Efficient Machine-Learning-Aided Screening of Hydrogen Adsorption on Bimetallic Nanoclusters

Abstract

Nanoclusters add an additional dimension in which to look for promising catalyst candidates, since catalytic activity of materials often changes at the nanoscale. However, the large search space of relevant atomic sites exacerbates the challenge for computational screening methods and requires the development of new techniques for efficient exploration. We present an automated workflow that systematically manages simulations from the generation of nanoclusters through the submission of production jobs, to the prediction of adsorption energies. The presented workflow was designed to screen nanoclusters of arbitrary shapes and size, but in this work the search was restricted to bimetallic icosahedral clusters and the adsorption was exemplified on the hydrogen evolution reaction. We demonstrate the efficient exploration of nanocluster configurations and screening of adsorption energies with the aid of machine learning. The results show that the maximum of the d-band Hilbert-transform ϵ_u is correlated strongly with adsorption energies and could be a useful screening property accessible at the nanocluster level.

Keywords: adsorption; catalysis; computational screening; hydrogen evolution reaction; machine learning; nanoclusters; workflow automation.

Figure 1

Workflow sketch shows the detailed steps from cluster generation to the prediction of the adsorption energy distributions. FPS stands for farthest point sampling.

Figure 2

Clusters of a given composition (e.g., the depicted Cu₁₃Co₄₂) were generated automatically by Monte Carlo assuming various combinations of interaction and segregation energies. Experimentally observable composites such as core–shell, segregated, ordered, and random as well as structures in-between emerged naturally.

Figure 3

Through Delaunay tetrahedralization the whole surface is triangulated and surface atoms are detected. Adsorption vectors of top, bridge, and hollow sites are defined as the average of outward-pointing normal vectors of surface triangles containing the site point.

Figure 4

d-band center ϵ_d of the 86 most stable nanoclusters. The error bars indicate the standard deviation of the distribution among surface atoms split into edges and vertices.

Figure 5

d-band center plus half d-bandwidth ϵ_d^w of the 86 most stable nanoclusters. The error bars indicate the standard deviation of the distribution among surface atoms split into edges and vertices.

Figure 6

d-band maximum of the hilbert-transform ϵ_u of the 86 most stable nanoclusters. The error bars indicate the standard deviation of the distribution among surface atoms split into edges and vertices.

Figure 7

(a) Learning curve of KRR. The errors are averaged over 20 randomized runs and the error bars indicate the standard deviation of those errors. Training, validation and test set are in blue, yellow and green, respectively. (b) Calculated vs predicted hydrogen adsorption energy of 1767 DFT calculations.

Figure 8

(a) Predicted hydrogen adsorption energy distribution. The mean and standard deviation is given for each composition. (b) Effect of surface reconstruction and adsorption site drift on the machine learning accuracy. Yellow points represent adsorbates retaining their initial adsorption site, purple points represent adsorbates which drifted to neighboring sites. The green bars average the SOAP distance metric over an interval of 0.1 eV adsorption energy error.

Figure 9

Electronic descriptors of surface atoms which form the adsorption site against the adsorption energy. From left to right, the columns show (a) all adsorption sites, (b) all top sites, (c) only pure adsorption sites (top, bridge, and hollow sites made up of a single atomic type), and (d) only adsorption sites from pure nanoclusters. Each subplot has its own correlation coefficient R.

Figure 10

t-SNE plots for LDOS of the d-band of an element in various nanoclusters. A colormap of the concentration of an element in a nanocluster is added to correlate the t-SNE clusters with the concentration.

Figure 11

Comparison of adsorption energies of only top nanocluster adsorption sites with a periodic slab data set from ref (67). The error bars display the standard deviation of the distribution of adsorption energies. The first element mention denotes the binding site. (a) A histogram of the difference in adsorption energies. (b) A parity plot with the parity line y = x is shown in red.

Figure 12

Comparison of adsorption energies of nanocluster adsorption sites (blue) with a data set of slabs with higher Miller indices from ref (20) (red). The minimum (average) of the latter data for a given composition is depicted in orange (black).