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arxiv: 2605.08728 · v1 · submitted 2026-05-09 · ❄️ cond-mat.mtrl-sci

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Multi-Fidelity Computational Screening of High-Entropy MBenes for CO₂ Electroreduction

Sree Harsha Bharadwaj H , Raghavan Ranganathan
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Pith reviewed 2026-05-12 02:11 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci
keywords high-entropy MBenesCO2 electroreductionmachine learning interatomic potentialDFT screening2D materialscomputational hydrogen electrodeMACE potentialdisordered surfaces
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The pith

A DFT-MLIP-AIMD screening pipeline identifies 45 thermodynamically stable high-entropy MBenes that support CO2 adsorption and reduction to CO.

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

The paper screens 56 equiatomic quinary compositions of high-entropy MBenes, a family of two-dimensional materials, to find candidates for turning CO2 into CO via electroreduction. Disordered structures are generated with the MCSQS algorithm and relaxed with DFT, yielding 45 compositions with negative formation energies that indicate thermodynamic stability. A MACE machine-learning interatomic potential is trained on the DFT data to compute CO2 adsorption energies and locate active sites on the complex, disordered surfaces, after which the computational hydrogen electrode model ranks steps along the CO2-to-CO pathway. Short AIMD runs at 500 K confirm that the structures remain intact over a few picoseconds. The integrated workflow is presented as a practical route to design tunable 2D catalysts for carbon conversion.

Core claim

Through Monte Carlo special quasirandom structures, 56 quinary HE-MBene supercells are constructed from the {Ti, V, Cr, Mo, Nb, Ta, Zr, Hf} pool and relaxed with DFT (PBE+D3), of which 55 converge and 45 display negative formation energies. A MACE MLIP fine-tuned on this dataset reproduces adsorption and pristine energies with RMSEs of 3.49 and 3.0 meV/atom, permitting rapid identification of active metal sites via projected density-of-states matching between d-orbitals and CO2 molecular orbitals. The computational hydrogen electrode model is then applied to evaluate the rate-determining step of the CO2-to-CO pathway, while AIMD trajectories at 500 K over 2.5 ps assess short-time structural.

What carries the argument

MACE machine-learning interatomic potential fine-tuned on DFT data, used to predict CO2 adsorption energies and active sites across disordered high-entropy MBene surfaces.

If this is right

  • 45 of the 56 compositions exhibit negative formation energies and are therefore thermodynamically stable.
  • The MLIP enables efficient screening of CO2 binding on chemically disordered surfaces that would be computationally prohibitive with direct DFT.
  • Active sites are localized on transition-metal atoms whose d-states overlap with CO2 frontier orbitals.
  • The CHE model supplies a consistent ranking of the CO2-to-CO pathway across all candidates.
  • Short AIMD runs establish that the relaxed structures maintain integrity at 500 K for at least 2.5 ps.

Where Pith is reading between the lines

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

  • The same MLIP training strategy could be reused to screen adsorption of additional intermediates and thereby predict selectivity toward C2 or C3 products.
  • Phonon calculations, flagged as future work, would be required to confirm that the 45 candidates remain dynamically stable at operating temperatures.
  • The identified compositions provide concrete targets for experimental synthesis and electrochemical testing of HE-MBene electrodes.
  • The multi-fidelity pipeline could be transferred to other high-entropy 2D families or to different catalytic reactions such as nitrogen reduction.

Load-bearing premise

The fine-tuned MACE MLIP reproduces DFT-level CO2 adsorption energies and correctly identifies active sites on disordered HE-MBene surfaces, and the computational hydrogen electrode model accurately ranks the rate-determining step for CO2-to-CO conversion.

What would settle it

Full DFT calculations on a random subset of the 45 stable candidates that yield adsorption energy errors well above the reported 3.5 meV/atom MLIP RMSE, or experimental synthesis of a top-ranked composition that shows no measurable CO production under CO2 electroreduction conditions.

Figures

Figures reproduced from arXiv: 2605.08728 by Raghavan Ranganathan, Sree Harsha Bharadwaj H.

Figure 1
Figure 1. Figure 1: Multi-fidelity computational screening workflow demonstrating the progressive fil [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Compositional property maps for all 56 equiatomic quinary HE-MBene compositions computed from DFT. (a) Ground-state energy per atom (eV/atom). (b) Cohesive energy (eV/atom). (c) Formation energy per atom (eV/atom); compositions above zero (red cells) are thermodynamically unstable and were excluded from further analysis. (d) Average d-band centre relative to EF (eV); the narrow approximately 0.55 eV spread… view at source ↗
Figure 3
Figure 3. Figure 3: Element-resolved d-PDOS and planar-averaged electrostatic potential for the three zero-overpotential (within the CHE thermodynamic framework) HE-MBene candidates. Left panels (a, c, e): spin-polarised d-PDOS for each constituent metal element in HES ID-22, HES ID-53, and HES ID-54, respectively (solid lines: spin-up; dashed lines: spin-down). The average d-band center εd is annotated in each panel. The Cr … view at source ↗
Figure 4
Figure 4. Figure 4: Representative MACE-computed phonon band structures and density of states for HE-MBene compositions. (a) HES ID-22, (b) HES ID-53, and (c) HES ID￾54 — the three zero-overpotential candidates — all showing fully positive phonon frequencies across the Brillouin zone, confirming dynamical stability. (d) HES ID-21, a representative dynamically unstable structure (minimum frequency = −0.93 THz); imaginary modes… view at source ↗
Figure 5
Figure 5. Figure 5: MACE MLIP training diagnostics and global CO2 adsorption statistics. (a) Training convergence curves showing RMSE on energies (pink circles), MAE on energies (orange squares), and RMSE on forces (green triangles) as functions of training epoch; conver￾gence to 3.49 meV/atom energy RMSE and approximately 38 meV/Å force RMSE confirms chemical accuracy. (b) Parity plot of MACE-predicted versus DFT-computed en… view at source ↗
Figure 6
Figure 6. Figure 6: DFT CO2 adsorption energy maps across the HE-MBene compositional space. (a) On-top site CO2 adsorption energies (∆Eads, eV) for the primary subset of compo￾sitions. The PDOS-identified active adsorption element is labelled in each cell (V: vanadium; Cr: chromium; Ti: titanium; Hf: hafnium). Compositions where CO2 adsorbs dissociatively or with ∆Eads ≥ 0 are excluded from further analysis; stars (⋆) mark gl… view at source ↗
Figure 7
Figure 7. Figure 7: CHE free energy profiles for CO2RR and HER selectivity assessment at zero applied potential (U = 0 V vs. RHE). (a) Free energy profiles for the two-electron CO2-to-CO pathway. Coloured solid lines: the three zero-overpotential candidates (HES ID￾22, blue; HES ID-53, orange; HES ID-54, green), all exhibiting monotonically downhill profiles confirming UL = 0.00 V vs. RHE. Grey lines: the remaining 15 composi… view at source ↗
Figure 8
Figure 8. Figure 8: Atomic snapshots of the rate-determining COOH* intermediate on the three zero-overpotential HE-MBene catalysts. Columns (a)–(c): HES ID-22, HES ID-53, and HES ID-54, respectively. Rows 1–3: three sequential side-view orientations (translated along z) revealing the monodentate adsorption geometry and the local elemental environment surrounding the active site. Red sphere: O; small grey sphere: H; pink spher… view at source ↗
Figure 9
Figure 9. Figure 9: AIMD thermal stability analysis at 500 K for five representative HE￾MBene compositions. (a) Root-mean-square displacement (RMSD, Å) as a function of simulation time (ps) under NVT conditions. Plateau RMSD values of 0.12–0.20 Å for HES IDs 13, 30, 36, and 54 are consistent with equilibrium lattice vibrations; the absence of a monotonically rising RMSD rules out amorphisation or surface reconstruction. HES I… view at source ↗
Figure 10
Figure 10. Figure 10: Atomic snapshots at the start and end of AIMD trajectories at 500 K confirming lattice preservation. Top-view supercell snapshots at t = 0 ps (left column) and t = 2.5 ps (right column) for HES IDs 54, 13, 25, 30, and 36 (rows top to bottom). Atom colour coding per individual legends; boron atoms are pink. The hexagonal M1B1 lattice topology is preserved throughout in all five compositions, with no atomic… view at source ↗
read the original abstract

High-entropy MBenes (HE-MBenes) represent a promising, unexplored class of 2D materials for electrocatalysis. In this work, we present a systematic computational screening of 56 equiatomic quinary HE-MBene compositions from the {Ti, V, Cr, Mo, Nb, Ta, Zr, Hf} pool for CO$_2$ adsorption and electroreduction. Using the Monte Carlo Special Quasirandom Structure (MCSQS) algorithm, we generated disordered M$_1B_1$-type supercells and assessed structural stability via DFT (PBE+D3) in VASP. Of the 56 candidates, 55 passed relaxation, with 45 exhibiting negative formation energies, confirming thermodynamic stability. To efficiently screen CO$_2$ adsorption across disordered surfaces, we developed a machine-learning interatomic potential (MLIP) using the MACE architecture. Fine-tuned on our DFT dataset, the model achieved energy RMSEs of 3.49 and 3.0 meV/atom for adsorbed and pristine sets, respectively. Active sites were identified via PDOS analysis, matching metal d-orbital signatures with CO$_2$ molecular orbitals. The rate-determining step of the CO$_2$-to-CO pathway was evaluated using the computational hydrogen electrode (CHE) model. Short-time structural integrity was assessed via AIMD at 500 K over 2.5 ps; phonon-based stability remains a priority for future work. Our results establish an integrated DFT-MLIP-AIMD framework for the rational design of high-entropy 2D materials tailored for CO$_2$ conversion.

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 / 2 minor

Summary. The manuscript presents a multi-fidelity screening of 56 equiatomic quinary high-entropy MBenes (HE-MBenes) drawn from the {Ti, V, Cr, Mo, Nb, Ta, Zr, Hf} pool for CO₂ electroreduction. MCSQS-generated disordered M₁B₁ supercells are relaxed with DFT (PBE+D3), yielding 55 successful relaxations and 45 structures with negative formation energies. A MACE MLIP is fine-tuned on the DFT dataset (reported energy RMSE 3.49 meV/atom on adsorbed configurations) to enable high-throughput CO₂ adsorption screening; active sites are assigned via PDOS analysis and the CO₂-to-CO pathway is ranked with the computational hydrogen electrode (CHE) model. Short-time thermal stability is checked with AIMD at 500 K. The central claim is that the integrated DFT-MLIP-AIMD workflow establishes a rational-design framework for high-entropy 2D materials in CO₂ conversion.

Significance. If the MLIP predictions for adsorption energies and site rankings on disordered surfaces prove reliable, the work would supply a practical high-throughput protocol for exploring compositionally complex 2D electrocatalysts that are otherwise intractable with direct DFT. The combination of MCSQS disorder modeling, MLIP acceleration, and CHE pathway evaluation is a timely contribution to the high-entropy materials literature.

major comments (2)
  1. [Abstract and MLIP section] Abstract and MLIP training/validation section: the reported energy RMSE of 3.49 meV/atom on the adsorbed DFT set implies absolute energy errors of ~0.14–0.35 eV for typical 40–100-atom MCSQS supercells. Because CO₂ adsorption energy is a difference of three independent configurations, uncorrelated errors can reach ~0.5 eV—comparable to or larger than the binding-energy variations used to rank sites and compositions. No held-out validation set of MLIP versus DFT adsorption energies on disordered HE-MBene surfaces, nor any error-propagation analysis, is provided; this directly affects the reliability of the screening results that support the “rational design” claim.
  2. [Abstract and Results on structural stability] Abstract and stability results: while 55/56 structures are reported as successfully relaxed and 45 as having negative formation energies, the manuscript supplies no tabulated formation energies, no comparison against ordered or binary MBene baselines, and no error bars on the DFT energies. These omissions make it impossible to assess how close the “stable” candidates lie to the convex hull or whether the 45/56 fraction is robust to the chosen exchange-correlation functional.
minor comments (2)
  1. [Abstract] The abstract states that phonon-based stability “remains a priority for future work,” yet the AIMD runs are only 2.5 ps; a brief note on the expected phonon convergence criteria or supercell size used for the AIMD would clarify the scope of the current stability assessment.
  2. [Active-site identification] The PDOS-based active-site assignment is described only qualitatively; a short quantitative metric (e.g., overlap integral or projected DOS peak alignment) would strengthen the link between electronic structure and adsorption preference.

Simulated Author's Rebuttal

2 responses · 2 unresolved

We thank the referee for their insightful and constructive comments. We address each major comment below and outline the revisions we will implement to enhance the manuscript.

read point-by-point responses

  1. Referee: [Abstract and MLIP section] Abstract and MLIP training/validation section: the reported energy RMSE of 3.49 meV/atom on the adsorbed DFT set implies absolute energy errors of ~0.14–0.35 eV for typical 40–100-atom MCSQS supercells. Because CO₂ adsorption energy is a difference of three independent configurations, uncorrelated errors can reach ~0.5 eV—comparable to or larger than the binding-energy variations used to rank sites and compositions. No held-out validation set of MLIP versus DFT adsorption energies on disordered HE-MBene surfaces, nor any error-propagation analysis, is provided; this directly affects the reliability of the screening results that support the “rational design” claim.

    Authors: We agree that validating the MLIP on adsorption energy differences for the disordered HE-MBene surfaces is crucial for supporting the screening results. The RMSE value is calculated on the total energies of the training configurations, which include both pristine and adsorbed structures. To address this, we will include in the revised manuscript a held-out validation set consisting of DFT-computed adsorption energies on selected disordered surfaces, along with a direct comparison to MLIP predictions. Additionally, we will provide an error propagation analysis to estimate the uncertainty in the CO₂ adsorption energies and site rankings. This will better substantiate the reliability of the MLIP-accelerated screening. revision: yes

  2. Referee: [Abstract and Results on structural stability] Abstract and stability results: while 55/56 structures are reported as successfully relaxed and 45 as having negative formation energies, the manuscript supplies no tabulated formation energies, no comparison against ordered or binary MBene baselines, and no error bars on the DFT energies. These omissions make it impossible to assess how close the “stable” candidates lie to the convex hull or whether the 45/56 fraction is robust to the chosen exchange-correlation functional.

    Authors: We appreciate this observation and will revise the manuscript to include a supplementary table with the formation energies for all relaxed structures. We will also add a discussion comparing our results to known stabilities of binary MBenes from the literature. Details on the DFT convergence criteria will be provided to address the robustness of the energies. However, constructing the full convex hull for these quinary systems is computationally prohibitive as it requires evaluating numerous competing phases, and we will clarify this limitation in the text. Similarly, while PBE+D3 is a standard choice for such screenings, a full functional sensitivity analysis across all 56 compositions is beyond the current scope but noted as future work. revision: partial

standing simulated objections not resolved
  • Full convex hull construction to precisely determine the stability of the 45 candidates relative to all possible phases.
  • Comprehensive testing of the results' dependence on the exchange-correlation functional for the entire set of 56 compositions.

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper generates MCSQS supercells, computes formation energies and relaxations directly with DFT (PBE+D3), trains a MACE MLIP on that DFT dataset to accelerate adsorption-energy evaluation on additional disordered configurations, identifies sites with standard PDOS analysis, ranks the CO2-to-CO pathway with the external CHE model, and checks short-time stability with AIMD. None of these steps reduce the reported stabilities, adsorption rankings, or design conclusions to the inputs by construction; the MLIP functions as a surrogate with explicit RMSE metrics rather than a definitional tautology, and no self-citations or uniqueness theorems are invoked as load-bearing premises. The workflow remains self-contained against standard external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The screening rests on standard DFT approximations and MLIP transferability assumptions rather than new axioms or entities; no free parameters are explicitly fitted to the final CO2 reduction metrics in the abstract.

axioms (2)
  • domain assumption PBE+D3 functional provides sufficient accuracy for structural stability and formation energies of HE-MBenes
    Invoked for all DFT relaxations and energy calculations in VASP.
  • domain assumption The computational hydrogen electrode model correctly identifies the rate-determining step for CO2-to-CO on these surfaces
    Used to evaluate the pathway after active site identification.

pith-pipeline@v0.9.0 · 5607 in / 1546 out tokens · 61772 ms · 2026-05-12T02:11:08.436840+00:00 · methodology

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