Semi-grand canonical Monte Carlo simulation of the acrolein induced surface segregation and aggregation of AgPd with machine learning surrogate models
Mingjie Liu, Yilin Yang and John R. Kitchin, “Semi-grand canonical Monte Carlo simulation of the acrolein induced surface segregation and aggregation of AgPd with machine learning surrogate models”, The Journal of Chemical Physics 154(13), 134701 (2021). https://doi.org/10.1063/5.0046440
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Question
Dilute AgPd single-atom alloys are candidate catalysts for selectively hydrogenating the C=O bond of acrolein, but experiments disagree on whether small Pd additions help or hurt selectivity, and Pd islands on the surface are known to degrade it. Whether isolated Pd atoms stay isolated under reaction conditions depends on how adsorbed acrolein shifts Pd segregation and aggregation, which is too expensive to sample with DFT alone because of the many alloy configurations and the cost of relaxing an adsorbed molecule. The paper asks whether a workflow combining machine learning surrogate models with semi-grand canonical Monte Carlo (SGCMC) can predict the surface composition and Pd ensembles of AgPd(111) with and without acrolein at 373 K (Liu et al. 2021).
Approach
Reference data came from VASP with the PBE functional, and slab relaxations used the active learning relaxation method of Yang and co-workers. A first DFT screen compared Pd segregation energies, acrolein adsorption energies, and their sum (segregation energy plus the adsorption energy relative to pure Ag) for 16 configurations of a 3x3x4 Ag(111) slab with 0 to 4 surface Pd atoms. Three surrogate models then supplied the Monte Carlo energies. Two SingleNN potentials with Behler-Parrinello symmetry functions (two hidden layers of 30 tanh nodes, 8:1:1 split, early stopping) predicted bulk AgPd energies (123 small-cell plus 690 larger-cell configurations, the latter limited to at most 22% Pd) and AgPd(111) slab energies (203 configurations of 3x3x4 slabs with pure Ag bottom layers). For acrolein, the authors defined a pseudo-adsorption energy (relaxed adsorbate-plus-slab energy minus the unrelaxed bare slab energy), which folds in surface relaxation and the gas-phase reference so relaxation of the bare slab need not be computed. They computed it for 540 configurations on top, bridge and hollow sites, described each site by symmetry-function fingerprints of a pseudo-atom placed at the site, and predicted new sites by nearest-neighbor lookup on Euclidean fingerprint distance (287 unique fingerprints, keeping the most negative energy among duplicates).
SGCMC with a bulk 10x10x10 cell gave the mapping between the Ag-to-Pd exchange chemical potential and bulk Pd concentration. Bare-slab runs used 12x12x4 slabs and runs with acrolein used 30x30x4 slabs at roughly 1/9 monolayer coverage (molecules at least 6.5 Å apart), with acrolein reassigned to the most favorable available sites whenever a first-layer atom changed. Errors were propagated by repeating runs with five SingleNNs from different data splits, or by adding 0.05 eV Gaussian noise to the adsorption labels.
Key findings
In the DFT screen, segregation energy rose stepwise with the number of surface Pd atoms, and only one configuration, a single surface Pd under acrolein, had a net favorable energy. Test errors were 1.6 meV/atom for the bulk SingleNN and 0.5 meV/atom for the slab SingleNN, about equal to the spread across models trained on different splits. Leave-one-out testing of the adsorption model gave an RMSE of 0.100 eV overall (0.038, 0.121 and 0.093 eV for top, bridge and hollow sites); the authors argue that periodic-image artifacts in the 3x3 cells inflate this and estimate about 0.05 eV for configurations actually met in the simulations.
The chemical potential varied nearly linearly with bulk Pd fraction below 10%, and switching to a Vegard’s-law lattice constant made essentially no difference below 10% Pd. In vacuum the first layer stayed essentially pure Ag until bulk Pd exceeded 20%, with Pd enriched in the second layer; a full 10x10x5 slab check showed the pure-Ag bottom-layer assumption inflates second-layer Pd by less than 2.5 percentage points below 10% bulk Pd. With acrolein the first layer held about 11% Pd for bulk Pd from 5% to 6.5%, corresponding to each acrolein bound to one isolated Pd, while extra Pd went into the second layer. Near 6.5% bulk Pd, Pd began to aggregate into dimers forming bridge sites. Label noise of 0.05 eV mainly changed the second-layer composition and had little effect on the first layer.
Significance
The work shows that adsorbates can undo the isolation that defines a single-atom alloy: acrolein pulls Pd to the AgPd surface and starts forming Pd dimers at bulk Pd fractions where the clean surface is nearly pure Ag. Methodologically it extends SingleNN-driven segregation Monte Carlo to an adsorbate-covered surface by using a cheap fingerprint lookup for adsorption energies. The authors note the results inherit PBE’s limitations, ignore acrolein-acrolein interactions and other adsorbates such as hydrogen, and would benefit from a more transferable adsorption model.