arxiv: 2605.07670 · v1 · submitted 2026-05-08 · ❄️ cond-mat.mtrl-sci

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Harnessing Structural Disorder: Unraveling Hydrogen Evolution in Monolayer Amorphous Carbon via First-Principles Simulations and Machine-Learned Potentials

Ashutosh Krishna Amaram, Raghavan Ranganathan, Sreehari M S

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Pith reviewed 2026-05-11 02:20 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci

keywords monolayer amorphous carbonhydrogen evolution reactionmachine-learned interatomic potentialsdensity functional theorystructural disordercarbon-based catalystsactive sites

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The pith

Monolayer amorphous carbon shows hydrogen adsorption energies near zero at some sites, outperforming crystalline carbons for hydrogen evolution.

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

The paper examines the hydrogen evolution reaction on monolayer amorphous carbon generated by melt-quench simulations and compares it to crystalline forms such as graphene and graphyne. Density functional theory calculations on thirty distinct local environments produce a distribution of hydrogen adsorption free energies that includes values close to the ideal zero, unlike the limited sites available in ordered carbons. A finetuned machine-learned interatomic potential then maps the free-energy landscape across the full surface, identifying roughly fifteen percent of sites as favorable. Structural analysis ties the best activity to seven-membered rings, local curvature, and ripple height. The central suggestion is that deliberate control of these disordered features could allow MAC to reach performance levels comparable to noble-metal catalysts.

Core claim

MAC contains a mix of sp2 and sp3 carbons arranged in five-, six-, and seven-membered rings. DFT sampling of thirty local environments yields Delta GH values ranging from -0.02 eV to +1.35 eV, while beta-graphyne, the best crystalline case, reaches only +0.34 eV. The finetuned MACE MLIP extends the survey to the entire surface and predicts values from -0.91 eV to +1.70 eV, with approximately fifteen percent of sites below +0.25 eV. Seven-membered rings, curvature, and ripple height are shown to improve adsorption energetics.

What carries the argument

The distribution of hydrogen adsorption free energies across diverse local atomic environments in MAC, first computed by DFT on sampled sites and then predicted across the full surface by a finetuned MACE machine-learned interatomic potential.

If this is right

Crystalline carbon materials possess only a small number of active sites, with beta-graphyne providing the best Delta GH of +0.34 eV.
Roughly fifteen percent of sites across the MAC surface exhibit Delta GH below +0.25 eV according to the MLIP survey.
Seven-membered rings, local curvature, and ripple height each correlate with improved hydrogen adsorption energetics.
Careful optimization of local structural features in MAC could allow it to reach catalytic activity comparable to noble-metal catalysts.

Where Pith is reading between the lines

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

Controlling ripple amplitude or the fraction of seven-membered rings during synthesis could further increase the density of optimal sites.
The same melt-quench plus MLIP workflow could be used to screen other amorphous two-dimensional materials for catalytic applications.
If the predicted active-site fraction holds in experiment, MAC would offer a low-cost, abundant alternative to platinum-group metals in water electrolyzers.
Similar disorder-driven improvements might appear in related reactions such as CO2 reduction on the same amorphous carbon platform.

Load-bearing premise

The thirty sampled local environments together with the finetuned MLIP predictions accurately represent the catalytic performance and active-site density of real synthesized MAC without experimental validation.

What would settle it

Synthesis of MAC followed by direct measurement of its hydrogen evolution overpotential or turnover frequency to test whether the predicted fraction of sites with Delta GH below +0.25 eV matches observed catalytic rates.

Figures

Figures reproduced from arXiv: 2605.07670 by Ashutosh Krishna Amaram, Raghavan Ranganathan, Sreehari M S.

**Figure 2.** Figure 2: (a) The MAC structure obtained after melt-quench simulation. (b) Ring statistics and (c) Hybridization distribution in MAC. 3.3 HER performance of MAC 3.3.1 Approach 1: DFT Evaluation of H Adsorption on MAC For studying H adsorption, a single H atom was placed 2Å above the random target C atoms. The local environment within a specific radius around each sampled site was extracted and subjected to DFT struc… view at source ↗

**Figure 3.** Figure 3: The local environment with radius (a) 8.5 Å, (b) 9.0 Å, and (c) 9.5 Å. (d) A radar plot showing the alignment of different properties with varying radius. Environment Radius (Å) Bond length (Å) Angle (degrees) C1-C-C3 C1-C-C2 C2-C-C3 C-C1 C-C2 C-C3 α β γ α β γ α β γ 8.5 1.44 1.43 1.46 130.9 24.7 24.4 29.2 29.1 121.7 107.2 36.7 36.1 9 1.43 1.44 1.48 130.5 25.2 24.3 28.7 29.0 122.3 107.1 36.9 35.9 9.5 1.43 1… view at source ↗

**Figure 7.** Figure 7: Schematic representation of the MLIP workflow for predicting the free energy change landscape of H adsorption and governing structural factors [PITH_FULL_IMAGE:figures/full_fig_p016_7.png] view at source ↗

read the original abstract

Disorder and defective coordination in the catalytic plane are crucial for enhancing the Hydrogen Evolution Reaction (HER) on two-dimensional catalysts. Amorphous materials are disordered, making them catalytically adaptive for many reactions. In this work, the HER capabilities of Monolayer Amorphous Carbon (MAC) were studied in comparison with crystalline carbon derivatives, such as pristine graphene (GE) and graphyne derivatives. MAC generated from melt-quench simulations revealed a diverse framework of predominantly sp2 and sp3 carbons with numerous 5-, 6-, and 7-membered rings. Density Functional Theory (DFT) calculations investigated free-energy variations in hydrogen adsorption for each material. According to Sabatier's principle, optimum activity is achieved when the Gibbs free energy (Delta GH) change approaches zero. Crystalline carbon materials possess limited active sites, with beta-graphyne showing the best Delta GH value of +0.34 eV. The adsorption study for MAC was conducted in 30 distinct local environments, where core structural properties were analyzed against varying radii. Calculations showed a Delta GH distribution for MAC ranging from -0.02 eV to +1.35 eV. To evaluate activity across the entire MAC surface, a MACE MLIP foundation model was finetuned, achieving optimal energy and force fitting of 1.67 meV/atom and 29.15 meV/A, respectively. The MLIP predicted Delta GH values from -0.91 eV to +1.70 eV, with approximately 15% of sites exhibiting values below +0.25 eV. Feature analysis revealed that 7-membered rings, curvature, and ripple height enhance HER activity. Our findings suggest that, with careful optimization of local features, MAC can be tuned to compete with noble metal catalysts.

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.

Desk Editor's Note private letter to a colleague

MAC shows a broad Delta GH spread from disorder with MLIP suggesting 15% active sites, but the extrapolation from 30 DFT points lacks confirmation on the new low-energy predictions.

read the letter

The main thing to know is that monolayer amorphous carbon shows a wider spread of hydrogen binding energies than the crystalline versions, with the ML potential pointing to about 15% of sites being reasonably active, tied to specific structural features like 7-membered rings. They generate the MAC via melt-quench, run DFT on 30 sampled sites to get the Delta GH range, then fine-tune MACE to scan the rest. The fitting errors are small, and they correlate activity with curvature and ripple height. This gives a clear picture of how disorder helps compared to graphene or graphyne, where sites are more limited. The weak part is that the MLIP predictions for the favorable sites below the DFT range aren't checked with additional DFT calculations. Without a held-out test or direct confirmation on the extrapolated low-energy sites, the 15% figure and the suggestion that it can compete with noble metals stay provisional. The methods are standard, but this gap affects how much weight the conclusions can carry. Readers working on 2D materials for catalysis or using ML potentials for surface chemistry will get the most from it. It is worth a serious referee because the simulation approach is grounded and the question matters, even if revisions will be needed around the validation. Recommendation: Send it for peer review.

Referee Report

2 major / 2 minor

Summary. The manuscript presents first-principles DFT calculations on hydrogen adsorption in monolayer amorphous carbon (MAC) generated via melt-quench, comparing it to crystalline carbon structures like graphene and graphyne. DFT on 30 sites yields Delta G_H from -0.02 to 1.35 eV. A MACE MLIP is finetuned on these data with low errors and then used to predict Delta G_H across the full MAC structure, revealing a broader range (-0.91 to 1.70 eV) with ~15% of sites below 0.25 eV. Feature analysis links better activity to 7-membered rings, curvature, and ripple height, concluding that local feature optimization can make MAC competitive with noble metal HER catalysts.

Significance. Should the MLIP-based extrapolation hold, the work offers a promising route to earth-abundant, tunable 2D carbon catalysts for HER by exploiting structural disorder. The combination of limited DFT sampling with MLIP scaling is methodologically efficient, and the reported fitting accuracies (energy MAE 1.67 meV/atom, force MAE 29.15 meV/Å) are strong. The identification of specific structural motifs (7-rings, curvature) as activity enhancers provides concrete design principles.

major comments (2)

Results (MLIP predictions paragraph): The claim that approximately 15% of sites exhibit Delta G_H below +0.25 eV (and thus can compete with noble metals) rests on MLIP predictions that extend the Delta G_H range beyond the DFT training data (-0.02 to +1.35 eV to -0.91 to +1.70 eV). No training/validation split details, cross-validation on unseen motifs, or follow-up DFT calculations on MLIP-predicted low-Delta G_H sites are described, leaving the expanded low-Delta G_H tail unverified and directly impacting the active-site density estimate.
Methods (DFT sampling and MLIP finetuning): The 30 sampled local environments for DFT may not sufficiently represent the diversity of 5-, 6-, and 7-membered rings and curvature variations in the melt-quench MAC structure. Without evidence of systematic sampling or validation that the MLIP generalizes to all ring/curvature combinations, the extrapolation to the full surface risks missing or overestimating favorable sites.

minor comments (2)

Abstract: The force error is reported as '29.15 meV/A'; this should be corrected to 'meV/Å' for proper units.
Throughout: The manuscript would benefit from a clearer description of how the 30 local environments were selected (e.g., random sampling, stratified by ring size) to allow reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and methodological approach, as well as for the detailed comments that help improve the manuscript. We address each major comment below and commit to revisions that strengthen the validation of our MLIP predictions and sampling strategy.

read point-by-point responses

Referee: Results (MLIP predictions paragraph): The claim that approximately 15% of sites exhibit Delta G_H below +0.25 eV (and thus can compete with noble metals) rests on MLIP predictions that extend the Delta G_H range beyond the DFT training data (-0.02 to +1.35 eV to -0.91 to +1.70 eV). No training/validation split details, cross-validation on unseen motifs, or follow-up DFT calculations on MLIP-predicted low-Delta G_H sites are described, leaving the expanded low-Delta G_H tail unverified and directly impacting the active-site density estimate.

Authors: We agree that explicit validation details are required to support the extrapolated range and the 15% active-site estimate. In the revised manuscript, we will report the training/validation split (80/20 random split on the 30 DFT configurations) with separate test-set errors for energy and forces. We will also add cross-validation results stratified by ring size and curvature. Furthermore, we will perform additional DFT calculations on 5-10 MLIP-predicted sites with Delta G_H < 0.25 eV that were held out from training, to directly verify the low-energy tail and refine the active-site fraction if needed. revision: yes
Referee: Methods (DFT sampling and MLIP finetuning): The 30 sampled local environments for DFT may not sufficiently represent the diversity of 5-, 6-, and 7-membered rings and curvature variations in the melt-quench MAC structure. Without evidence of systematic sampling or validation that the MLIP generalizes to all ring/curvature combinations, the extrapolation to the full surface risks missing or overestimating favorable sites.

Authors: The 30 sites were deliberately chosen from the melt-quench MAC to span the observed distributions of ring sizes (5-, 6-, 7-membered) and local curvature/ripple heights, as described in the Methods. Nevertheless, we accept that more transparent documentation is needed. In the revision we will expand the Methods section with a table or figure showing the distribution of ring types and curvature metrics across the sampled sites versus the full structure, and we will include a feature-based validation (e.g., parity plots of MLIP vs. DFT Delta G_H grouped by ring size) to demonstrate generalization. If the referee deems it essential, we can also enlarge the DFT set in a future iteration. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's workflow consists of independent DFT calculations on 30 sampled local environments in the MAC structure, followed by finetuning a MACE MLIP on those data and applying the model to predict Delta GH across the full melt-quench structure. This is a standard simulation-to-ML extrapolation pipeline; the wider predicted range (-0.91 to +1.70 eV) and the ~15% active-site fraction are model outputs, not quantities defined by or forced to equal the training inputs. No self-definitional equations, fitted parameters renamed as predictions, load-bearing self-citations, or ansatz smuggling appear in the abstract or described chain. The central claim therefore rests on external computational steps rather than reducing to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The work depends on standard assumptions in computational materials science regarding simulation protocols and the accuracy of electronic structure methods, with additional fitted elements from the machine learning model.

free parameters (1)

MACE MLIP finetuning parameters
The model was finetuned on DFT data, involving choices in architecture and training that affect the predicted energies and forces.

axioms (2)

domain assumption The melt-quench protocol generates a realistic model of monolayer amorphous carbon
Invoked in the generation of the MAC structure for subsequent calculations.
domain assumption DFT calculations provide accurate relative free energies for hydrogen adsorption
Basis for all Delta GH values reported.

pith-pipeline@v0.9.0 · 5652 in / 1362 out tokens · 64649 ms · 2026-05-11T02:20:46.522019+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

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