Understanding the response of the surface of metallic solids to external electric field sources is crucial to characterize electrode–electrolyte interfaces. Continuum electrostatics offer a simple description of the induced charge density at the electrode surface. However, such a simple description does not take into account features related to the atomic structure of the solid and to the molecular nature of the solvent and of the dissolved ions. In order to illustrate such effects and assess the ability of continuum electrostatics to describe the induced charge distribution, we investigate the behavior of a gold electrode interacting with sodium or chloride ions fixed at various positions, in a vacuum or in water, using all-atom constant-potential classical molecular dynamics simulations. Our analysis highlights important similarities between the two approaches, especially under vacuum conditions and when the ion is sufficiently far from the surface, as well as some limitations of the continuum description, namely, neglecting the charges induced by the adsorbed solvent molecules and the screening effect of the solvent when the ion is close to the surface. While the detailed features of the charge distribution are system-specific, we expect some of our generic conclusions on the induced charge density to hold for other ions, solvents, and electrode surfaces. Beyond this particular case, the present study also illustrates the relevance of such molecular simulations to serve as a reference for the design of improved implicit solvent models of electrode–electrolyte interfaces.

1.
J. D.
Jackson
,
Classical Electrodynamics
, 2nd ed. (
Wiley
,
New York
,
1975
).
2.
V.
Ballenegger
and
J.-P.
Hansen
, “
Local dielectric permittivity near an interface
,”
Europhys. Lett.
63
(
3
),
381
(
2003
).
3.
V.
Ballenegger
and
J.-P.
Hansen
, “
Dielectric permittivity profiles of confined polar fluids
,”
J. Chem. Phys.
122
(
11
),
114711
(
2005
).
4.
D. J.
Bonthuis
,
S.
Gekle
, and
R. R.
Netz
, “
Dielectric profile of interfacial water and its effect on double-layer capacitance
,”
Phys. Rev. Lett.
107
(
16
),
166102
(
2011
).
5.
A.
Schlaich
,
E. W.
Knapp
, and
R. R.
Netz
, “
Water dielectric effects in planar confinement
,”
Phys. Rev. Lett.
117
(
4
),
048001
(
2016
).
6.
P.
Loche
,
C.
Ayaz
,
A.
Schlaich
,
D. J.
Bonthuis
, and
R. R.
Netz
, “
Breakdown of linear dielectric theory for the interaction between hydrated ions and graphene
,”
J. Phys. Chem. Lett.
9
,
6463
6468
(
2018
).
7.
P.
Loche
,
C.
Ayaz
,
A.
Wolde-Kidan
,
A.
Schlaich
, and
R. R.
Netz
, “
Universal and nonuniversal aspects of electrostatics in aqueous nanoconfinement
,”
J. Phys. Chem. B
124
(
21
),
4365
4371
(
2020
).
8.
A. P.
dos Santos
,
Y.
Uematsu
,
A.
Rathert
,
P.
Loche
, and
R. R.
Netz
, “
Consistent description of ion-specificity in bulk and at interfaces by solvent implicit simulations and mean-field theory
,”
J. Chem. Phys.
153
(
3
),
034103
(
2020
).
9.
M. H.
Motevaselian
and
N. R.
Aluru
, “
Universal reduction in dielectric response of confined fluids
,”
ACS Nano
14
(
10
),
12761
12770
(
2020
).
10.
F.
Jiménez-Ángeles
,
K. J.
Harmon
,
T. D.
Nguyen
,
P.
Fenter
, and
M.
Olvera de la Cruz
, “
Nonreciprocal interactions induced by water in confinement
,”
Phys. Rev. Res.
2
(
4
),
043244
(
2020
).
11.
J.-F.
Olivieri
,
J. T.
Hynes
, and
D.
Laage
, “
Confined water’s dielectric constant reduction is due to the surrounding low dielectric media and not to interfacial molecular ordering
,”
J. Phys. Chem. Lett.
12
(
17
),
4319
4326
(
2021
).
12.
N. D.
Lang
and
W.
Kohn
, “
Theory of metal surfaces: Induced surface charge and image potential
,”
Phys. Rev. B
7
,
3541
3550
(
1973
).
13.
J.
Jung
,
J. E.
Alvarellos
,
E.
Chacón
, and
P.
García-González
, “
Self-consistent density functional calculation of the image potential at a metal surface
,”
J. Phys.: Condens. Matter
19
(
26
),
266008
(
2007
).
14.
E. K.
Yu
,
D. A.
Stewart
, and
S.
Tiwari
, “
Ab initio study of polarizability and induced charge densities in multilayer graphene films
,”
Phys. Rev. B
77
,
195406
(
2008
).
15.
S.
Sakong
and
A.
Groß
, “
The electric double layer at metal-water interfaces revisited based on a charge polarization scheme
,”
J. Chem. Phys.
149
(
8
),
084705
(
2018
).
16.
K.
Schwarz
and
R.
Sundararaman
, “
The electrochemical interface in first-principles calculations
,”
Surf. Sci. Rep.
75
(
2
),
100492
(
2020
).
17.
S.
Sakong
and
A.
Groß
, “
Water structures on a Pt(111) electrode from ab initio molecular dynamic simulations for a variety of electrochemical conditions
,”
Phys. Chem. Chem. Phys.
22
(
19
),
10431
10437
(
2020
).
18.
J.-B.
Le
,
A.
Chen
,
L.
Li
,
J.-F.
Xiong
,
J.
Lan
,
Y.-P.
Liu
,
M.
Iannuzzi
, and
J.
Cheng
, “
Modeling electrified Pt(111)-had/water interfaces from ab initio molecular dynamics
,”
JACS Au
1
(
5
),
569
577
(
2021
).
19.
J.-B.
Le
and
J.
Cheng
, “
Modeling electrified metal/water interfaces from ab initio molecular dynamics: Structure and Helmholtz capacitance
,”
Curr. Opin. Electrochem.
27
,
100693
(
2021
).
20.
L.
Scalfi
,
M.
Salanne
, and
B.
Rotenberg
, “
Molecular simulation of electrode-solution interfaces
,”
Annu. Rev. Phys. Chem.
72
(
1
),
189
(
2021
).
21.
J. I.
Siepmann
and
M.
Sprik
, “
Influence of surface topology and electrostatic potential on water/electrode systems
,”
J. Chem. Phys.
102
(
1
),
511
524
(
1995
).
22.
S. K.
Reed
,
O. J.
Lanning
, and
P. A.
Madden
, “
Electrochemical interface between an ionic liquid and a model metallic electrode
,”
J. Chem. Phys.
126
(
8
),
084704
(
2007
).
23.
A. P.
Willard
,
S. K.
Reed
,
P. A.
Madden
, and
D.
Chandler
, “
Water at an electrochemical interface—A simulation study
,”
Faraday Discuss.
141
,
423
441
(
2009
).
24.
L.
Pastewka
,
T. T.
Järvi
,
L.
Mayrhofer
, and
M.
Moseler
, “
Charge-transfer model for carbonaceous electrodes in polar environments
,”
Phys. Rev. B
83
(
16
),
165418
(
2011
).
25.
N.
Onofrio
and
A.
Strachan
, “
Voltage equilibration for reactive atomistic simulations of electrochemical processes
,”
J. Chem. Phys.
143
(
5
),
054109
(
2015
).
26.
H.
Nakano
and
H.
Sato
, “
A chemical potential equalization approach to constant potential polarizable electrodes for electrochemical-cell simulations
,”
J. Chem. Phys.
151
(
16
),
164123
(
2019
).
27.
F.
Iori
and
S.
Corni
, “
Including image charge effects in the molecular dynamics simulations of molecules on metal surfaces
,”
J. Comput. Chem.
29
(
10
),
1656
1666
(
2008
).
28.
I. L.
Geada
,
H.
Ramezani-Dakhel
,
T.
Jamil
,
M.
Sulpizi
, and
H.
Heinz
, “
Insight into induced charges at metal surfaces and biointerfaces using a polarizable Lennard–Jones potential
,”
Nat. Commun.
9
(
1
),
716
(
2018
).
29.
K.
Breitsprecher
,
K.
Szuttor
, and
C.
Holm
, “
Electrode models for ionic liquid-based capacitors
,”
J. Phys. Chem. C
119
,
22445
22451
(
2015
).
30.
D.
Boda
,
D.
Gillespie
,
W.
Nonner
,
D.
Henderson
, and
B.
Eisenberg
, “
Computing induced charges in inhomogeneous dielectric media: Application in a Monte Carlo simulation of complex ionic systems
,”
Phys. Rev. E
69
(
4
),
046702
(
2004
).
31.
S.
Tyagi
,
M.
Süzen
,
M.
Sega
,
M.
Barbosa
,
S. S.
Kantorovich
, and
C.
Holm
, “
An iterative, fast, linear-scaling method for computing induced charges on arbitrary dielectric boundaries
,”
J. Chem. Phys.
132
(
15
),
154112
(
2010
).
32.
M.
Girotto
,
A. P.
dos Santos
, and
Y.
Levin
, “
Simulations of ionic liquids confined by metal electrodes using periodic Green functions
,”
J. Chem. Phys.
147
(
7
),
074109
(
2017
).
33.
C.
Merlet
,
C.
Péan
,
B.
Rotenberg
,
P. A.
Madden
,
P.
Simon
, and
M.
Salanne
, “
Simulating supercapacitors: Can we model electrodes as constant charge surfaces?
,”
J. Phys. Chem. Lett.
4
,
264
268
(
2013
).
34.
B.
Uralcan
,
I. A.
Aksay
,
P. G.
Debenedetti
, and
D. T.
Limmer
, “
Concentration fluctuations and capacitive response in dense ionic solutions
,”
J. Phys. Chem. Lett.
7
(
13
),
2333
2338
(
2016
).
35.
Z.
Li
,
G.
Jeanmairet
,
T.
Méndez-Morales
,
B.
Rotenberg
, and
M.
Salanne
, “
Capacitive performance of water-in-salt electrolytes in supercapacitors: A simulation study
,”
J. Phys. Chem. C
122
(
42
),
23917
23924
(
2018
).
36.
S.
Ntim
and
M.
Sulpizi
, “
Role of image charges in ionic liquid confined between metallic interfaces
,”
Phys. Chem. Chem. Phys.
22
(
19
),
10786
10791
(
2020
).
37.
D.
Bagchi
,
T. D.
Nguyen
, and
M.
Olvera de la Cruz
, “
Surface polarization effects in confined polyelectrolyte solutions
,”
Proc. Natl. Acad. Sci. U. S. A.
117
(
33
),
19677
19684
(
2020
).
38.
C. Y.
Son
and
Z.-G.
Wang
, “
Image-charge effects on ion adsorption near aqueous interfaces
,”
Proc. Natl. Acad. Sci. U. S. A.
118
(
19
),
e2020615118
(
2021
).
39.
D. T.
Limmer
,
A. P.
Willard
,
P.
Madden
, and
D.
Chandler
, “
Hydration of metal surfaces can be dynamically heterogeneous and hydrophobic
,”
Proc. Natl. Acad. Sci. U. S. A.
110
(
11
),
4200
4205
(
2013
).
40.
A.
Serva
,
M.
Salanne
,
M.
Havenith
, and
S.
Pezzotti
, “
Size dependence of hydrophobic hydration at electrified gold/water interfaces
,”
Proc. Natl. Acad. Sci. U. S. A.
118
(
15
),
e2023867118
(
2021
).
41.
N.
Bonnet
,
T.
Morishita
,
O.
Sugino
, and
M.
Otani
, “
First-principles molecular dynamics at a constant electrode potential
,”
Phys. Rev. Lett.
109
,
266101
(
2012
).
42.
K.
Kiyohara
and
K.
Asaka
, “
Monte Carlo simulation of porous electrodes in the constant voltage ensemble
,”
J. Phys. Chem.
111
,
15903
15909
(
2007
).
43.
D. T.
Limmer
,
C.
Merlet
,
M.
Salanne
,
D.
Chandler
,
P. A.
Madden
,
R.
van Roij
, and
B.
Rotenberg
, “
Charge fluctuations in nanoscale capacitors
,”
Phys. Rev. Lett.
111
,
106102
(
2013
).
44.
C.
Merlet
,
D. T.
Limmer
,
M.
Salanne
,
R.
van Roij
,
P. A.
Madden
,
D.
Chandler
, and
B.
Rotenberg
, “
The electric double layer has a life of its own
,”
J. Phys. Chem. C
118
,
18291
18298
(
2014
).
45.
J. B.
Haskins
and
J. W.
Lawson
, “
Evaluation of molecular dynamics simulation methods for ionic liquid electric double layers
,”
J. Chem. Phys.
144
(
18
),
184707
(
2016
).
46.
L.
Scalfi
,
D. T.
Limmer
,
A.
Coretti
,
S.
Bonella
,
P. A.
Madden
,
M.
Salanne
, and
B.
Rotenberg
, “
Charge fluctuations from molecular simulations in the constant-potential ensemble
,”
Phys. Chem. Chem. Phys.
22
,
10480
10489
(
2020
).
47.
P.
Cats
,
R. S.
Sitlapersad
,
W. K.
den Otter
,
A. R.
Thornton
, and
R.
van Roij
, “
Capacitance and structure of electric double layers: Comparing Brownian dynamics and classical density functional theory
,”
J. Solution Chem.
(published online) (
2021
).
48.
L.
Scalfi
,
T.
Dufils
,
K. G.
Reeves
,
B.
Rotenberg
, and
M.
Salanne
, “
A semiclassical Thomas–Fermi model to tune the metallicity of electrodes in molecular simulations
,”
J. Chem. Phys.
153
(
17
),
174704
(
2020
).
49.
T. R.
Gingrich
and
M.
Wilson
, “
On the Ewald summation of Gaussian charges for the simulation of metallic surfaces
,”
Chem. Phys. Lett.
500
(
1–3
),
178
183
(
2010
).
50.
H. J. C.
Berendsen
,
J. R.
Grigera
, and
T. P.
Straatsma
, “
The missing term in effective pair potentials
,”
J. Phys. Chem.
91
,
6269
6271
(
1987
).
51.
L. X.
Dang
, “
Mechanism and thermodynamics of ion selectivity in aqueous solutions of 18-crown-6 ether: A molecular dynamics study
,”
J. Am. Chem. Soc.
117
,
6954
6960
(
1995
).
52.
A.
Berg
,
C.
Peter
, and
K.
Johnston
, “
Evaluation and optimization of interface force fields for water on gold surfaces
,”
J. Chem. Theory Comput.
13
(
11
),
5610
5623
(
2017
).
53.
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
, “
MetalWalls: A classical molecular dynamics software dedicated to the simulation of electrochemical systems
,”
J. Open Source Software
5
(
53
),
2373
(
2020
).
54.
G. J.
Martyna
,
M. L.
Klein
, and
M.
Tuckerman
, “
Nosé–Hoover chains: The canonical ensemble via continuous dynamics
,”
J. Chem. Phys.
97
,
2635
2643
(
1992
).
55.
A.
Serva
,
L.
Scalfi
,
B.
Rotenberg
, and
M.
Salanne
, “
Effect of the metallicity on the capacitance of gold–aqueous sodium chloride interfaces
,”
J. Chem. Phys.
155
(
4
),
044703
(
2021
).
56.
M.
Rami Reddy
and
M.
Berkowitz
, “
The dielectric constant of SPC/E water
,”
Chem. Phys. Lett.
155
(
2
),
173
176
(
1989
).
57.
D. J.
Bonthuis
,
S.
Gekle
, and
R. R.
Netz
, “
Profile of the static permittivity tensor of water at interfaces: Consequences for capacitance, hydration interaction and ion adsorption
,”
Langmuir
28
(
20
),
7679
7694
(
2012
).
58.
F.
Deißenbeck
,
C.
Freysoldt
,
M.
Todorova
,
J.
Neugebauer
, and
S.
Wippermann
, “
Dielectric properties of nanoconfined water: A canonical thermopotentiostat approach
,”
Phys. Rev. Lett.
126
(
13
),
136803
(
2021
).
59.
L.
Fumagalli
,
A.
Esfandiar
,
R.
Fabregas
,
S.
Hu
,
P.
Ares
,
A.
Janardanan
,
Q.
Yang
,
B.
Radha
,
T.
Taniguchi
,
K.
Watanabe
,
G.
Gomila
,
K. S.
Novoselov
, and
A. K.
Geim
, “
Anomalously low dielectric constant of confined water
,”
Science
360
(
6395
),
1339
1342
(
2018
).
60.
A.
Grossfield
, “
Dependence of ion hydration on the sign of the ion’s charge
,”
J. Chem. Phys.
122
(
2
),
024506
(
2005
).
61.
A.
Mukhopadhyay
,
A. T.
Fenley
,
I. S.
Tolokh
, and
A. V.
Onufriev
, “
Charge hydration asymmetry: The basic principle and how to use it to test and improve water models
,”
J. Phys. Chem. B
116
(
32
),
9776
9783
(
2012
).
62.
L.
Ding
,
M.
Levesque
,
D.
Borgis
, and
L.
Belloni
, “
Efficient molecular density functional theory using generalized spherical harmonics expansions
,”
J. Chem. Phys.
147
(
9
),
094107
(
2017
).
63.
G.
Jeanmairet
,
B.
Rotenberg
,
M.
Levesque
,
D.
Borgis
, and
M.
Salanne
, “
A molecular density functional theory approach to electron transfer reactions
,”
Chem. Sci.
10
,
2130
2143
(
2019
).
64.
G.
Jeanmairet
,
B.
Rotenberg
,
D.
Borgis
, and
M.
Salanne
, “
Study of a water-graphene capacitor with molecular density functional theory
,”
J. Chem. Phys.
151
(
12
),
124111
(
2019
).
65.
H.
Berthoumieux
, “
Gaussian field model for polar fluids as a function of density and polarization: Toward a model for water
,”
J. Chem. Phys.
148
(
10
),
104504
(
2018
).
66.
H.
Berthoumieux
and
F.
Paillusson
, “
Dielectric response in the vicinity of an ion: A nonlocal and nonlinear model of the dielectric properties of water
,”
J. Chem. Phys.
150
(
9
),
094507
(
2019
).
67.
M.
Vatin
,
A.
Porro
,
N.
Sator
,
J.-F.
Dufrêche
, and
H.
Berthoumieux
, “
Electrostatic interactions in water: A nonlocal electrostatic approach
,”
Mol. Phys.
119
(
5
),
e1825849
(
2021
).
68.
G.
Pireddu
,
L.
Scalfi
, and
B.
Rotenberg
(
2021
). “
A molecular perspective on induced charges on a metallic surface
,” Zenodo. .
You do not currently have access to this content.