A crucial aspect in the simulation of electrochemical interfaces consists in treating the distribution of electronic charge of electrode materials that are put in contact with an electrolyte solution. Recently, it has been shown how a machine-learning method that specifically targets the electronic charge density, also known as SALTED, can be used to predict the long-range response of metal electrodes in model electrochemical cells. In this work, we provide a full integration of SALTED with MetalWalls, a program for performing classical simulations of electrochemical systems. We do so by deriving a spherical harmonics extension of the Ewald summation method, which allows us to efficiently compute the electric field originated by the predicted electrode charge distribution. We show how to use this method to drive the molecular dynamics of an aqueous electrolyte solution under the quantum electric field of a gold electrode, which is matched to the accuracy of density-functional theory. Notably, we find that the resulting atomic forces present a small error of the order of 1 meV/Å, demonstrating the great effectiveness of adopting an electron-density path in predicting the electrostatics of the system. Upon running the data-driven dynamics over about 3 ns, we observe qualitative differences in the interfacial distribution of the electrolyte with respect to the results of a classical simulation. By greatly accelerating quantum-mechanics/molecular-mechanics approaches applied to electrochemical systems, our method opens the door to nanosecond timescales in the accurate atomistic description of the electrical double layer.

1.
J. M.
Dawlaty
,
S.
Perkin
,
M.
Salanne
, and
A. P.
Willard
,
J. Chem. Phys.
159
,
150401
(
2023
).
2.
K.
Schwarz
and
R.
Sundararaman
,
Surf. Sci. Rep.
75
,
100492
(
2020
).
3.
A.
Groß
,
Curr. Opin. Electrochem.
40
,
101345
(
2023
).
4.
K.
Goloviznina
,
J. N.
Canongia Lopes
,
M.
Costa Gomes
, and
A. A. H.
Pádua
,
J. Chem. Theory Comput.
15
,
5858
(
2019
).
5.
C.-Y.
Li
,
J.-B.
Le
,
Y.-H.
Wang
,
S.
Chen
,
Z.-L.
Yang
,
J.-F.
Li
,
J.
Cheng
, and
Z.-Q.
Tian
,
Nat. Mater.
18
,
697
(
2019
).
6.
R.
Khatib
,
A.
Kumar
,
S.
Sanvito
,
M.
Sulpizi
, and
C. S.
Cucinotta
,
Electrochim. Acta
391
,
138875
(
2021
).
7.
A.
Chen
,
J.-B.
Le
,
Y.
Kuang
, and
J.
Cheng
,
J. Chem. Phys.
157
,
094702
(
2022
).
8.
G.
Jeanmairet
,
B.
Rotenberg
, and
M.
Salanne
,
Chem. Rev.
122
,
10860
(
2022
).
9.
L.
Scalfi
,
T.
Dufils
,
K. G.
Reeves
,
B.
Rotenberg
, and
M.
Salanne
,
J. Chem. Phys.
153
,
174704
(
2020
).
10.
K.
Goloviznina
,
J.
Fleischhaker
,
T.
Binninger
,
B.
Rotenberg
,
H.
Ers
,
V.
Ivanistsev
,
R.
Meissner
,
A.
Serva
, and
M.
Salanne
, arXiv: 2404.07848 (
2024
).
11.
J. D.
Elliott
,
M.
Chiricotto
,
A.
Troisi
, and
P.
Carbone
,
Carbon
207
,
292
(
2023
).
12.
S.-J.
Shin
,
J. W.
Gittins
,
M. J.
Golomb
,
A. C.
Forse
, and
A.
Walsh
,
J. Am. Chem. Soc.
145
,
14529
(
2023
).
13.
Z.
Wei
,
J. D.
Elliott
,
A. A.
Papaderakis
,
R. A.
Dryfe
, and
P.
Carbone
,
J. Am. Chem. Soc.
146
,
760
(
2024
).
14.
S.-J.
Shin
,
H.
Choi
,
S.
Ringe
,
D. H.
Won
,
H.-S.
Oh
,
D. H.
Kim
,
T.
Lee
,
D.-H.
Nam
,
H.
Kim
, and
C. H.
Choi
,
Nat. Commun.
13
,
5482
(
2022
).
15.
S.-J.
Shin
,
D. H.
Kim
,
G.
Bae
,
S.
Ringe
,
H.
Choi
,
H.-K.
Lim
,
C. H.
Choi
, and
H.
Kim
,
Nat. Commun.
13
,
174
(
2022
).
16.
N.
Abidi
and
S. N.
Steinmann
,
ACS Appl. Mater. Interfaces
15
,
25009
(
2023
).
17.
K.
Takahashi
,
H.
Nakano
, and
H.
Sato
,
J. Chem. Phys.
157
,
234107
(
2022
).
18.
A.
Grisafi
,
A.
Bussy
,
M.
Salanne
, and
R.
Vuilleumier
,
Phys. Rev. Mater.
7
,
125403
(
2023
).
19.
A.
Coretti
,
C.
Bacon
,
R.
Berthin
,
A.
Serva
,
L.
Scalfi
,
I.
Chubak
,
K.
Goloviznina
,
M.
Haefele
,
A.
Marin-Laflèche
,
B.
Rotenberg
,
S.
Bonella
, and
M.
Salanne
,
J. Chem. Phys.
157
,
184801
(
2022
).
20.
T.
Dufils
,
G.
Jeanmairet
,
B.
Rotenberg
,
M.
Sprik
, and
M.
Salanne
,
Phys. Rev. Lett.
123
,
195501
(
2019
).
21.
A.
Grisafi
,
A. M.
Lewis
,
M.
Rossi
, and
M.
Ceriotti
,
J. Chem. Theory Comput.
19
,
4451
(
2023
).
22.
A. M.
Lewis
,
A.
Grisafi
,
M.
Ceriotti
, and
M.
Rossi
,
J. Chem. Theory Comput.
17
,
7203
(
2021
).
23.
T. D.
Kühne
,
M.
Iannuzzi
,
M.
Del Ben
,
V. V.
Rybkin
,
P.
Seewald
,
F.
Stein
,
T.
Laino
,
R. Z.
Khaliullin
,
O.
Schütt
,
F.
Schiffmann
,
D.
Golze
,
J.
Wilhelm
,
S.
Chulkov
,
M. H.
Bani-Hashemian
,
V.
Weber
,
U.
Borštnik
,
M.
Taillefumier
,
A. S.
Jakobovits
,
A.
Lazzaro
,
H.
Pabst
,
T.
Müller
,
R.
Schade
,
M.
Guidon
,
S.
Andermatt
,
N.
Holmberg
,
G. K.
Schenter
,
A.
Hehn
,
A.
Bussy
,
F.
Belleflamme
,
G.
Tabacchi
,
A.
Glöß
,
M.
Lass
,
I.
Bethune
,
C. J.
Mundy
,
C.
Plessl
,
M.
Watkins
,
J.
VandeVondele
,
M.
Krack
, and
J.
Hutter
,
J. Chem. Phys.
152
,
194103
(
2020
).
24.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
25.
J.
VandeVondele
and
J.
Hutter
,
J. Chem. Phys.
127
,
114105
(
2007
).
26.
S.
Goedecker
,
M.
Teter
, and
J.
Hutter
,
Phys. Rev. B
54
,
1703
(
1996
).
27.
M.
Guidon
,
J.
Hutter
, and
J.
VandeVondele
,
J. Chem. Theory Comput.
5
,
3010
(
2009
).
28.
A.
Bussy
,
O.
Schütt
, and
J.
Hutter
,
J. Chem. Phys.
158
,
164109
(
2023
).
29.
K. R.
Briling
,
A.
Fabrizio
, and
C.
Corminboeuf
,
J. Chem. Phys.
155
,
024107
(
2021
).
30.
A.
Grisafi
and
M.
Ceriotti
,
J. Chem. Phys.
151
,
204105
(
2019
).
31.
A.
Grisafi
,
J.
Nigam
, and
M.
Ceriotti
,
Chem. Sci.
12
,
2078
(
2021
).
32.
K. K.
Huguenin-Dumittan
,
P.
Loche
,
N.
Haoran
, and
M.
Ceriotti
,
J. Phys. Chem. Lett.
14
,
9612
(
2023
).
33.
G.
Fraux
,
P.
Loche
,
S.
Kliavinek
,
K. K.
Huguenin-Dumittan
,
D.
Tisi
, and
A.
Goscinski
(2014). “rascaline,” GitHub. https://github.com/Luthaf/rascaline
34.
A.
Marin-Laflèche
,
M.
Haefele
,
L.
Scalfi
,
A.
Coretti
,
T.
Dufils
,
G.
Jeanmairet
,
S. K.
Reed
,
A.
Serva
,
R.
Berthin
,
C.
Bacon
,
S.
Bonella
,
B.
Rotenberg
,
P. A.
Madden
, and
M.
Salanne
,
J. Open Source Software
5
,
2373
(
2020
).
35.
D.
Marx
and
J.
Hutter
,
Ab Initio Molecular Dynamics: Basic Theory and Advanced Methods
(
Cambridge University Press
,
2009
).
36.
J. L. F.
Abascal
and
C.
Vega
,
J. Chem. Phys.
123
,
234505
(
2005
).
37.
T.
Yagasaki
,
M.
Matsumoto
, and
H.
Tanaka
,
J. Chem. Theory Comput.
16
,
2460
(
2020
).
38.
G. L.
Stoychev
,
A. A.
Auer
, and
F.
Neese
,
J. Chem. Theory Comput.
13
,
554
(
2017
).
39.
S.
Nosé
,
J. Chem. Phys.
81
,
511
(
1984
).
40.
A.
Serva
,
L.
Scalfi
,
B.
Rotenberg
, and
M.
Salanne
,
J. Chem. Phys.
155
,
044703
(
2021
).
41.
L.
Scalfi
,
D. T.
Limmer
,
A.
Coretti
,
S.
Bonella
,
P. A.
Madden
,
M.
Salanne
, and
B.
Rotenberg
,
Phys. Chem. Chem. Phys.
22
,
10480
(
2020
).
42.
W.
Schmickler
,
Chem. Rev.
96
,
3177
(
1996
).
43.
T. W.
Ko
,
J. A.
Finkler
,
S.
Goedecker
, and
J.
Behler
,
Nat. Commun.
12
,
398
(
2021
).
44.
C. G.
Staacke
,
S.
Wengert
,
C.
Kunkel
,
G.
Csányi
,
K.
Reuter
, and
J. T.
Margraf
,
Mach. Learn.: Sci. Technol.
3
,
015032
(
2022
).
45.
Y.
Shao
,
L.
Andersson
,
L.
Knijff
, and
C.
Zhang
,
Electron. Struct.
4
,
014012
(
2022
).
46.
T.
Dufils
,
L.
Knijff
,
Y.
Shao
, and
C.
Zhang
,
J. Chem. Theory Comput.
19
,
5199
(
2023
).
47.
S.
Batzner
,
A.
Musaelian
,
L.
Sun
,
M.
Geiger
,
J. P.
Mailoa
,
M.
Kornbluth
,
N.
Molinari
,
T. E.
Smidt
, and
B.
Kozinsky
,
Nat. Commun.
13
,
2453
(
2022
).
48.
S.
Klawohn
,
J. P.
Darby
,
J. R.
Kermode
,
G.
Csányi
,
M. A.
Caro
, and
A. P.
Bartók
,
J. Chem. Phys.
159
,
174108
(
2023
).
49.
C.
Choi
,
D. S.
Ashby
,
D. M.
Butts
,
R. H.
DeBlock
,
Q.
Wei
,
J.
Lau
, and
B.
Dunn
,
Nat. Rev. Mater.
5
,
5
(
2019
).
50.
S.
Ringe
,
E. L.
Clark
,
J.
Resasco
,
A.
Walton
,
B.
Seger
,
A. T.
Bell
, and
K.
Chan
,
Energy Environ. Sci.
12
,
3001
(
2019
).
51.
See https://github.com/cp2k/cp2k for the official trunk version of the CP2K program suitable to generate the training data of electronic charge densities.
52.
See https://github.com/andreagrisafi/SALTED/releases/tag/v3.0.0 for the latest SALTED release used to produce the results of this work.
53.
See https://gitlab.com/andreagrisafi/metalwalls/-/tree/salted_interface?ref_type=heads for a modified version of the MetalWalls program which includes the interface with SALTED.
54.
See https://zenodo.org/doi/10.5281/zenodo.11175494 for information about the training configurations, the CP2K inputs used to perform the reference quantum-mechanical calculations, the SALTED model and training data, the SALTED/MetalWalls simulation setup and trajectories.
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