Machine Learning in Catalysis: Analysis and Prediction of CO Adsorption on Multi-elemental Nanoparticle using Metal Coordination-based Regression Model

Abstract

Information about molecular adsorption strength is important in every catalytic reaction. The ability to compare and determine relevant molecular active sites of interaction is necessary for fast screening of potential catalysts specially in a vast spectrum of probable candidates. In this study, we used the metal-coordination of the adsorption sites as a descriptor of the adsorption energy of CO on the PtRuIr ternary alloy nanoparticle. Using multiple regression model, we are able to predict the adsorption energy and specify some important descriptors that controls the strength of CO adsorption energy. This will enable a fast prediction of CO adsorption energy on PtRuIr nanoparticles with varying compositions and possible different morphologies using only the information of the structure of the catalyst. And open up the possibility of predicting adsorption interaction of other combinations of alloys with higher number of metallic compositions for fast screening of appropriate molecule-surface interaction.

1 Introduction

The catalyst's ability to proceed a reaction relies on the interaction of the reactant, intermediate and product molecules with the catalyst's surface. Antecedent knowledge on the molecule-surface interaction could determine viable reaction paths and approximate the catalyst's capability towards an intended reaction. The idea of generating a method to easily determine the strength of molecule-surface interaction would open the possibility for a fast screening of promising catalysts. The use of density functional theory (DFT)-based calculations and analysis in the understanding of molecule-surface interaction guided the design of promising catalyst and accelerated the discovery of other unconventional materials. However, a further step into the realm of the next-generation catalysts, the so-called multi-elemental materials or those comprising with 3 or more elements and with relatively high surface ratio such as in nanoparticles (NP), needs additional consideration due to its high computational cost.

With the current developments in data-driven analysis and machine learning techniques, the collections of DFT-based information could be used to efficiently treat systems that are computationally difficult for DFT calculations alone. As such, neural network potential (NNP) can be used to efficiently treat this purpose. A universal NNP called PreFerred Potential (PFP) is a series of trained dataset model of universal empirical interatomic potentials derived from DFT-based calculations [1, 2]. It is capable conducting atomic simulations, which could handle any combinations of 45 elements in the periodic table. The comparison of adsorption energies obtained from DFT and PFP were previously studied and shows good accuracy [3, 4]. However, the significant difference in calculation time enables one to gather a large amount of data with the use of PFP.

Complexity brought about by the presence of different metals comprising a multi-elemental alloy and variety of structure-related adsorption sites of the NP makes describing molecular adsorption thorough and computationally demanding. Enabling a simple way to describe the adsorption energy based on adsorption position could generate a concise description of molecular interaction with the surface. Adsorption position description that is sensitive to the morphology of the nanoparticle was previously done using generalized coordination number (GCN). GCN is a generalization of the concept of coordination number by considering the coordination of the first nearest neighbors [5]. The use of morphology-based descriptors that is structure-sensitive to describe molecule adsorption energy has been previously reported in literatures where O atom adsorption was analyzed in a Pt₃M NP alloy (M = Co, Ni, or Cu) with Pt-skin layer [6]. In this study, we used machine learning regression models to describe molecular adsorption energy using descriptors based on the metal-coordination of the adsorption site and its network of metal interaction inspired by GCN. As a sample study, we analyze CO adsorption on different concentrations of Pt_1-x-yRu_xIr_y ternary alloy NP using: (1) NNP via PFP to determine CO adsorption energy on the ternary alloy NP, and (2) analysis of the trend of adsorption energy via multiple regression models using metal-coordination-based descriptors. With this, we can determine a way to predict the adsorption energy of CO on different Pt_1-x-yRu_xIr_y ternary alloy NP with varying concentrations using only information of the structure. This study could provide an initial step towards fast determination of adsorption interaction based only on the structure of the catalyst, and hence could cater to a fast screening of promising catalysts.

2 Methods

The Pt_1-x-yRu_xIr_y ternary alloy NP model assumes the truncated octahedral face-center-cubic (fcc) structure with 201 atoms (Figure 1 inset). We used different concentrations of the ternary alloy: A-Pt_0.2Ru_0.2Ir_0.6, B-Pt_0.2Ru_0.4Ir_0.4, C-Pt_0.2Ru_0.6Ir_0.2, D-Pt_0.2Ru_0.2Ir_0.6, E-Pt_0.4Ru_0.4Ir_0.2, F-Pt_0.6Ru_0.2Ir_0.2, and G-Pt_0.33Ru_0.33Ir_0.33. For each concentration, CO adsorption on 3 NP with randomly generated atomic configurations were used as the train and test for the regression model, and CO adsorption on the computationally determined NP with stable atomic configurations were used as an addition test set (Figure S1). This set of NPs was obtained using supervised learning (SL) method via multiple regression analysis in combination with DFT-based first-principles calculation and multicanonical Monte-Carlo (MCMC) simulation with Wang-Landau sampling as described in ref [7, 8]. CO adsorption on the NP was scanned through all possible adsorption sites via the ontop, bridge, 3f hollow and 4f hollow sites. Each adsorption configuration was optimized PFP as implemented in the Matlantis atomistic simulation software [1]. The accuracy of CO adsorption energy obtained via PFP was previously verified against DFT-based calculation results [3, 4]. We used the version 4 of PFP with LBFGS algorithm for the optimization of the atomic positions, with a force criterion of 0.01 eV/Å. In this calculation, we did not consider the DFT+U correction and the Van der Waals corrections (CalcMode=CRYSTAL_U0). Each adsorption site was described in terms of the metal coordination of the site (Figure 2) as inspired by GCN. Machine learning was then used to predict the adsorption energy via multiple regression method with the metal-coordination as the descriptors of the regression. To train the regression model, 80% of the data were randomly chosen as training set and the other 20% were used as test set. Comparison of R² and Mean absolute error (MAE) were used to describe the accuracy of the regression model used.

Figure 1.

 Comparison of adsorption energy using generalized coordination number (GCN) of the adsorption sites. The adsorption energy on the different sites as described by GCN was compared on a Pt_0.2Ru_0.2Ir_0.6 NP optimized at 1000K. Ontop, bridge, 3f hollow and 4f hollow adsorption sites are in circle, star, triangle and tri left symbols, respectively. The kind of metal of each adsorption sites are indicated by colors. Inset: illustration of the truncated octahedra nanoparticle with 201 atoms labelled with its parts. Yellow, green and blue represents Pt, Ru and Ir atoms, respectively. Vesta software was used for the visualization of the atomic configuration [9]

Figure 2.

 Describing adsorption sites in based on metal coordination. The adsorption sites were described in terms of the network of metal coordination until the coordinating atoms of the neighbors of the adsorption site. The nomenclature of the descriptor are as follows: atom of the adsorption site—atom neighbor of the adsorption site—coordinating atom of the neighbor of the adsorption site. In this figure, the atomic adsorption site is Ir1, and examples of its neighbors are Ir2, Pt3, Pt1, Ir3 (black broken arrows), the atoms coordinating the neighbors (e.g. Pt1) are Ir2, Ru1, Pt2, etc. (pink arrow). Therefore, an example of metal-coordination descriptors are: one IrPtIr (for Ir1Pt1Ir2), one IrPtRu (for Ir1Pt1Ru1), one IrIrPt (for Ir1Ir3Pt1), etc. until all the combinations in the network are counted. Inset: Illustration of the CO ontop adsorbed on a {111} facet of the NP showing the network of metal coordination of the atom at the adsorption site up to the coordinating atom of the nearest neighbor of the atom at the adsorption site (pink lines). Vesta software was used for the visualization of the atomic configuration [9].

From the multiple regression model, the predicted adsorption energy, E_ads, can be expressed as$E_{ads}$, can be expressed as

  

$E_{ads}=\left({\displaystyle \sum }_{i,j,k}{X}_{{\text{M}}_i{\text{M}}_j{\text{M}}_k}\right)+X_o$

where $X_{{\text{M}}_i{\text{M}}_j{\text{M}}_k}$ is the coefficient of regression for each metal-coordination-based descriptors. ${\text{M}}_i{\text{M}}_{\text{j}}{\text{M}}_k$is the metal-coordination-based descriptor: ${\text{M}}_i$ is the type of atom at the adsorption site, ${\text{M}}_j$ is the neighbor atom of the adsorption site and ${\text{M}}_k$ is atom coordinating the neighbor of the adsorption site. i, j and k spans through the atom of the adsorption site, all neighbor atoms of the adsorption site, and coordinating atom of the neighbor of the adsorption site, respectively; and $X_o$ is the constant of the regression.

3 Results and Discussions

Initial analysis of CO adsorption using comparison of adsorption energy against the GCN of the adsorption site shows that the adsorption energy is dependent on the type of atom where it is interacting and site of adsorption as described by GCN (Figure 1 and S2). Generally, CO adsorption on the Pt_1-x-yRu_xIr_y ternary alloy NP shows stronger adsorption on low coordinated sites such as near the vertex and the edge sites, for all the types of coordinating atom (Figure S3). This difference is more prominent on adsorption on the ontop sites. Furthermore, preference for adsorption on the Ir/Ru site over the Pt is observed at all adsorption sites. Therefore, for the Pt_1-x-yRu_xIr_y ternary alloy NP, CO near the edge and vertex has relatively stronger adsorption, and is enhanced if the adsorptions site is ontop of either Ir/Ru atom. It is also observed that there is a slight difference in adsorption energy for the same type of adsorption position, e.g. ontop site with GCN 4.25, and type of atom in the adsorption site, e.g. Pt. For this type of adsorption position, there is range of adsorption energy from about -2.1 eV to about -2.3 eV for the same nanoparticle (Figure 1). This difference is due to the changes in the electronic configurations brought about by the difference in the network of atoms coordinating the atom in the adsorption sites. And these differences in the adsorption energy increases the complexity of the describing CO adsorption for a particular nanoparticle. As such, we need to develop a simple way to predict the adsorption energy considering these differences.

Using the network of metals coordinating the atoms in the adsorption sites as descriptors, we are able to differentiate each adsorption site and describe its corresponding adsorption energy. Using the data from CO adsorption on the 3 NP with atomic configurations randomly arranged for each Pt_1-x-yRu_xIr_y NP concentration, we are able to generate a training dataset for the prediction of adsorption energy using multiple regression model and metal-coordination-based descriptors. Figure 3 shows the comparison of the calculated adsorption energy using PFP and the adsorption energy predicted using metal-coordination-based regression model for CO adsorption on the ontop sites. The distribution of the predicted test set shows relatively good comparison. The R² also shows high correlation of about 0.868 for test set and 0.835 for the train set, and the value of the MAE is also small with value of about 0.0909 eV for the test set and 0.0982 for the train set. Figure 4 shows the distribution of the coefficient of regression. The constant of regression is a negative value, -3.0084 eV, and the values of the coefficient of regression for each descriptor are all positive. With this, a higher value of the coefficient will contribute to a weaker adsorption and a lower value will contribute to stronger adsorption energy. Comparison of the values of the coefficient of regression shows that generally, adsorption on the Pt ontop will results in a weaker adsorption energy as indicated by the higher values of coefficient than that of adsorption on the Ir and Ru ontop. Furthermore, adsorption on Ir and Ru that is coordinated to Pt will result in a stronger CO adsorption. These results are consistent with the analysis of CO adsorption energy using adsorption energy vs GCN plot (Figure 1) such that adsorption on Ir/Ru and on low coordinated sites will results in stronger adsorption. Furthermore, we can also describe the network of interactions that would provide a strong or weak adsorption, as needed in the reaction. As such, with the use of these information, we can intently design a NP surface that would provide an appropriate adsorption energy by controlling the NP structure. We used the same regression coefficients to determine ontop adsorption energy for a set of NPs with the same concentrations but with optimized atomic configurations. These data are not part of the training-test dataset. Figure 5 shows the comparison of the calculated and the predicted adsorption energy and the corresponding values of the R² and MAE. The relatively high value of R² and low MAE shows that the predicted values of ontop adsorption energies are in good agreement with the calculated values even if these datasets are not part of the training set. With this, adsorption prediction can be attained by using only the information about the structure, i.e., the network of atoms coordinating the adsorption site, and data on the coefficient of regression. These results can be helpful for the description of adsorption, which is related to reaction and will be important for the design of catalyst. This also contributes to studies related to interpretable machine learning.

Figure 3.

 Comparison of the calculated and predicted CO adsorption energy on the Pt_1-x-yRu_xIr_y ternary alloy NP. The plot shows the comparison of CO adsorption energy between the calculated values using PFP and the predicted values using metal-coordination-based regression model. The plot shows the distribution of the test dataset and also shows the R² and MAE for the train and test set.

Figure 4.

 Distribution of the Coefficient of Regression. The plot shows the distribution of the coefficients of the different metal-coordination-based descriptors for CO ontop adsorption. Area in light blue, light green and light yellow are adsorption ontop of Ir, Ru and Pt sites, respectively. The constant of the regression is also shown. Higher value of coefficient contributes to weaker adsorption energy, and lower values of coefficient contributes to stronger adsorption energy. Specific values are tabulated in Table S1.

Figure 5.

 Comparison of the calculated and predicted CO adsorption energy on the atomic-configuration optimized NP. The plot shows the comparison of the calculated and predicted CO adsorption energy on different concentrations of NP alloys with atomic configurations optimized at 1000K. Inset: Comparison of the calculated values of R² and MAE.

Acknowledgement

This work was supported in part by the Ministry of the Environment, Japan "Demonstration Project of Innovative Catalyst Technology for Decarbonization through Regional Resource Recycling". DFT-based calculations were performed using MASAMUNE-IMR in Center for Computational Materials Science, Institute for Materials Research, Tohoku University (19S004).

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