Project

Accurate energy barriers for catalytic reaction pathways: an automatic training protocol for machine learning force fields

Lars L. Schaaf1, Edvin Fako2, Sandip De2, Ansgar Schäfer2, Gábor Csányi1

  1. 1Engineering Laboratory, University of Cambridge
  2. 2BASF SE, Ludwigshafen am Rhein

npj Computational Materials 9, 180, 2023

Paper arXiv

Key contributions

  • A hands-off training protocol. Active learning drives the whole loop, so the force field is built without hand-curating a training set for each new surface or reaction.
  • DFT-quality barriers, at force-field cost. Final energy barriers land within 0.05 eV of the baseline DFT across the CO₂-to-methanol pathway on indium oxide.
  • A better path for a well-studied reaction. The speedup makes it affordable to search many paths per reaction rather than one, which turns up an alternative route with a 40% lower activation energy than the previously established rate-limiting step.
  • Finite temperature matters. Umbrella sampling — around 6M force calls, far out of reach for direct ab initio simulation — gives free-energy barriers at 300 K and 500 K that differ substantially from the 0 K minimum-energy path.
  • Transferable. The same protocol carries over to the experimentally relevant but previously unexplored top-layer-reduced indium oxide surface, and to single-atom dopants from only ~50 doped configurations.
Energy along the CO2-to-methanol reaction intermediates on indium oxide: baseline DFT, the force field on the literature path, and the force field on its own optimised path, with structure insets and a strip of intermediate geometries.
Hands-off training, with close agreement to baseline DFT. Energy along the CO₂-to-methanol intermediates on indium oxide. The trained force field tracks DFT on the literature path, and finds a lower-energy route of its own.

Abstract

In this study, we introduce a training protocol for developing machine learning force fields (MLFFs), capable of accurately determining energy barriers in catalytic reaction pathways. The protocol is validated on the extensively explored hydrogenation of carbon dioxide to methanol over indium oxide. With the help of active learning, the final force field obtains energy barriers within 0.05 eV of Density Functional Theory. Thanks to the computational speedup, not only do we reduce the cost of routine in-silico catalytic tasks, but also find a 40% reduction in the previously established rate-limiting step. Furthermore, we illustrate the importance of finite-temperature effects and compute free energy barriers. The transferability of the protocol is demonstrated on the experimentally relevant, yet unexplored, top-layer reduced indium oxide surface. The ability of MLFFs to enhance our understanding of extensively studied catalysts underscores the need for fast and accurate alternatives to direct ab-initio simulations.

Figures

Two energy-versus-reaction plots side by side. Left, lower barriers: the optimised path sits below the literature path. Right, finite temperature: free energy paths lie well below the 0 K path.
The two headline results. Left — searching multiple paths per reaction finds barriers below the literature path. Right — finite-temperature free-energy paths sit substantially below the 0 K minimum-energy path.
Energy versus NEB image for the rate-limiting step, comparing the literature path with the optimised path, with structure insets at the transition state.
Lower barriers from multiple paths per reaction. Nudged elastic band profiles for the rate-limiting step: the optimised path peaks well below the literature path.
Free energy versus collective variable, showing the 0 K reference path, the 0 K minimum energy path, and free energy paths at 300 K and 500 K.
Umbrella sampling, ~6M force calls. Free-energy paths at 300 K and 500 K compared with the 0 K minimum-energy path — a calculation that is impractical with direct ab initio simulation.
Adsorption energy across reaction intermediates for the oxygen-vacancy and platinum-doped surfaces, comparing DFT with the MACE force field.
Single-atom dopants from ~50 doped configurations. Adsorption energies across the reaction intermediates for the oxygen-vacancy and Pt-doped surfaces; the force field tracks DFT on both.
Histogram of adsorption energies above a dense render of many overlaid adsorbate structures on the oxide surface.
A plethora of adsorbate structures. The distribution of adsorption energies over sampled configurations, showing how much the result depends on actually finding the global minimum rather than the first structure that relaxes.

Citation

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@article{schaaf2023catalytic,
  title   = {Accurate energy barriers for catalytic reaction pathways:
             an automatic training protocol for machine learning force fields},
  author  = {Schaaf, Lars L. and Fako, Edvin and De, Sandip
             and Sch{\"a}fer, Ansgar and Cs{\'a}nyi, G{\'a}bor},
  journal = {npj Computational Materials},
  volume  = {9},
  number  = {1},
  pages   = {180},
  year    = {2023},
  doi     = {10.1038/s41524-023-01124-2}
}