MAD-SURF: a machine learning interatomic potential for molecular adsorption on coinage metal surfaces

TL;DR

MAD-SURF offers a practical framework for accelerating atomistic simulations and advancing data-driven workflows in surface science, and achieves accuracy comparable to the underlying DFT reference while enabling simulations orders of magnitude faster than density functional theory.

Abstract

Predicting how organic molecules adsorb, assemble, and interact on metal surfaces is central to surface chemistry and molecular electronics, particularly in the context of interpreting high-resolution scanning probe microscopy. Yet, the application of first-principles simulations to interfaces is hampered by the computational cost for evaluating the electronic structure for the large number of atoms typically involved. We hereby present MAD-SURF, a machine learning interatomic potential specifically tailored for molecular adsorption on coinage metal surfaces. Trained on a broad dataset spanning diverse molecules, adsorption motifs, surfaces, molecular dynamics trajectories and non-covalent aggregates, MAD-SURF achieves accuracy comparable to the underlying DFT reference while enabling simulations orders of magnitude faster than density functional theory. The model reliably reproduces energies, forces and adsorption geometries across the three coinage metal substrates. We demonstrate its capabilities on experimentally characterized systems, including organic monolayers, polycyclic aggregates, flexible biomolecules and the long-range herringbone reconstruction of gold. By merging accuracy, speed, and generalizability, MAD-SURF offers a practical framework for accelerating atomistic simulations and advancing data-driven workflows in surface science.

Figures (7)

• Figure 1: Pipeline for the construction of the dataset. (a) Representative molecules spanning functional groups relevant to on-surface chemistry, including aromatics, amines, carbonyls, halogens, hydroxyls, ethers, nitro groups, and extended $\pi$-conjugated systems. (b) Computational workflow for dataset generation: molecular and surface structures are combined and sampled using Bayesian Optimization Structure Search (BOSS), Normal Mode Sampling (NMS), ab initio Molecular Dynamics (AIMD), and Automated Interaction Site Screening (AISS). The resulting configurations are evaluated with Density Functional Theory to obtain reference energies and forces, and subsequently used for MLIP training. (c) Example snapshots from the final dataset, illustrating MD trajectories of metals and molecules both in the gas phase and adsorbed.
• Figure 2: Comparison of different training strategies for a subset containing the best of each type. (a) Plot of the metrics used to evaluate the trained potentials: mean absolute error (MAE) in per-atom energies (meV), forces (meV/Å), adsorption height differences and RMSD values (Å) between DFT reference and MAD-SURF geometries, sorted by increasing RMSD values. (b) Parity plot over the adsorption heights (Å) of the test molecules on Cu(111), Ag(111) and Au(111) for the DFT reference and MAD-SURF geometries. Note that the per-atom energy MAE for the MACE-MPA-0 foundational model is based on plane-wave DFT (VASP), which cannot be compared directly against our reference based on localized basis sets (FHI-aims).
• Figure 3: Aggregated aromatic hydrocarbons from petroleum on Cu(111). NC-AFM experimental (a–d) images and simulations with the Probe Particle Model HapalaPRB2014_ppm (Lennard–Jones plus point charges) (e–h) of different thermalized products from 2,7-dimethylpyrene adsorbed on Cu(111). (i–l) Top view of the atomic structures used for the AFM simulations, obtained through our MLIP-based relaxation pipeline. Experimental images reproduced with permission from Chen et al. chen_gross_acs_fuels.
• Figure 4: Organic monolayer domains of pentacene and PTCDA on coinage metal surfaces. Rows from top to bottom correspond to the herringbone monolayer of pentacene on Cu(111) (a-c), the herringbone phase of PTCDA on Cu(111) (d-f), the herringbone phase of PTCDA on Ag(111) (g-i), and the brick-wall phase of PTCDA on Ag(110) (j-l). For each system, the left panel shows an experimental Scanning Tunneling Microscopy (STM) topograph, the middle panel the MAD-SURF–relaxed structural model with atoms color-coded by height, and the right panel a simulated STM image obtained using the Tersoff–Hamann approximation TersoffHamann and the same tunnelling bias as in the corresponding experiment. Experimental STM images are reproduced with permission from Smerdon et al. smerdon_monolayer_2011 for pentacene/Cu(111) (15×15 nm$^{2}$, $V_\mathrm{gap}=0.5$ V, $I_\mathrm{T}=0.6$ nA), from Wagner et al. wagner_initial_2007 for PTCDA/Cu(111) ($V_\mathrm{gap}=0.6$ V, $I_\mathrm{T}=10$ pA), and from Glöckler et al. glockler_highly_1998 for PTCDA/Ag(111) ($V_\mathrm{gap}=2.0$ V, $I_\mathrm{T}=0.6$ nA) and PTCDA/Ag(110) ($V_\mathrm{gap}=0.9$ V, $I_\mathrm{T}=1.3$ nA).
• Figure 5: Biomolecular adsorbate $\beta$-cyclodextrin on Au(111). (a) Top and side views of the gas-phase structure, highlighting the two faces that can adsorb on the substrate. (b,c) Experimental and simulated constant-height images of $\beta$-cyclodextrin adsorbed on Au(111) exposing the primary-face orientation, where the narrow rim forms a closed hydrogen-bonding network. (d,e) Experimental and simulated images of the secondary-face orientation, defined by the seven secondary OH groups forming the wider rim. (f,g) Top and side views of the atomic structures used for the AFM simulations, obtained through our MLIP-based relaxation pipeline. AFM simulations performed with the Probe Particle Model HapalaPRB2014_ppm (Lennard–Jones plus point charges) Experimental images reproduced with permission from Grabarics et al. Grabarics2024Nov.