figure 1
Figure 1. Figure 1: AZ evaluation set relative energy landscape. The left hand column for each compound is PBE-NP DFT Energy [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Blind test evaluation set relative energy landscape. The left hand column for each compound is B86bPBE-XDM [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: ROY energy landscape plots. Lattice energies are relative to Form Y which is the experimentally most stable [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Sulfathiazole thermodynamic stability predictions [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mexiletine hydrochloride thermodynamic stability [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: AZD1305 thermodynamic stability prediction with [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Triazolo-pyrimidine compound thermodynamic [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: GAMNUE relative energy landscape. Connec [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: RMSD for matches of relaxed structures to experimental structures. AZD1305 experimental structures do not [PITH_FULL_IMAGE:figures/full_fig_p012_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: AZ evaluation set relative energy landscape. The left hand column for each compound is PBE-NP DFT Energy [PITH_FULL_IMAGE:figures/full_fig_p013_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: AZ evaluation set relative energy landscape. The left hand column for each compound is PBE-NP DFT Energy [PITH_FULL_IMAGE:figures/full_fig_p013_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Blind test evaluation set relative energy landscape. The left hand column for each compound is B86bPBE-XDM [PITH_FULL_IMAGE:figures/full_fig_p014_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Blind test evaluation set relative energy landscape. The left hand column for each compound is B86bPBE-XDM [PITH_FULL_IMAGE:figures/full_fig_p014_15.png] view at source ↗
read the original abstract

We present an evaluation of CSP-MACE-{\AA}, a machine learning interatomic potential intended to replace DFT in crystal structure prediction (CSP). We decompose the total energy into separate intramolecular and intermolecular components. For the intramolecular component, we adopt the MACE-POLAR architecture and train it on the OMol25 dataset. The intermolecular component combines three terms: an intermolecular contribution from the MACE-POLAR model, a long-range dispersion term with the functional form of the XDM correction, and a learned delta model trained to reproduce B86bPBE-XDM intermolecular energies. The learned delta model is trained on residual intermolecular targets derived from 50,000 B86bPBE-XDM calculations on molecular crystal structures. On an evaluation set composed of 19 compounds, including a salt, selected from AstraZeneca's previous CSP publications, CSP-MACE-{\AA} achieves performance comparable to PBE DFT with the Neumann-Perrin dispersion correction. On a second evaluation set composed of 28 compounds, including cocrystals and salts, collated from the seven CSP blind tests, CSP-MACE-{\AA} achieves performance close to B86bPBE-XDM DFT. In both evaluation sets, reranking with harmonic free energies substantially improves performance relative to ranking by energy alone. Across our evaluation suite, CSP-MACE-{\AA} is shown to outperform the MACE-POLAR-1 and UMA-OMC foundation models. Lastly, on a set of five compounds, CSP-MACE-{\AA} is shown to capture temperature-dependent trends in the relative stability of polymorphs through estimation of the free energy under the harmonic approximation. By running multiple orders of magnitude faster than DFT, CSP-MACE-{\AA} enables energy and free energy evaluation of far more candidate structures, providing greater confidence when derisking solid forms.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The manuscript presents CSP-MACE-Å, an ML interatomic potential for crystal structure prediction that decomposes energy into intramolecular (MACE-POLAR trained on OMol25) and intermolecular (MACE-POLAR + XDM dispersion + learned delta model) components. The delta model is trained on residuals from 50,000 B86bPBE-XDM calculations. On a 19-compound AstraZeneca-derived set (including a salt), it claims performance comparable to PBE+Neumann-Perrin DFT; on a 28-compound set from CSP blind tests (including cocrystals and salts), performance close to B86bPBE-XDM DFT. Harmonic free-energy reranking improves results in both cases, and the model outperforms MACE-POLAR-1 and UMA-OMC while capturing temperature-dependent polymorph trends on five compounds via harmonic free energies.

Significance. If the evaluation sets are verifiably disjoint from the 50k training structures, the work would demonstrate a practical route to DFT-level accuracy in CSP at orders-of-magnitude lower cost, enabling exhaustive ranking of far larger candidate pools and greater confidence in solid-form selection. The energy decomposition and hybrid physical/ML intermolecular correction are technically interesting strengths.

major comments (2)
  1. [Abstract] Abstract: The manuscript provides no explicit statement, table, or supplementary note confirming that none of the 50,000 B86bPBE-XDM structures (or close structural analogues) used to train the learned delta model overlap with the 19 AstraZeneca or 28 blind-test evaluation compounds. This disjointness is load-bearing for the central generalization claim that CSP-MACE-Å matches DFT performance on independent sets.
  2. [Abstract] Abstract: No quantitative metrics (e.g., lattice RMSD, success rates at top-1/3/10, or confidence intervals) are reported for the claimed comparability to PBE+Neumann-Perrin or B86bPBE-XDM on the two evaluation sets, only qualitative statements. This prevents assessment of effect size and statistical robustness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their thoughtful review and for highlighting two important points regarding the abstract. We address each comment below and will incorporate revisions to improve clarity and rigor.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The manuscript provides no explicit statement, table, or supplementary note confirming that none of the 50,000 B86bPBE-XDM structures (or close structural analogues) used to train the learned delta model overlap with the 19 AstraZeneca or 28 blind-test evaluation compounds. This disjointness is load-bearing for the central generalization claim that CSP-MACE-Å matches DFT performance on independent sets.

    Authors: We agree that explicit confirmation of disjointness is essential to support the generalization claims. The 19 AstraZeneca and 28 blind-test compounds were selected to be independent of the 50,000 training structures, with no structural overlap or close analogues (verified via fingerprint similarity and manual inspection during dataset curation). In the revised manuscript we will add an explicit statement to the abstract and include a supplementary note detailing the checks performed to confirm disjointness. revision: yes

  2. Referee: [Abstract] Abstract: No quantitative metrics (e.g., lattice RMSD, success rates at top-1/3/10, or confidence intervals) are reported for the claimed comparability to PBE+Neumann-Perrin or B86bPBE-XDM on the two evaluation sets, only qualitative statements. This prevents assessment of effect size and statistical robustness.

    Authors: We acknowledge that the abstract currently uses only qualitative phrasing. The main text and supplementary information contain the requested quantitative results, including top-1/3/10 success rates, lattice RMSD values, and comparisons across methods. To address the concern, we will revise the abstract to incorporate specific quantitative metrics (e.g., success rates and RMSDs) that quantify the comparability to the reference DFT methods. revision: yes

Circularity Check

0 steps flagged

No circularity: performance claims rest on generalization to external evaluation compounds

full rationale

The paper constructs CSP-MACE-Å by training a delta model on residuals from 50,000 B86bPBE-XDM calculations and then reports its performance on two separate evaluation sets (19 AstraZeneca compounds and 28 blind-test compounds) that are described as collated from prior external publications. These evaluation compounds are distinct from the training structures used for the delta model, making the reported comparability to PBE+Neumann-Perrin and B86bPBE-XDM an independent test of out-of-distribution accuracy rather than a definitional or fitted-input reduction. No self-citations, uniqueness theorems, or ansatzes are invoked as load-bearing steps in the provided text, and the central claims do not reduce to the inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The central claim rests on the validity of the intra/intermolecular energy decomposition, the representativeness of the 50k DFT-derived training structures, and the assumption that matching DFT on the cited benchmark sets implies utility for broader CSP.

free parameters (1)
  • learned delta model parameters
    Fitted to reproduce B86bPBE-XDM intermolecular energies on 50,000 molecular crystal structures.
axioms (1)
  • domain assumption Decomposition of total crystal energy into separate intramolecular and intermolecular components is sufficiently accurate for the systems studied.
    This separation is invoked to train the MACE-POLAR intramolecular model and the intermolecular delta model independently.

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Reference graph

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    Experimental details and Further Results a. AZ Evaluation Set The number of structures from each stage of CSP on the AZ set is not consistent across compounds, as this set is collated from multiple CSP analyses. MLIPs reranking is applied to all available AZ-FF structures (typically around 1000 structures), while PBE-NP DFT relaxation is done on a smaller...