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

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 ϵu is correlated strongly with adsorption energies and could be a useful screening property accessible at the nanocluster level.

finding the nearest neighbour composition around an atom in the pool of all configurations.
The most segregated clusters were never the most stable. No continuous trend in segregation and stability could be observed, segregation was often alternating, most prominently in compositions of (A27B28). For clusters containing titanium, the most segregated were less stable than in clusters not containing them. The effect was most prominent in TiNi, TiCo and PtTi, but not present in TiCu. Core-shell structures were found at the compositions and Cu 13 Pt 42 . The reverse core-shell structures tended to be one of the least stable configurations in that composition. There appeared to be a continuous trend in core-shell likelihood and stability, in bimetallic combinations where a core-shell structure existed, but this trend was exempt in compositions of (A27B28). Platinum could be found on the shell in all cases A 13 Pt 42 , titanium however never formed core-shell structures A 13 Ti 42 despite their similar Wigner-Seitz radii.
In figure S3 the change in nanocluster stability is compared to the nanocluster similarity.
The relative energy change of energy minimum by adding an additional nanocluster to a set for a given composition is depicted in red. Nanocluster similarity to the previous nanoclusters measured by average global SOAP is shown in blue. Both quantities decrease with increasing nanocluster set size, but the nanocluster stability did not converge within a set of 10 nanoclusters per composition. The nanocluster sets were ordered by farthest point sampling. Figure S1. Excess energies of nanoclusters. The convex hulls are indicated by the red dotted lines.   Figure S3. Relative energy change of energy minimum by adding an additional nanocluster to a set for a given composition (red). Nanocluster similarity (zero means perfect match) to the previous nanoclusters measured by average global SOAP (blue). The nanoclusters were ordered by farthest point sampling.

CORRELATION ELLIPSES
The figures S4, S5 and S6 depict, given a certain composition, the mean and the variance of d , w d and u , respectively. The x-axes not only indicate the element composition but also the energy spread of the clusters among a certain composition (s. green length bar). The correlation ellipses show the standard deviation of the descriptor around its mean (y-direction) as well as the standard deviation of the cluster energies around their mean (x-direction).
A flat (near-horizontal) ellipsis signifies a descriptor insensitive to the varying cluster stability. In contrast, a steep (near-vertical) ellipsis means that despite clusters have com-

NEAREST NEIGHBOURS d-BAND CENTER
In figure S7 a linear trend between the ratio of nearest-neighbour atom types and the d-band center of the LDOS of a surface atom was observed for all bimetallic nanoclusters.
The ratio of next-nearest neighbours also seemed to play a role but there did not seem to be a monotonous trend. The ratio of next-nearest neighbours could not explain the large distribution in d-band center at a given ratio of nearest-neighbour metal identities, neither was it explained by whether the center metal was located at a vertex or edge position.

REDUCED CORE PLATINUM NANOCLUSTER
A Pt 55 cluster with a reduced core, taken as the global minimum from Ref. [1]. The descriptor values in table S1 do not change significantly compared to a Pt 55 icosahedron.   We see that the deviation is not significant. Thus, it can be concluded that the s and p states do not include much information, when comparing LDOS with the element's concentration.
Figure S10-S12 show the correlation of the t-SNE clusters of the descriptors of ε d , ε w d , and ε u with the element concentration in the nanocluster. These plots are used to compare the average MI for these descriptors with the LDOS, used as is, of the same d-band.