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arxiv: 2606.25853 · v1 · pith:AFZH37ELnew · submitted 2026-06-24 · ❄️ cond-mat.mtrl-sci

A Combined Tight Binding with Machine Learning Potential Model for Magnesium Compounds

Jiwen Yu , Arash A. Mostofi , Andrew Horsfield This is my paper

Pith reviewed 2026-06-25 20:09 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords DFTBMACEmachine learning potentialmagnesium compoundshybrid modelelectronic structurestructural relaxationphonon calculations
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The pith

Replacing the pair potential in DFTB with a MACE machine learning potential improves accuracy for magnesium systems while retaining electronic structure information.

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

The paper introduces a hybrid DFTB+MACE model for magnesium-based systems in which the standard repulsive pair potential of density functional tight binding is replaced by a many-body MACE potential. The MACE component is trained only on the residuals between full DFT energies and forces and the DFTB values (excluding the pair term). This hybrid is tested on structural relaxations of MgO-CO2 adsorption, molecular dynamics of water clusters, and phonon spectra of fcc and bcc MgO, showing better accuracy than conventional DFTB with pair potentials in most cases and at only moderate extra cost. The approach also supplies explicit electronic structures, which most pure machine-learning potentials cannot provide. The central goal is to reach length and time scales beyond first-principles methods while preserving charge-transfer information.

Core claim

The DFTB+MACE model, formed by substituting the repulsive pair potential with a MACE many-body term trained on DFT minus DFTB differences, yields improved accuracy over DFTB plus pair potential for structural, dynamical, and vibrational properties of magnesium compounds while still delivering electronic structures at moderate added computational expense.

What carries the argument

The DFTB+MACE hybrid potential in which MACE replaces the conventional repulsive pair potential and is trained on the DFT-DFTB energy and force residuals.

If this is right

  • Structural relaxations of MgO-CO2 adsorption systems reach higher accuracy than with DFTB plus pair potential.
  • Molecular dynamics of water clusters and phonon spectra of both fcc-MgO and bcc-MgO become feasible with better fidelity at moderate extra cost.
  • Simulations can extend to length and time scales beyond direct DFT while an explicit electronic-structure description is retained.
  • Charge-transfer processes in magnesium materials can be studied at scales inaccessible to pure first-principles methods.

Where Pith is reading between the lines

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

  • The same residual-training strategy could be applied to other elemental or compound systems where a tight-binding baseline already exists.
  • Expanding the original MACE training set to cover a wider range of magnesium configurations would be expected to reduce generalization errors in new simulations.
  • The hybrid framework offers a practical route for studying defect migration or interface charge transfer in magnesium-based batteries or catalysts at intermediate scales.

Load-bearing premise

The MACE component trained on DFT minus DFTB differences will generalize accurately to the structural relaxations, molecular dynamics trajectories, and phonon calculations performed in the study.

What would settle it

Running the DFTB+MACE model on a set of magnesium structures outside the original training distribution and finding that its errors in energy or forces exceed those of standard DFTB plus pair potential would falsify the accuracy claim.

Figures

Figures reproduced from arXiv: 2606.25853 by Andrew Horsfield, Arash A. Mostofi, Jiwen Yu.

Figure 1
Figure 1. Figure 1: The predicted force values for the Mg-C-O-H system against the reference values [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The mean absolute error of forces and normalized calculation time for the Mg-c [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: The cohesive energy of (a) fcc-MgO and (b) bcc-MgO against the lattice constant. [PITH_FULL_IMAGE:figures/full_fig_p016_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Phonon spectrum of fcc-MgO calculated by (a) PBE-DFT, (b) DFTB+MACE, (c) [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Phonon spectrum of bcc-MgO calculated by (a) PBE-DFT, (b) DFTB+MACE, [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: The structure for the adsorption of CO2 on the (a) MgO (100) surface and (b) MgO (110) surface calculated by the DFTB+MACE model. The coral balls represent Mg atoms, the blue ball represents the C atom and the red balls represent O atoms. 22 [PITH_FULL_IMAGE:figures/full_fig_p022_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: (a) The initial geometry of a water bulk, (b) the predicted force value against the [PITH_FULL_IMAGE:figures/full_fig_p024_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) the initial geometry of a water bulk on (0001) surface of Mg(OH) [PITH_FULL_IMAGE:figures/full_fig_p026_8.png] view at source ↗
read the original abstract

We present a model for magnesium-based systems that combines density functional tight binding (DFTB) with MACE, a machine learning interatomic potential (DFTB+MACE). In this model, the conventional repulsive potential, pair potential, is replaced by a many-body MACE potential. The MACE component of the model is trained on the difference between density functional theory (DFT) energies and forces and the corresponding DFTB values, but neglecting the pair potential contribution. Using this model we performed structural relaxation of MgO-CO2 adsorption systems, molecular dynamics calculations of water clusters and phonon spectrum calculations of stable fcc-MgO and metastable bcc-MgO structures. We compare the performance of our model with a pure MACE model and with DFT. We demonstrate that the DFTB+MACE model achieves improved accuracy relative to DFTB with a pair potential, in many cases with only a moderate increase in computational cost. In addition, it can provide electronic structures that most of the machine learning potentials cannot. The training dataset, originally developed for MACE, may not fully represent all regions of the potential surface we may encounter during simulations. Expanding the dataset for a wider potential surface is expected to further enhance predictive accuracy of DFTB+MACE model. Overall, the resulting DFTB+MACE framework enables simulations at length and time scales beyond the reach of first-principles methods while retaining an explicit description of electronic structures, making it particularly attractive for studying charge-transfer in materials.

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 / 1 minor

Summary. The manuscript introduces a hybrid DFTB+MACE model for magnesium-based systems in which the conventional repulsive pair potential of DFTB is replaced by a MACE many-body ML potential. The MACE component is trained on DFT minus DFTB energy/force differences (explicitly neglecting the pair-potential contribution). The model is applied to structural relaxations of MgO-CO2 adsorption systems, molecular-dynamics simulations of water clusters, and phonon calculations for stable fcc-MgO and metastable bcc-MgO; results are compared with pure MACE and DFT. The central claim is that DFTB+MACE improves accuracy relative to DFTB+pair potential, often at only moderate extra cost, while retaining an explicit electronic-structure description unavailable to most ML potentials.

Significance. If the claimed accuracy gains are shown to hold without uncontrolled extrapolation, the hybrid framework would usefully combine DFTB's electronic-structure access and linear-scaling potential with ML accuracy, enabling charge-transfer studies at length and time scales inaccessible to pure DFT. The approach is conceptually attractive for magnesium compounds, but its significance is currently limited by the absence of quantitative validation that the encountered configurations lie inside the training distribution.

major comments (2)
  1. [Abstract and Results (relaxations, MD, phonons)] Abstract (training description) and Results sections on relaxations/MD/phonons: the MACE component is trained on DFT-DFTB differences that neglect the pair potential, yet the manuscript itself states that the original MACE training set 'may not fully represent all regions of the potential surface we may encounter during simulations' of MgO-CO2, water clusters, and fcc/bcc-MgO phonons. No distribution-overlap test, nearest-neighbor analysis, or out-of-distribution error metric is reported to confirm that the local environments sampled in the reported calculations lie inside the training domain; this directly undermines the load-bearing claim of improved accuracy over DFTB+pair.
  2. [Results] Results (comparison statements): the claim that DFTB+MACE 'achieves improved accuracy relative to DFTB with a pair potential, in many cases with only a moderate increase in computational cost' is presented without tabulated RMSE values, error bars, or direct numerical comparisons against both DFTB+pair and pure MACE for the same observables (energies, forces, phonon frequencies). Without these data the central accuracy claim cannot be evaluated.
minor comments (1)
  1. [Abstract] Abstract: the final paragraph acknowledges the training-set limitation but offers only the generic remedy of 'expanding the dataset'; a concrete proposal (e.g., active-learning loop or targeted augmentation for water/MgO interfaces) would strengthen the discussion.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive review. The comments highlight important points on validation and quantitative presentation that we address below. We agree that strengthening these aspects will improve the manuscript.

read point-by-point responses

  1. Referee: Abstract (training description) and Results sections on relaxations/MD/phonons: the MACE component is trained on DFT-DFTB differences that neglect the pair potential, yet the manuscript itself states that the original MACE training set 'may not fully represent all regions of the potential surface we may encounter during simulations' of MgO-CO2, water clusters, and fcc/bcc-MgO phonons. No distribution-overlap test, nearest-neighbor analysis, or out-of-distribution error metric is reported to confirm that the local environments sampled in the reported calculations lie inside the training domain; this directly undermines the load-bearing claim of improved accuracy over DFTB+pair.

    Authors: We acknowledge the manuscript already notes this limitation of the training set. No explicit distribution-overlap or nearest-neighbor analysis was performed in the original work. The reported comparisons to DFT and pure MACE provide supporting evidence of utility within the sampled regimes, but we agree that direct domain-overlap metrics would strengthen the presentation. We will add a nearest-neighbor analysis of the encountered configurations relative to the training set and a brief discussion of extrapolation risks in the revised manuscript. revision: yes

  2. Referee: Results (comparison statements): the claim that DFTB+MACE 'achieves improved accuracy relative to DFTB with a pair potential, in many cases with only a moderate increase in computational cost' is presented without tabulated RMSE values, error bars, or direct numerical comparisons against both DFTB+pair and pure MACE for the same observables (energies, forces, phonon frequencies). Without these data the central accuracy claim cannot be evaluated.

    Authors: The original manuscript presents comparisons primarily through figures rather than tabulated numerical summaries. We agree that explicit RMSE tables, error bars, and side-by-side numerical values for energies, forces, and phonon frequencies would make the accuracy claims more readily evaluable. We will add a summary table with these quantitative metrics (including direct comparisons to DFTB+pair and pure MACE) in the revised Results section. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical training against external DFT data

full rationale

The paper presents DFTB+MACE as a hybrid model in which the MACE component is trained on the difference between external DFT energies/forces and DFTB values (explicitly neglecting the pair potential). All performance claims (improved accuracy over DFTB+pair, parity with pure MACE on relaxations/MD/phonons) are framed as outcomes of direct comparison to independent DFT reference calculations rather than any internal derivation or self-referential fit. No equations, self-citations, or uniqueness arguments are shown that would reduce the reported accuracy gains to quantities defined inside the paper; the procedure is a standard external-data training workflow and remains self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract-only review prevents enumeration of specific free parameters, axioms, or invented entities; the central modeling choice (MACE capturing the DFT-DFTB residual) is treated as an empirical assumption rather than a derived result.

pith-pipeline@v0.9.1-grok · 5802 in / 1159 out tokens · 15090 ms · 2026-06-25T20:09:22.441295+00:00 · methodology

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