Supplementary data and model for: "Harnessing Structural Disorder: Unraveling Hydrogen Evolution in Monolayer Amorphous Carbon via First-Principles Simulations and Machine-Learned Potentials" Sreehari M S, Ashutosh Krishna Amaram, Raghavan Ranganathan — Department of Materials Engineering, IIT Gandhinagar. (https://doi.org/10.1038/s41699-026-00735-9)

Model Description

A MACE machine-learning interatomic potential, naively fine-tuned from the MACE-MATPES-PBE0 foundation model, used to predict the Gibbs free energy of hydrogen adsorption (ΔG_H) across the surface of monolayer amorphous carbon (MAC).

Base checkpoint: MACE-MATPES-PBE0 (medium, 9,063,204 parameters, 89 elements)
Fine-tuning strategy: naive fine-tuning (output head only, no replay), 655,534 parameters updated
Radial cutoff: 6 Å
Framework: mace-torch, PyTorch, ASE

Training Data

MAC structures (~200 atoms) were generated via LAMMPS melt-quench (ReaxFF) at multiple quench rates (10 K/ps, 100 K/ps), equilibration temperatures (300 K, 400 K, 500 K), and vacancy concentrations (3%, 5%, 6%), giving 24 structural protocols. DFT single-point and relaxation calculations (VASP, PAW-PBE, DFT-D3, 400 eV cutoff) on these configurations and their H-adsorbed counterparts produced the training set.

Total DFT frames: 1,572 (MAC and MAC–H)
Split: 1,415 train / 157 validation (~10%)
Test set: 175 (MAC and MAC-H), mostly independent static and relaxation-trajectory frames, filtered for non-redundancy (no consecutive frames, ≥0.08 eV energy separation)

Files provided in data/ (train/val/test) and dft_deltaG_benchmark/ (VASP input/output for the benchmark adsorption sites).

Model Performance

Metric	Value
Energy RMSE (test)	1.65 meV/atom
Force RMSE (test)	29.15 meV/Å
ΔG_H MAE vs. DFT (independent benchmark)	0.161 eV
Activity classification accuracy (\|ΔG_H\| < 0.1 eV threshold)	95%

Intended Use

Predicting site-resolved ΔG_H across MAC surfaces (undoped, various vacancy concentrations/quench rates) as a scalable alternative to exhaustive DFT sampling, and as the basis for extracting local structural descriptors (coordination number, curvature, ring statistics, hexagonal order, ripple height) that govern HER activity in monolayer amorphous carbon. Not validated for other amorphous carbon polymorphs, doped variants, or non-H adsorbates without re-fine-tuning.

How to Use

This model is loaded via mace_mp and used with ASE's structural optimizers. Relaxation follows a hybrid FIRE→LBFGS scheme: FIRE handles the initial rugged energy landscape down to fmax = 0.1 eV/Å, then LBFGS refines to the final convergence criterion of fmax = 0.01 eV/Å — this combination was benchmarked in the paper as the most efficient for MAC's amorphous, noisy energy surface.

python

from mace.calculators import mace_mp
from ase.io import read, write
from ase.optimize import FIRE, LBFGS
import numpy as np

# Load structure
atoms = read('dft_deltaG_benchmark/4%_vacancy_100kps_QR/site_001/POSCAR', format='vasp')
atoms.set_pbc(True)

# Load fine-tuned MACE model
atoms.calc = mace_mp(
    model="model/6_MACE_MAC_HER.model",
    default_dtype="float64",
    device="cuda",  # or "cpu"
)

print("Initial energy:", atoms.get_potential_energy(), "eV")
print("Initial max force:", np.max(np.abs(atoms.get_forces())), "eV/Å")

# Stage 1: FIRE — coarse relaxation of the rugged landscape
fire = FIRE(atoms, logfile=None, dt=0.05, maxstep=0.05, dtmax=0.5, Nmin=10, finc=1.05, fdec=0.5)
fire.run(fmax=0.1)

# Stage 2: LBFGS — fine convergence
lbfgs = LBFGS(atoms, logfile=None, maxstep=0.05, memory=100)
lbfgs.run(fmax=0.01)

print("Final energy:", atoms.get_potential_energy(), "eV")
write('CONTCAR-relaxed', atoms, format='vasp', direct=True)

ΔG_H for a given site is then obtained from separate relaxations of the pristine MAC surface and the H-adsorbed configuration, following the standard adsorption free-energy expression (see paper Eq. 2–3).

Files in This Repository

model/ — fine-tuned MACE checkpoint
dft_deltaG_benchmark/ — VASP input/output files for benchmark adsorption sites (isolated local environments and full-surface relaxations)
data/ — train/val/test splits (1,572 DFT frames)
scripts/ — feature extraction (local environment descriptors: coordination number, curvature, ring statistics, hexagonal order, ripple height), MACE structure relaxation using ASE module and python notebook for feature analysis.

Citation

@article{ms2026harnessing, title={Harnessing structural disorder: unraveling hydrogen evolution in monolayer amorphous carbon via first-principles simulations and machine-learned potentials}, author={MS, Sreehari and Amaram, Ashutosh Krishna and Ranganathan, Raghavan}, journal={npj 2D Materials and Applications}, year={2026}, publisher={Nature Publishing Group UK London} }

sms-cmeg/mac_HER_supplimentary

MAC-HER: Fine-tuned MACE MLIP for Hydrogen Adsorption ΔG Prediction on Monolayer Amorphous Carbon