Study of the adsorption sites of high entropy alloys for CO2 reduction using graph convolutional network

Abstract

Carbon dioxide reduction is a major step toward building a cleaner and safer environment. There is a surge of interest in exploring high-entropy alloys (HEAs) as active catalysts for CO2 reduction; however, so far, it is mainly limited to quinary HEAs. Inspired by the successful synthesis of octonary and denary HEAs, herein, the CO2 reduction reaction (CO2RR) performance of an HEA composed of Ag, Au, Cu, Pd, Pt, Co, Ga, Ni, and Zn is studied by developing a high-fidelity graph neural network (GNN) framework. Within this framework, the adsorption site geometry and physics are employed through the featurization of elements. Particularly, featurization is performed using various intrinsic properties, such as electronegativity and atomic radius, to enable not only the supervised learning of CO2RR performance descriptors, namely, CO and H adsorption energies, but also the learning of adsorption physics and generalization to unseen metals and alloys. The developed model evaluates the adsorption strength of ∼3.5 and ∼0.4 billion possible sites for CO and H, respectively. Despite the enormous space of the AgAuCuPdPtCoGaNiZn alloy and the rather small size of the training data, the GNN framework demonstrated high accuracy and good robustness. This study paves the way for the rapid screening and intelligent synthesis of CO2RR-active and selective HEAs.

Full text

APL Machine Learning ARTICLE pubs.aip.org/aip/aml
Study of the adsorption sites of high
entropy alloys for CO2reduction using
graph convolutional network
Cite as: APL Mach. Learn. 2, 026103 (2024); doi: 10.1063/5.0198043
Submitted: 16 January 2024 •Accepted: 13 March 2024 •
Published Online: 3 April 2024
H. Oliaei1and N. R. Aluru2,a)
AFFILIATIONS
1Department of Mechanical Science and Engineering, University of Illinois at Urbana–Champaign, Urbana, Illinois 61801, USA
2Oden Institute for Computational Engineering and Sciences, Walker Department of Mechanical Engineering,
The University of Texas at Austin, Austin, Texas 78712, USA
a)Author to whom correspondence should be addressed: aluru@utexas.edu
ABSTRACT
Carbon dioxide reduction is a major step toward building a cleaner and safer environment. There is a surge of interest in exploring high-
entropy alloys (HEAs) as active catalysts for CO2reduction; however, so far, it is mainly limited to quinary HEAs. Inspired by the successful
synthesis of octonary and denary HEAs, herein, the CO2reduction reaction (CO2RR) performance of an HEA composed of Ag, Au, Cu, Pd, Pt,
Co, Ga, Ni, and Zn is studied by developing a high-fidelity graph neural network (GNN) framework. Within this framework, the adsorption
site geometry and physics are employed through the featurization of elements. Particularly, featurization is performed using various intrinsic
properties, such as electronegativity and atomic radius, to enable not only the supervised learning of CO2RR performance descriptors, namely,
CO and H adsorption energies, but also the learning of adsorption physics and generalization to unseen metals and alloys. The developed
model evaluates the adsorption strength of ∼3.5 and ∼0.4 billion possible sites for CO and H, respectively. Despite the enormous space of
the AgAuCuPdPtCoGaNiZn alloy and the rather small size of the training data, the GNN framework demonstrated high accuracy and good
robustness. This study paves the way for the rapid screening and intelligent synthesis of CO2RR-active and selective HEAs.
©2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license
(https://creativecommons.org/licenses/by/4.0/). https://doi.org/10.1063/5.0198043
I. INTRODUCTION
While pure metals are limited in number and properties, struc-
tural alloying and composition fine-tuning allow for tailoring the
metallic properties such as strength, stiffness, weldability, mag-
netism, conductivity, corrosion resistance,1storage capacity,2and
catalytic activity.3For example, adding Cu to Ag, Ni to Fe, and Mg
to Al improves hardness, durability, and conductivity,4respectively.
Yeh et al. proposed that combining a considerable concentration of
five or more constituent metal elements would yield a high-entropy
alloy (HEA).5This category of materials has been studied to under-
stand their unique and tunable mechanical and electrical properties,
such as high yield strength,6enhanced ductility,7and supercon-
ductivity.8Moreover, HEAs have attracted considerable attention
in the realm of energy storage and conversion. Hydrogen storage
is one of the applications of HEAs, and several HEAs, including
TiVZrNbHf9,10 and TiZrCrMnFeNi,11 exhibit improved hydrogen
storage compared to their monometallic counterparts. In another
study on Li-ion batteries, Co0.2Cu0.2Mg0.2Ni0.2Zn0.2 oxide proved
to be a promising anode material.12 The catalytic performance of
HEAs is a topic of interest that includes, but is not confined to, water
splitting, hydrogen evolution, and carbon dioxide reduction reac-
tion (CO2RR). In this study, we focus on the CO2RR performance of
HEAs.
There is an ongoing effort to discover active and selective
CO2RR catalysts, increasing the need to explore the field of HEAs.
An experimental study by Nellaiappan et al.13 revealed the superb
activity and selectivity of a quinary HEA (AgAuCuPdPt), which was
also studied computationally.14 To date, the available CO2RR-based
computational studies on HEAs are focused on quinary structures,
and alloys with more metal components remain unexplored.14–16
Despite the limited computational studies, beyond quinary struc-
tures have been successfully synthesized by several groups. Yao et al.
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proposed a thermal shock-based process for the stable solid-solution
synthesis of nanoparticles comprising up to eight different elements
(octonary HEA).17 Moreover, in a study by Gao et al., a fast-moving
bed pyrolysis strategy was proposed for the synthesis of nanoparti-
cles with up to ten elements (denary HEA) on granular supports.18
Both studies achieved the solid-solution nanoparticle stability and
synthesizability despite the immiscibility of some of the elements.
Moreover, both studies reported that their HEAs exhibited a preva-
lent face-centered cubic (fcc) crystal structure. Such results motivate
the in silico investigation of HEAs beyond quinary structures to
gain insights into their catalytic behavior. To address this matter,
herein, an fcc-structured nonary HEA, namely, AgAuCuPdPtCoGa-
NiZn, whose constituent elements are widely popular in the CO2RR
literature, is studied.14
In the design of nonary HEAs, the potential for changing
the elemental concentration along with the randomness of the
elemental distribution creates a high-dimensional space. Explor-
ing this gigantic space is a major challenge that is hampered by
pure synthesis or atomistic-scale simulation. Accordingly, to han-
dle this daunting task, there is a need for high-throughput machine
learning (ML) frameworks. To demonstrate the power of arti-
ficial intelligence in material science, a recent study by Toyao
reviews some of the successful applications of ML in the discov-
ery of alloy or intermetallic catalysts.19 As a first step, there is a
need for detecting the different binding sites of important CO2RR
reactants and their corresponding adsorption energies. While the
structure and geometry of these adsorption sites for our target
species, CO and H, are well known [on-top for CO and either
fcc-hollow or hexagonal close-packed (hcp)-hollow for H],14 the
challenge is to account for the different atomic distributions at these
sites (microstructures). To deal with the multitude of microstruc-
tures in a high-throughput manner, a graph convolutional net-
work (GCN) is employed, and a surrogate adsorption model is
developed.
An important merit of the GCN model is that it is devel-
oped based on the geometric and electronic-state features of the
microstructures. In fact, the adsorption process is closely related
to the atomic structure and electronic state of the adsorption site;
hence, providing relevant representative features allows the model
to learn the interplay. Accordingly, the GCN model can be gen-
eralized to different metal components. Another benefit of the
GCN model is its capacity to embody the microstructure geometry
and preserve desired symmetries, such as permutation invariance.
These advantages make GCN a suitable and promising model for
not only the study of HEAs but also for future studies on other
multicomponent structures. Furthermore, by taking advantage of
the graph structure, the adsorption and binding of the various
reactants, CO and H, can be modeled in a single GCN, which
eliminates the need for developing a separate model. This graph-
based framework may accelerate the investigation of the huge realm
of HEAs in addition to opening new opportunities for catalyst
discovery.
II. METHODS
A. CO2RR performance descriptors: ΔECO and ΔEH
A common way of characterizing the catalytic performance of
a surface is to use the adsorption energies of key intermediates.20
In the context of CO2RR, a primary and prevailing intermediate is
CO, and multiple studies have introduced the adsorption energy
of CO as a crucial descriptor for the CO2RR performance.21–23 In
addition, hydrogen evolution, a reaction competing with CO2/CO
reduction, is necessary to study, especially in aqueous systems.24,25 A
study reported that these two descriptors can explain CO2reduction
to products other than CO (hydrocarbons or alcohols).26 Therefore,
herein, the adsorption strengths of CO and H species to the surface,
namely, ΔECO and ΔEH, respectively, are used to evaluate the CO2RR
performance.
B. Adsorption sites of CO and H and their
configurational space
A microstructure is defined as a group of surface atoms at
the adsorption site and immediate to the reactant. The favorable
adsorption sites (with the lowest energies) and microstructures
for CO and H adsorbates have been comprehensively determined
in the literature; “on-top” is the preferred binding site for CO,
whereas H is adsorbed at either “fcc-hollow” or “hcp-hollow” sites.14
Figure 1(a)(i) shows a schematic representation of these sites and
their corresponding microstructures. Figure 1(a)(i)(1)–(3) depicts
the on-top microstructure with ten atoms, fcc-hollow microstruc-
ture with nine atoms, and hcp-hollow microstructure with seven
atoms, respectively. Each structure comprises three zones based on
the proximity to the reactant.
Given the three microstructure categories and the presence of
nine metal components in our target alloy, the configuration size
of each category can be estimated. The on-top, fcc-hollow, and
hcp-hollow groups hold 910, 99, and 97distinct microstructures,
respectively. For brevity and facile referencing, these sets are labeled
as T1, T2, and T3, respectively.
One computational study on oxygen reduction conducted cal-
culations to determine the impact of in-zone metal permutations
on the adsorption energy and concluded that the effect is not sig-
nificant.27 Therefore, given a specific metal composition in a zone,
energy calculations for one specific zone ordering should give a
good binding energy estimate for the rest of the permutations.
Accordingly, in-zone permutations are ignored, and only distinct in-
zone metal combinations are focused on. Consequently, the T1, T2,
and T3 sets boil down to 4459 455 (9×3003 ×165), 4 492125 (165
×165 ×165), and 245025 (165 ×165 ×9) microstructures, respec-
tively. For conciseness, these sets are represented by C1, C2, and C3,
respectively.
C. First-principles-based data for microstructure
energies, ΔECO and ΔEH
The microstructures available in the C1, C2, and C3 sets and
their corresponding ΔECO and ΔEHare further studied. A study by
Pedersen et al.14 calculates the adsorption energies for two quinary
alloys, AgAuCuPdPt and CoCuGaNiZn, which construct a subspace
of our nonary HEA, AgAuCuPdPtCoGaNiZn, and forms a suit-
able density functional theory (DFT)-based dataset for training and
developing our model. Their dataset is obtained by modeling the
adsorption of key reactants on the (111) plane of a 2 ×2×5 slab and
includes 1503, 1674, and 1343 data points from C1, C2, and C3 sets,
respectively.
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FIG. 1. (a) Framework of the graph construction. (i) Top view ofthe (111) plane of a material with an fcc structure. The on-top, fcc-hollow, and hcp-hollow microstructures are
represented in 1–3, respectively. For each microstructure, the alloy atoms closest to the adsorbate are defined and categorized into three zones. Each zone is assigned a
specific color. 1: On-top microstructure with a CO molecule adsorbate (small red circle). The microstructure comprises ten atoms; 2: fcc-hollow microstructure with nine atoms,
and the small white circle represents the H adsorbate; and 3: hcp-hollow microstructure with seven atoms and the H adsorbate. (ii) Featurization of microstructure atoms
using atom-intrinsic, microstructure index, and zone index features. f1denotes a set of metal-intrinsic features, including atomic radius and electronegativity. f2denotes the
microstructure category (1, 2, or 3) in a one-hot encoded fashion. Similarly, f3represents the one-hot encoded zone index. (iii) Graph construction using featurized atoms.
Each colored graph node represents an atom of the same color from the microstructure. The graphs are fully connected. (b) GCN architecture for modeling CO and H binding
energies, ΔEads. The different layers of the GCN model are shown. The model includes node transformations, graph convolution, pooling, dense layers, and output layer,
respectively.
D. GCN to predict microstructural ΔECO and ΔEH
The graph neural network (GNN) is a category of neural
networks that operates on graph-structured data to leverage their
relational information that might be lost by using conventional
deep-learning approaches. A graph comprises nodes and edges,
denoted by G={V,E}, where Vand Eshow the nodes and edges,
respectively. Several studies on the prediction of metal properties
demonstrate the remarkably high accuracy of GNNs, leading to a
significant improvement over the traditional ML models.28 In the
current framework, a GNN is employed to incorporate the structure
and geometry of the data in addition to preserving their invari-
ance properties. One such property is the permutation invariance,
which implies that the in-zone permutation of metals should not
change the surface–reactant binding energy. In this study, every
graph represents one microstructure, and each node represents an
atom in the microstructure. V={vi∈R13i=1, ...,N}shows the
set of all nodes, each with 13 attributes, where Nis the total num-
ber of atoms in the microstructure, i.e., 10, 9, and 7 for on-top,
fcc-hollow, and hcp-hollow, respectively. A fully connected graph
is used for the microstructure representation, i.e., every two nodes
are linked together with an edge and E={{i,j}i,j∈Vand i≠j}.
By exploiting the graph construction, the full-connectivity property,
and the message-passing scheme, the permutation invariance can be
satisfied.
A majority of GNNs are message-passing GNNs that update
node representations based on the information aggregation from
neighboring nodes.29 A special and prominent case of the message-
passing paradigm is a GCN, where an aggregation concept similar
to image convolution is implemented. Herein, a GCN, whose con-
volution layer performs a weighted sum of representations from
neighboring nodes and the node itself, is used. Mathematically, the
convolution layer works as follows:
hl
v=al
N(v) ∑
nεN(v)
hl−1
n+blhl−1
v+cl, (1)
where hl
vand hl−1
vare the hidden representations of node vat lay-
ers land l−1, respectively. N(v)is the neighborhood of node vand
N(v)={n;{n,v}∈E}. The weights are aland bl, and the bias is cl;
all three are node-agnostic and layer-specific learnable parameters
of the model. h0represents the input feature and corresponds to the
13-dimensional node feature or attribute. The goal is to predict the
binding energy of different microstructures, represented as graphs;
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therefore, a regression model at the graph level is developed to map
graph representations of microstructures to the binding energy. A
pooling layer is used to travel from the hidden representations of
nodes (atoms) to a graph-level prediction for binding energy. In
other words, the pooling layer combines the hidden representations
of nodes into a single vector.
E. Featurization
A vital part of developing and training the GCN model is
the selection of appropriate features. While the available deep-
learning models achieve a good performance on the HEA catalysts,
to the best of our knowledge, most of them use low-information
features. However, low-information encoding limits the general-
izability of the model and proper learning of the adsorption and
microstructure–binding interplay. Therefore, in this study, featur-
ization is performed using the intrinsic properties of atoms. One
of the major goals of this study is to simultaneously achieve model
interpretability and feature simplicity. For feature simplicity, the
models for material design select features pertinent to the size and
electronic structure of the atom.20 In fact, these features help to
not only identify the metal characteristics that are critical to the
CO2RR performance but also include a wider range of metals and
enlighten the path for future metal selection and HEA discovery.
As another simplicity criterion, the accessibility of these features is
crucial. Accordingly, features that are already available in databases
such as NIST30 or Materials Project31 are prioritized because they
eliminate the need for excess simulations. According to the available
literature,16,20 the following intrinsic attributes are selected: atomic
number (Z), mass (m), atomic radius (ra), covalent radius (rc), elec-
tronegativity (χ), electron affinity (Ea), and first ionization energy
(I1). The values of these features for each metal are listed in Table S1.
Moreover, additional features are used to embody the microstruc-
ture category and geometry (zone index information), which is also
illustrated in Fig. 1(a)(ii). For the microstructure category, a three-
dimensional feature in a one-hot-encoded fashion is defined, where
(1, 0, 0), (0, 1, 0), and (0, 0, 1) represent the on-top, fcc-hollow,
and hcp-hollow microstructures, respectively. Moreover, the zone
indices are one-hot encoded in a similar way as elaborated in Fig.
1(a)(ii); the closest, second closest, and third closest zones are shown
by (1, 0, 0), (0, 1, 0), and (0, 0, 1), respectively. These features along
with the seven intrinsic features form a 13-dimensional feature set
that is used to develop and train the GCN model.
III. RESULTS
A. Graph construction, GCN training,
and performance
A single GCN is trained for all three cases, namely, on-top CO
adsorption, fcc-hollow H adsorption, and hcp-hollow H adsorption.
The pipeline for graph construction and model training is illustrated
in Fig. 1, and the implementation is performed using the PyTorch
Geometric (PyG)32 package. Figure 1(a)(i)–(iii)– explains the pro-
cedure of graph construction for the on-top (CO), fcc-hollow, and
hcp-hollow (H) cases using microstructure geometry along with
metal-intrinsic and zone-wise features. Moreover, Fig. 1(b) shows
the architecture of the GCN used to model the binding energies.
The constructed graphs with a node input of size of 13 (seven
metal-intrinsic descriptors along with the three zone-wise and three
microstructure-related features) are fed to the neural network. First,
a transformation of size 13 ×256 is applied on the input features
to increase the number of parameters of the model. Then, two lay-
ers of convolutions of sizes 256 ×128 and 128 ×128 are applied to
aggregate information from neighboring atoms. The graphs that are
studied herein are fully connected, which means that the zones are
inter- and intra-connected using edges within the graph structure.
This full connectivity results in a quick mixing of information within
the graph, and two convolutional layers are sufficient to extract use-
ful information. Additional convolutional layers are also tested, but
no significant improvement in the performance is observed. After-
ward, a pooling function (mean pooling) is applied to find a united
representation for each graph. Particularly, the pooling procedure
takes the mean over all the nodes within each graph to reduce graph
data into a single vector. In addition, for better regularization and to
avoid overfitting, the pooling step is followed by a dropout layer. In
the last stage, a multilayer perceptron (MLP) with one hidden layer
of size 128 ×64 is applied to the graph representation, followed by
a 64 ×1 output layer. A rectified linear unit (ReLU) activation func-
tion is used for all layers except for the dropout and output layers.
The hyperparameters are optimized using a grid-search method, and
the optimal hyperparameters are listed in Table S2. Moreover, model
training and minimization of the regression loss are performed using
an Adam optimizer. By performing early stopping, the mean abso-
lute error (MAE) is 0.055 eV, more specifically, 0.062 eV for CO,
0.057 eV for fcc-hollow H, and 0.048 eV for hcp-hollow H categories.
In addition, the overall root mean squared error (RMSE) is 0.072 eV,
with values of 0.082, 0.073, and 0.058 eV for CO, fcc-hollow H, and
hcp-hollow H, respectively.
Two quinary HEAs, AgAuCuPdPt and CoCuGaNiZn, and their
corresponding microstructures, as explained in Sec. II C, are used
to train the GCN model. Figure 2 shows a comprehensive illustra-
tion of the energies predicted by the GCN model along with their
DFT counterparts. Moreover, the energy distributions of the GCN
and DFT studies are shown in Fig. 2. The GCN learns the distri-
bution of both HEAs with a good performance. In another study, a
Gaussian process regression (GPR) model is developed on the same
dataset, where a separate network for each microstructure category
is selected and trained, and featurization is based on the quan-
tity of each of the five elements in the microstructure.14 The GPR
model achieves MAE values of 0.064, 0.064, and 0.052 eV for CO,
fcc-hollow H, and hcp-hollow H categories, respectively. The GCN
model achieves moderately superior accuracy compared to the GPR
model. With regard to model generalizability, the GCN model devel-
ops a single network, which outperforms the GPR model in terms
of both applicability to unseen elements and model interpretabil-
ity. Upon computing the feature importance, we can investigate the
impact of each intrinsic property on the adsorption strength.
Roy et al.16 study two quinary HEAs and proposed an ML
model with 22 features (15 regional and seven intrinsic features)
that achieves a root-mean-squared error (RMSE) of ∼0.14 eV for CO
and 0.055 eV for H (hcp-hollow) adsorbates. The 15-dimensional
regional feature comes from five elements multiplied by three
regions and is constructed based on the quantity of each metal.
The use of a fixed-sized (15) set of features limits the generaliz-
ability of their ML model to specific metals and quinary alloys, but
other elements and a higher number of components (6 ≤) are also
available and left unexplored. The GCN model achieves superior
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FIG. 2. Comparison of the predicted adsorption energies using the GCN model (ΔEGCN) with the energies from DFT calculations (ΔEDFT). (a) Comparison of the binding
energies of CO for the on-top microstructure. The side plots show the histograms of binding energies, i.e., the horizontal and vertical plots represent the DFT data and GCN
output distribution, respectively. (b) Comparison of the binding energies of H for the fcc-hollow microstructure. (c) Comparison of the binding energies of H for the hcp-hollow
microstructure. Blue and red indicate the data for the CoCuGaNiZn and AgAuCuPdPt datasets, respectively. The diagonal solid line represents ΔEGCN =ΔEDFT, and the
diagonal dashed lines are ±0.1 eV offsets of the solid line. In addition, on the histogram plots, the dashed lines and their annotations demonstrate the binding energies of the
monometallic microstructures.
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FIG. 3. Evaluation of the importance of the intrinsic features for microstructure energies predicted by the GCN. (a) Feature importance values for the on-top CO adsorbate.
(b) Feature importance values for the fcc-hollow H adsorbate. (c) Feature importance values for the hcp-hollow H adsorbate. For each microstructure group, the importance
values are normalized by the highest value within that group. A higher importance value of a feature indicates the higher reliance of the GCN model on that feature to make
accurate predictions.
accuracy for the CO adsorbate, whereas for the H adsorbate, its
error is marginally higher than Roy’s ML model. Compared to the
GCN model that allows for training a single model on the various
adsorbates’ data, this ML model should be trained separately on each
adsorbate category. Moreover, in graphs, by construction, the nodes
along with the zone-wise features take care of the atomic distribu-
tion and composition description, and no constraint is imposed on
the number of components in the HEA or the type of metals. Such
advantages allow us to interrogate the nonary structure of the AgAu-
CuPdPtCoGaNiZn alloy in this study and further extend the model
to other types of components.
B. Feature importance
Performing feature importance and quantifying the contribu-
tion/effect of features within a dataset allows for gaining insights
into the underlying mechanism in addition to interpreting the pre-
dictive power of an ML model. After training the GCN model, we
use the GNNExplainer33 algorithm, which applies attribute masks
to explain the model predictions at the graph level. GNNExplainer
is a model-agnostic algorithm, which maximizes the mutual infor-
mation between possible subsets of node features and the GNN’s
prediction. Figure 3 shows the results of feature importance for each
of the three microstructure categories. Each plot [(a)–(c)] includes
the importance values of the 7 intrinsic features. For better consis-
tency, we normalized the importance values by the maximum value;
hence, they range from 0 to 1. A feature with a higher value exhibits
a higher reliance of the GCN model on that feature to make accu-
rate predictions and gain a better performance. For all the three
groups, the geometry and size of the atom exhibit the highest sig-
nificance, with covalent and atomic radii being the most influential
features for CO and H binding. The H atom is small, and its adsorp-
tion is governed by weak van der Waals forces, whereas upon the
adsorption of a CO molecule, stronger bonds are formed. This is
also evident from the range of adsorption energies in Fig. 2. Con-
sequently, the covalent radius exhibits higher importance than the
atomic radius in the case of CO adsorption. Next, the electronic
structure features, including electronegativity and electron affinity,
display moderately high importance values, which are inferior to
the atomic geometry and radii. Electronegativity of surface atoms
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FIG. 4. Distribution of the error indicator for the three microstructure categories. (a) Error distribution for the on-top CO microstructure. (b) Error distribution for the fcc-hollow
H microstructure. (c) Error distribution for the hcp-hollow H microstructure. The vertical dashed lines exhibit the percentile upper bounds; from left to right showing 0%, 25%,
50%, 75%, and 100% percentiles. The low error value of a microstructure corresponds to the low uncertainty of the GCN ensemble model for that structure.
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has been used as an electronic structure descriptor for describing
the adsorption properties of transition metals and intermetallics,
as it helps to reflect the d-band characteristics.34 Ultimately, the
atomic number and mass appear to be the least informative among
the features. The fact that atomic mass is secondary to atomic
geometry and electronic structure properties arises from adsorp-
tion processes and interactions being determined by the distances
and energies associated with atomic interactions and chemical
bonding.
C. Out-of-sample adsorption prediction: Assessing
model robustness
So far, the model is trained and tested on a small subset
of C1, C2, and C3 sets; herein, it is deployed to evaluate the
binding energies for the rest of the microstructures within these
sets. The goal is to assess the ability of the model to maintain
its performance in the face of variations in the distribution and
composition of the microstructure atoms. An ensemble model
approach, including four models, is applied for the purpose of
uncertainty quantification and assessing model robustness. Four
models with different weight initializations are trained on the same
dataset as explained in Sec. III A. Then, for each microstructure
within the C1, C2, and C3 sets, we define an error indicator as
follows:
εm=ΔEw(Gm)−ΔEw(Gm)2,
where mruns over the microstructures within each of the three cate-
gories, on-top CO, fcc-hollow H, and hcp-hollow H adsorption. Gm
represents the graph corresponding to the mth microstructure. In
addition, ΔEwshows the adsorption energy predicted by each model.
Figure 4 shows the distribution of εmfor each category. The fcc-
hollow category displays great robustness with low uncertainties. We
see that 75% of the data achieve error values below 0.03 eV, which is
remarkably low for modeling the adsorption energies. Moreover, the
on-top microstructure shows acceptable uncertainties with 75% of
the error values falling below 0.06 eV. These two categories achieve
robustness superior to the hcp-hollow microstructure. We attribute
the higher uncertainty of the hcp-hollow microstructure to train-
ing data scarcity. The training data points for this category could
be centered around the monometallic structures, which prevents
the GCN model to properly learn/detect the underlying pattern.
The performance of any of the categories may be improved by
applying an active learning scheme where the most uncertain data
points are labeled and added to the data pool iteratively. However,
implementation of such a framework falls within the scope
of future work and is beyond the current study’s intended
focus.
D. Activity and selectivity
So far, the binding energies for the different sites (microstruc-
tures) at which the CO and H molecules are absorbed have been
assessed. There exist activity and selectivity measures14 to link
these various sites and their energy predictions to a specific HEA
composition in addition to providing a ground for evaluating the
performance of the composition. The activity–selectivity map for
different HEA compositions, from binary to nonary, is illustrated in
Fig. S1.
IV. CONCLUSIONS
This study presents a high-throughput, high-fidelity framework
based on a GCN and intrinsic features of elements to model adsorp-
tion sites of the CO2RR-catalyst HEAs with different numbers of
components. The model accounts for the possible adsorption sites
for two important CO2RR intermediates, CO and H species, to
evaluate the adsorption energies and their relation to the surface
descriptors. The use of a graph-based model allows for incorporat-
ing the geometry of the adsorption sites in addition to the required
symmetries, specifically permutation-invariance of atoms, within
the sites. These properties are very challenging to accomplish with
the conventional machine learning models. Moreover, the metal
components that we study are Ag, Au, Cu, Pd, Pt, Co, Ga, Ni,
and Zn, but the model can be generalized to other metals of inter-
est because it is built upon intrinsic and informative features. The
GCN model is explained by performing feature importance, which
ranks the significance of the different intrinsic features in making
accurate and reliable predictions. Consequently, atomic and cova-
lent radii as well as electronegativity exhibit remarkable importance.
Moreover, the robustness of the GCN model is evaluated using a
model ensemble approach; the hcp-hollow H adsorption site exhib-
ited uncertainty/error values above 0.1 eV for 20% of the data,
which is not very significant but may be reduced by performing an
active learning framework in a future study. The proposed GCN
framework paves the way for efficiently modeling the adsorption
of different intermediates and all possible adsorption sites. Fur-
thermore, the activity–selectivity map may help one to screen the
different HEA compositions and select the compositions with a
desired performance.
SUPPLEMENTARY MATERIAL
Additional information supporting the findings of this work
is provided as a separate file. The supplementary material includes
information about the elemental intrinsic properties, optimal hyper-
parameters of the GCN model, and the activity–selectivity map.
ACKNOWLEDGMENTS
This work was supported by the Center for Enhanced Nanoflu-
idic Transport (CENT), an Energy Frontier Research Center funded
by the U.S. Department of Energy, Office of Science, Basic Energy
Sciences, under Award No. DE-SC0019112. The authors also
acknowledge the use of HAL supercomputing resources at the Uni-
versity of Illinois at Urbana-Champaign. Furthermore, this work
partially used the Lonestar6 resource from the Texas Advanced
Computing Center (TACC) at the University of Texas at Austin
under Allocation No. DMR22008.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
APL Mach. Learn. 2, 026103 (2024); doi: 10.1063/5.0198043 2, 026103-8
© Author(s) 2024

APL Machine Learning ARTICLE pubs.aip.org/aip/aml
Author Contributions
H. Oliaei: Conceptualization (equal); Data curation (equal); Formal
analysis (equal); Investigation (equal); Methodology (equal); Soft-
ware (equal); Validation (equal); Visualization (equal); Writing –
original draft (equal); Writing – review & editing (equal). N. R.
Aluru: Funding acquisition (equal); Project administration (equal);
Resources (equal); Supervision (equal).
DATA AVAILABILITY
The data that support the findings of this study are openly avail-
able for practitioners through a GitHub repository at https://github.
com/multinanogroup/GCN-for-Modeling-CO2RR-catalyst-High-
Entropy-Alloys.35
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APL Mach. Learn. 2, 026103 (2024); doi: 10.1063/5.0198043 2, 026103-9
© Author(s) 2024