We uncover the origin of unique electronic structures of single-atom alloys (SAAs) by interpretable deep learning. The approach integrates tight-binding moment theory with graph neural networks to accurately describe the local electronic structure of transition and noble metal sites upon perturbation. We emphasize the complex interplay of interatomic orbital coupling and on-site orbital resonance, which shapes the d-band characteristics of an active site, shedding light on the origin of free-atom-like d-states that are often observed in SAAs involving d10 metal hosts. This theory-infused neural network approach significantly enhances our understanding of the electronic properties of single-site catalytic materials beyond traditional theories.

1.
Q.
Gao
,
X.
Han
,
Y.
Liu
, and
H.
Zhu
, “
Electrifying energy and chemical transformations with single-atom alloy nanoparticle catalysts
,”
ACS Catal.
14
(
8
),
6045
6061
(
2024
).
2.
T.
Zhang
,
A. G.
Walsh
,
J.
Yu
, and
P.
Zhang
, “
Single-atom alloy catalysts: Structural analysis, electronic properties and catalytic activities
,”
Chem. Soc. Rev.
50
(
1
),
569
588
(
2021
).
3.
G.
Giannakakis
,
M.
Flytzani-Stephanopoulos
, and
E. C. H.
Sykes
, “
Single-atom alloys as a reductionist approach to the rational design of heterogeneous catalysts
,”
Acc. Chem. Res.
52
(
1
),
237
247
(
2018
).
4.
J.
Liu
,
F. R.
Lucci
,
M.
Yang
,
S.
Lee
,
M. D.
Marcinkowski
,
A. J.
Therrien
,
C. T.
Williams
,
E. C. H.
Sykes
, and
M.
Flytzani-Stephanopoulos
, “
Tackling CO poisoning with single-atom alloy catalysts
,”
J. Am. Chem. Soc.
138
(
20
),
6396
6399
(
2016
).
5.
X.
Zhang
,
G.
Cui
,
H.
Feng
,
L.
Chen
,
H.
Wang
,
B.
Wang
,
X.
Zhang
,
L.
Zheng
,
S.
Hong
, and
M.
Wei
, “
Platinum–copper single atom alloy catalysts with high performance towards glycerol hydrogenolysis
,”
Nat. Commun.
10
(
1
),
5812
(
2019
).
6.
F. R.
Lucci
,
M. T.
Darby
,
M. F. G.
Mattera
,
C. J.
Ivimey
,
A. J.
Therrien
,
A.
Michaelides
,
M.
Stamatakis
, and
E. C. H.
Sykes
, “
Controlling hydrogen activation, spillover, and desorption with Pd–Au single-atom alloys
,”
J. Phys. Chem. Lett.
7
(
3
),
480
485
(
2016
).
7.
R.
Réocreux
,
P. L.
Kress
,
R. T.
Hannagan
,
V.
Çınar
,
M.
Stamatakis
, and
E. C. H.
Sykes
, “
Controlling hydrocarbon (de)hydrogenation pathways with bifunctional PtCu single-atom alloys
,”
J. Phys. Chem. Lett.
11
(
20
),
8751
8757
(
2020
).
8.
X.
Cheng
,
Y.
Wang
,
Y.
Lu
,
L.
Zheng
,
S.
Sun
,
H.
Li
,
G.
Chen
, and
J.
Zhang
, “
Single-atom alloy with Pt-Co dual sites as an efficient electrocatalyst for oxygen reduction reaction
,”
Appl. Catal., B
306
,
121112
(
2022
).
9.
Q.
Gao
,
B.
Yao
,
H. S.
Pillai
,
W.
Zang
,
X.
Han
,
Y.
Liu
,
S.-W.
Yu
,
Z.
Yan
,
B.
Min
,
S.
Zhang
et al, “
Synthesis of core/shell nanocrystals with ordered intermetallic single-atom alloy layers for nitrate electroreduction to ammonia
,”
Nat. Synth.
2
(
7
),
624
634
(
2023
).
10.
M. T.
Darby
,
E. C. H.
Sykes
,
A.
Michaelides
, and
M.
Stamatakis
, “
Carbon monoxide poisoning resistance and structural stability of single atom alloys
,”
Top. Catal.
61
(
5–6
),
428
438
(
2018
).
11.
R. T.
Hannagan
,
G.
Giannakakis
,
M.
Flytzani-Stephanopoulos
, and
E. C. H.
Sykes
, “
Single-atom alloy catalysis
,”
Chem. Rev.
120
(
21
),
12044
12088
(
2020
).
12.
A.
Gross
,
Theoretical Surface Science: A Microscopic Perspective
,
Originally Published in the Series: Advanced Texts in Physics Vol. 132
(
Springer
,
2003
).
13.
H.
Thirumalai
and
J. R.
Kitchin
, “
Investigating the reactivity of single atom alloys using density functional theory
,”
Top. Catal.
61
,
462
474
(
2018
).
14.
M. T.
Greiner
,
T. E.
Jones
,
S.
Beeg
,
L.
Zwiener
,
M.
Scherzer
,
F.
Girgsdies
,
S.
Piccinin
,
M.
Armbrüster
,
A.
Knop-Gericke
, and
R.
Schlögl
, “
Free-atom-like d states in single-atom alloy catalysts
,”
Nat. Chem.
10
(
10
),
1008
1015
(
2018
).
15.
T. D.
Spivey
and
A.
Holewinski
, “
Selective interactions between free-atom-like d-states in single-atom alloy catalysts and near-frontier molecular orbitals
,”
J. Am. Chem. Soc.
143
(
31
),
11897
11902
(
2021
).
16.
M.
Ernzerhof
and
G. E.
Scuseria
, “
Assessment of the Perdew–Burke–Ernzerhof exchange-correlation functional
,”
J. Chem. Phys.
110
(
11
),
5029
5036
(
1999
).
17.
J. K.
Nørskov
,
F.
Abild-Pedersen
,
F.
Studt
, and
T.
Bligaard
, “
Density functional theory in surface chemistry and catalysis
,”
Proc. Natl. Acad. Sci. U. S. A.
108
(
3
),
937
943
(
2011
).
18.
M.
Capdevila-Cortada
,
Z.
Łodziana
, and
N.
López
, “
Performance of DFT + U approaches in the study of catalytic materials
,”
ACS Catal.
6
,
8370
8379
(
2016
).
19.
A.
Walsh
and
K. T.
Butler
, “
Prediction of electron energies in metal oxides
,”
Acc. Chem. Res.
47
(
2
),
364
372
(
2014
).
20.
J.
Yan
,
J. S.
Hummelshøj
, and
J. K.
Nørskov
, “
Formation energies of group I and II metal oxides using random phase approximation
,”
Phys. Rev. B
87
(
7
),
075207
(
2013
).
21.
T.
Xie
and
J. C.
Grossman
, “
Crystal graph convolutional neural networks for an accurate and interpretable prediction of material properties
,”
Phys. Rev. Lett.
120
(
14
),
145301
(
2018
).
22.
S.-H.
Wang
,
H. S.
Pillai
,
S.
Wang
,
L. E. K.
Achenie
, and
H.
Xin
, “
Infusing theory into deep learning for interpretable reactivity prediction
,”
Nat. Commun.
12
(
1
),
5288
(
2021
).
23.
H. W.
Kuhn
,
Classics in Game Theory
(
Princeton University Press
,
1997
).
24.
F.
Cyrot-Lackmann
, “
On the electronic structure of liquid transitional metals
,”
Adv. Phys.
16
(
63
),
393
400
(
1967
).
25.
J. C.
Slater
and
G. F.
Koster
, “
Simplified LCAO method for the periodic potential problem
,”
Phys. Rev.
94
(
6
),
1498
(
1954
).
26.
B.
Hammer
and
J. K.
Nørskov
, “
Electronic factors determining the reactivity of metal surfaces
,”
Surf. Sci.
343
(
3
),
211
220
(
1995
).
27.
J. R.
Kitchin
,
J. K.
Nørskov
,
M. A.
Barteau
, and
J. G.
Chen
, “
Role of strain and ligand effects in the modification of the electronic and chemical properties of bimetallic surfaces
,”
Phys. Rev. Lett.
93
(
15
),
156801
(
2004
).
28.
L. T.
DeCarlo
, “
On the meaning and use of kurtosis
,”
Psychol. Methods
2
(
3
),
292
(
1997
).
29.
P. H.
Westfall
, “
Kurtosis as peakedness, 1905–2014. R.I.P.
,”
Am. Stat.
68
(
3
),
191
195
(
2014
).
30.
W. A.
Harrison
,
Electronic Structure and the Properties of Solids: The Physics of the Chemical Bond
,
Dover Books on Physics
(
Dover Publications
,
1989
).
31.
F.
Calle-Vallejo
,
D.
Loffreda
,
M. T. M.
Koper
, and
P.
Sautet
, “
Introducing structural sensitivity into adsorption–energy scaling relations by means of coordination numbers
,”
Nat. Chem.
7
(
5
),
403
410
(
2015
).
32.
X.
Ma
and
H.
Xin
, “
Orbitalwise coordination number for predicting adsorption properties of metal nanocatalysts
,”
Phys. Rev. Lett.
118
(
3
),
036101
(
2017
).
33.
D. A.
Patel
,
P. L.
Kress
,
L. A.
Cramer
,
A. M.
Larson
, and
E. C. H.
Sykes
, “
Elucidating the composition of PtAg surface alloys with atomic-scale imaging and spectroscopy
,”
J. Chem. Phys.
151
(
16
),
164705
(
2019
).
34.
A.
Kumar
,
V. Q.
Bui
,
J.
Lee
,
L.
Wang
,
A. R.
Jadhav
,
X.
Liu
,
X.
Shao
,
Y.
Liu
,
J.
Yu
,
Y.
Hwang
et al, “
Moving beyond bimetallic-alloy to single-atom dimer atomic-interface for all-pH hydrogen evolution
,”
Nat. Commun.
12
(
1
),
6766
(
2021
).
35.
Y.
Zhang
,
S.
Li
,
C.
Sun
,
P.
Wang
,
Y.
Yang
,
D.
Yi
,
X.
Wang
, and
J.
Yao
, “
Understanding and modifying the scaling relations for ammonia synthesis on dilute metal alloys: From single-atom alloys to dimer alloys
,”
ACS Catal.
12
(
15
),
9201
9212
(
2022
).
36.
Y.
Huang
,
S. H.
Wang
,
M.
Kamanuru
,
L. E.
Achenie
,
J. R.
Kitchin
, and
H.
Xin
, “
Unifying theory of electronic descriptors of metal surfaces upon perturbation
,”
Phys. Rev. B
110
(
12
),
L121404
(
2024
).
You do not currently have access to this content.