Electrochemistry is central to many applications, ranging from biology to energy science. Studies now involve a wide range of techniques, both experimental and theoretical. Modeling and simulations methods, such as density functional theory or molecular dynamics, provide key information on the structural and dynamic properties of the systems. Of particular importance are polarization effects of the electrode/electrolyte interface, which are difficult to simulate accurately. Here, we show how these electrostatic interactions are taken into account in the framework of the Ewald summation method. We discuss, in particular, the formal setup for calculations that enforce periodic boundary conditions in two directions, a geometry that more closely reflects the characteristics of typical electrolyte/electrode systems and presents some differences with respect to the more common case of periodic boundary conditions in three dimensions. These formal developments are implemented and tested in MetalWalls, a molecular dynamics software that captures the polarization of the electrolyte and allows the simulation of electrodes maintained at a constant potential. We also discuss the technical aspects involved in the calculation of two sets of coupled degrees of freedom, namely the induced dipoles and the electrode charges. We validate the implementation, first on simple systems, then on the well-known interface between graphite electrodes and a room-temperature ionic liquid. We finally illustrate the capabilities of MetalWalls by studying the adsorption of a complex functionalized electrolyte on a graphite electrode.
REFERENCES
1.
N.
Yao
, X.
Chen
, Z.-H.
Fu
, and Q.
Zhang
, “Applying classical, ab initio, and machine-learning molecular dynamics simulations to the liquid electrolyte for rechargeable batteries
,” Chem. Rev.
122
, 10970
–11021
(2022
).2.
R. E.
Warburton
, A. V.
Soudackov
, and S.
Hammes-Schiffer
, “Theoretical modeling of electrochemical proton-coupled electron transfer
,” Chem. Rev.
122
, 10599
–10650
(2022
).3.
A.
Groß
and S.
Sakong
, “Ab initio simulations of water/metal interfaces
,” Chem. Rev.
122
, 10746
–10776
(2022
).4.
X.
Zhao
, Z. H.
Levell
, S.
Yu
, and Y.
Liu
, “Atomistic understanding of two-dimensional electrocatalysts from first principles
,” Chem. Rev.
122
, 10675
–10709
(2022
).5.
F.
Dattila
, R. R.
Seemakurthi
, Y.
Zhou
, and N.
López
, “Modeling operando electrochemical CO2 reduction
,” Chem. Rev.
122
, 11085
–11130
(2022
).6.
G.
Jeanmairet
, B.
Rotenberg
, and M.
Salanne
, “Microscopic simulations of electrochemical double-layer capacitors
,” Chem. Rev.
122
, 10860
–10898
(2022
).7.
A.
Van der Ven
, Z.
Deng
, S.
Banerjee
, and S. P.
Ong
, “Rechargeable alkali-ion battery materials: Theory and computation
,” Chem. Rev.
120
, 6977
–7019
(2020
).8.
D.
Bedrov
, J.-P.
Piquemal
, O.
Borodin
, A. D.
MacKerell
, Jr., B.
Roux
, and C.
Schröder
, “Molecular dynamics simulations of ionic liquids and electrolytes using polarizable force fields
,” Chem. Rev.
119
, 7940
–7995
(2019
).9.
L.
Scalfi
, M.
Salanne
, and B.
Rotenberg
, “Molecular simulation of electrode-solution interfaces
,” Annu. Rev. Phys. Chem.
72
, 189
–212
(2021
).10.
A. A.
Kornyshev
, “Double-layer in ionic liquids: Paradigm change?
,” J. Phys. Chem. B
111
, 5545
–5557
(2007
).11.
C.-Y.
Li
, J.-B.
Le
, Y.-H.
Wang
, S.
Chen
, Z.-L.
Yang
, J.-F.
Li
, J.
Cheng
, and Z.-Q.
Tian
, “In situ probing electrified interfacial water structures at atomically flat surfaces
,” Nat. Mater.
18
, 697
–701
(2019
).12.
J. I.
Siepmann
and M.
Sprik
, “Influence of surface topology and electrostatic potential on water/electrode systems
,” J. Chem. Phys.
102
, 511
–524
(1995
).13.
I.-C.
Yeh
and M. L.
Berkowitz
, “Ewald summation for systems with slab geometry
,” J. Chem. Phys.
111
, 3155
–3162
(1999
).14.
J. B.
Haskins
and J. W.
Lawson
, “Evaluation of molecular dynamics simulation methods for ionic liquid electric double layers
,” J. Chem. Phys.
144
, 184707
(2016
).15.
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
, 084704
(2007
).16.
T. R.
Gingrich
and M.
Wilson
, “On the Ewald summation of Gaussian charges for the simulation of metallic surfaces
,” Chem. Phys. Lett.
500
, 178
–183
(2010
).17.
Z.
Wang
, Y.
Yang
, D. L.
Olmsted
, M.
Asta
, and B. B.
Laird
, “Evaluation of the constant potential method in simulating electric double-layer capacitors
,” J. Chem. Phys.
141
, 184102
(2014
).18.
S.
Plimpton
, “Fast parallel algorithms for short-range molecular dynamics
,” J. Comput. Phys.
117
, 1
–19
(1995
).19.
L. J. V.
Ahrens-Iwers
and R. H.
Meißner
, “Constant potential simulations on a mesh
,” J. Chem. Phys.
155
, 104104
(2021
).20.
S. R.
Tee
and D. J.
Searles
, “Fully periodic, computationally efficient constant potential molecular dynamics simulations of ionic liquid supercapacitors
,” J. Chem. Phys.
156
, 184101
(2022
).21.
C.
Schröder
and O.
Steinhauser
, “Simulating polarizable molecular ionic liquids with Drude oscillators
,” J. Chem. Phys.
133
, 154511
(2010
).22.
M.
Salanne
, “Simulations of room temperature ionic liquids: From polarizable to coarse-grained force fields
,” Phys. Chem. Chem. Phys.
17
, 14270
–14279
(2015
).23.
K.
Goloviznina
, J. N. C.
Lopes
, M. C.
Gomes
, and A. A. H.
Pádua
, “Transferable, polarizable force field for ionic liquids
,” J. Chem. Theory Comput.
15
, 5858
–5871
(2019
).24.
A.
Aguado
and P. A.
Madden
, “Ewald summation of electrostatic multipole interactions up to the quadrupolar level
,” J. Chem. Phys.
119
, 7471
–7483
(2003
).25.
N.
Ohtori
, M.
Salanne
, and P. A.
Madden
, “Calculations of the thermal conductivities of ionic materials by simulation with polarizable interaction potentials
,” J. Chem. Phys.
130
, 104507
(2009
).26.
M.
Pounds
, “Electrochemical charge transfer at a metallic electrode: A simulation study
,” Ph.D. thesis, University of Edinburgh
, 2009
.27.
A.
Coretti
, S.
Bonella
, and G.
Ciccotti
, “Communication: Constrained molecular dynamics for polarizable models
,” J. Chem. Phys.
149
, 191102
(2018
).28.
A.
Coretti
, L.
Scalfi
, C.
Bacon
, B.
Rotenberg
, R.
Vuilleumier
, G.
Ciccotti
, M.
Salanne
, and S.
Bonella
, “Mass-zero constrained molecular dynamics for electrode charges in simulations of electrochemical systems
,” J. Chem. Phys.
152
, 194701
(2020
).29.
M.
Pounds
, S.
Tazi
, M.
Salanne
, and P. A.
Madden
, “Ion adsorption at a metallic electrode: An ab initio based simulation study
,” J. Phys.: Condens. Matter
21
, 424109
(2009
).30.
S.
Tazi
, M.
Salanne
, C.
Simon
, P.
Turq
, M.
Pounds
, and P. A.
Madden
, “Potential-induced ordering transition of the adsorbed layer at the ionic liquid/electrified metal interface
,” J. Phys. Chem. B
114
, 8453
–8459
(2010
).31.
F.
Wang
, O.
Borodin
, M. S.
Ding
, M.
Gobet
, J.
Vatamanu
, X.
Fan
, T.
Gao
, N.
Eidson
, Y.
Liang
, S.
Greenbaum
, K.
Xu
, and C.
Wang
, “Hybrid aqueous/non-aqueous electrolyte for safe and high-energy Li-ion batteries
,” Joule
2
, 927
–937
(2018
).32.
D. T.
Margul
and M. E.
Tuckerman
, “A stochastic, resonance-free multiple time-step algorithm for polarizable models that permits very large time steps
,” J. Chem. Theory Comput.
12
, 2170
–2180
(2016
).33.
P.
Monmarché
, J.
Weisman
, L.
Lagardère
, and J.-P.
Piquemal
, “Velocity jump processes: An alternative to multi-timestep methods for faster and accurate molecular dynamics simulations
,” J. Chem. Phys.
153
, 024101
(2020
).34.
A.
Marin-Laflèche
, M.
Haefele
, L.
Scalfi
, A.
Coretti
, T.
Dufils
, G.
Jeanmairet
, S.
Reed
, A.
Serva
, R.
Berthin
, C.
Bacon
, S.
Bonella
, B.
Rotenberg
, P.
Madden
, and M.
Salanne
, “MetalWalls: A classical molecular dynamics software dedicated to the simulation of electrochemical systems
,” J. Open Source Software
5
, 2373
(2020
).35.
R.
Berthin
, A.
Serva
, K. G.
Reeves
, E.
Heid
, C.
Schröder
, and M.
Salanne
, “Solvation of anthraquinone and tempo redox-active species in acetonitrile using a polarizable force field
,” J. Chem. Phys.
155
, 074504
(2021
).36.
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
, 044703
(2021
).37.
A.
Aguado
, L.
Bernasconi
, and P. A.
Madden
, “Interionic potentials from ab initio molecular dynamics: The alkaline earth oxides CaO, SrO, and BaO
,” J. Chem. Phys.
118
, 5704
–5717
(2003
).38.
M.
Neumann
, “Dipole moment fluctuation formulas in computer simulations of polar systems
,” Mol. Phys.
50
, 841
–858
(1983
).39.
M.
Sprik
and M. L.
Klein
, “A polarizable model for water using distributed charge sites
,” J. Chem. Phys.
89
, 7556
–7560
(1988
).40.
J.
Kolafa
, “Time-reversible always stable predictor-corrector method for molecular dynamics of polarizable molecules
,” J. Comput. Chem.
25
, 335
–342
(2004
).41.
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
).42.
W. H.
Press
, B. P.
Flannery
, S. A.
Teukolsky
, and W. T.
Vetterling
, Numerical Recipes in C: The Art of Scientific Computing
(Cambridge University Press
, Cambridge, Cambridgeshire
, 1992
).43.
44.
T. D.
Kühne
, M.
Krack
, F. R.
Mohamed
, and M.
Parrinello
, “Efficient and accurate Car–Parrinello-like approach to Born–Oppenheimer molecular dynamics
,” Phys. Rev. Lett.
98
, 066401
(2007
).45.
F.
Aviat
, A.
Levitt
, B.
Stamm
, Y.
Maday
, P.
Ren
, J. W.
Ponder
, L.
Lagardère
, and J.-P.
Piquemal
, “Truncated conjugate gradient: An optimal strategy for the analytical evaluation of the many-body polarization energy and forces in molecular simulations
,” J. Chem. Theory Comput.
13
, 180
–190
(2017
).46.
G.
Golub
and C.
Van Loan
, “Matrix computations
,” in Johns Hopkins Studies in the Mathematical Sciences
(Johns Hopkins University Press
, 2013
).47.
Y.
Ishii
, S.
Kasai
, M.
Salanne
, and N.
Ohtori
, “Transport coefficients and the Stokes–Einstein relation in molten alkali halides with polarisable ion model
,” Mol. Phys.
113
, 2442
–2450
(2015
).48.
J. N. C.
Lopes
and A. A. H.
Pádua
, “Molecular force field for ionic liquids composed of triflate or bistriflimide anions
,” J. Phys. Chem. B
108
, 16893
–16898
(2004
).49.
J. N. C.
Lopes
, J.
Deschamps
, and A. A. H.
Pádua
, “Modeling ionic liquids using a systematic all-atom force field
,” J. Phys. Chem. B
108
, 11250
(2004
).50.
V.
Chaban
, “Polarizability versus mobility: Atomistic force field for ionic liquids
,” Phys. Chem. Chem. Phys.
13
, 16055
–16062
(2011
).51.
B. L.
Bhargava
and S.
Balasubramanian
, “Refined potential model for atomistic simulations of ionic liquid [bmim][PF6]
,” J. Chem. Phys.
127
, 114510
(2007
).52.
Y.
Zhang
and E. J.
Maginn
, “A simple AIMD approach to derive atomic charges for condensed phase simulation of ionic liquids
,” J. Phys. Chem. B
116
, 10036
–10048
(2012
).53.
K.
Goloviznina
, Z.
Gong
, M. F.
Costa Gomes
, and A. A. H.
Pádua
, “Extension of the CL&Pol polarizable force field to electrolytes, protic ionic liquids, and deep eutectic solvents
,” J. Chem. Theory Comput.
17
, 1606
–1617
(2021
).54.
K.
Goloviznina
, Z.
Gong
, and A. A. H.
Padua
, “The CL&Pol polarizable force field for the simulation of ionic liquids and eutectic solvents
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
12
, e1572
(2021
).55.
56.
E.
Heid
, A.
Szabadi
, and C.
Schröder
, “Quantum mechanical determination of atomic polarizabilities of ionic liquids
,” Phys. Chem. Chem. Phys.
20
, 10992
–10996
(2018
).57.
B. T.
Thole
, “Molecular polarizabilities calculated with a modified dipole interaction
,” Chem. Phys.
59
, 341
–350
(1981
).58.
W. L.
Jorgensen
, D. S.
Maxwell
, and J.
Tirado-Rives
, “Development and testing of the OPLS all-atom force field on conformational energetics and properties of organic liquids
,” J. Am. Chem. Soc.
118
, 11225
–11236
(1996
).59.
K. T.
Tang
and J. P.
Toennies
, “An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients
,” J. Chem. Phys.
80
, 3726
–3741
(1984
).60.
C.
Merlet
, B.
Rotenberg
, P. A.
Madden
, P.-L.
Taberna
, P.
Simon
, Y.
Gogotsi
, and M.
Salanne
, “On the molecular origin of supercapacitance in nanoporous carbon electrodes
,” Nat. Mater.
11
, 306
–310
(2012
).61.
L.
Martínez
, R.
Andrade
, E. G.
Birgin
, and J. M.
Martínez
, “PACKMOL: A package for building initial configurations for molecular dynamics simulations
,” J. Comput. Chem.
30
, 2157
–2164
(2009
).62.
R. L.
Gardas
, M. G.
Freire
, P. J.
Carvalho
, I. M.
Marrucho
, I. M. A.
Fonseca
, A. G. M.
Ferreira
, and J. A. P.
Coutinho
, “PρT measurements of imidazolium-based ionic liquids
,” J. Chem. Eng. Data
52
, 1881
–1888
(2007
).63.
G.
Feng
, S.
Li
, W.
Zhao
, and P. T.
Cummings
, “Microstructure of room temperature ionic liquids at stepped graphite electrodes
,” AIChE J.
61
, 3022
–3028
(2015
).64.
A.
Fang
and A.
Smolyanitsky
, “Simulation study of the capacitance and charging mechanisms of ionic liquid mixtures near carbon electrodes
,” J. Phys. Chem. C
123
, 1610
–1618
(2019
).65.
P. S.
Gil
, S. J.
Jorgenson
, A. R.
Riet
, and D. J.
Lacks
, “Relationships between molecular structure, interfacial structure, and dynamics of ionic liquids near neutral and charged surfaces
,” J. Phys. Chem. C
122
, 27462
–27468
(2018
).66.
S.
Li
, Z.
Zhao
, and X.
Liu
, “Electric double layer structure and capacitance of imidazolium-based ionic liquids with FSI- and Tf- anions at graphite electrode by molecular dynamic simulations
,” J. Electroanal. Chem.
851
, 113452
(2019
).67.
N. N.
Rajput
, J.
Monk
, R.
Singh
, and F. R.
Hung
, “On the influence of pore size and pore loading on structural and dynamical heterogeneities of an ionic liquid confined in a slit nanopore
,” J. Phys. Chem. C
116
, 5169
–5181
(2012
).68.
J.
Vatamanu
, O.
Borodin
, D.
Bedrov
, and G. D.
Smith
, “Molecular dynamics simulation study of the interfacial structure and differential capacitance of alkylimidazolium bis(trifluoromethanesulfonyl)imide [cnmim][TFSI] ionic liquids at graphite electrodes
,” J. Phys. Chem. C
116
, 7940
–7951
(2012
).69.
Z.
Hu
, J.
Vatamanu
, O.
Borodin
, and D.
Bedrov
, “A comparative study of alkylimidazolium room temperature ionic liquids with FSI and TFSI anions near charged electrodes
,” Electrochim. Acta
145
, 40
–52
(2014
).70.
E.
Mourad
, L.
Coustan
, S. A.
Freunberger
, A.
Mehdi
, A.
Vioux
, F.
Favier
, and O.
Fontaine
, “Biredox ionic liquids: Electrochemical investigation and impact of ion size on electron transfer
,” Electrochim. Acta
206
, 513
–523
(2016
).71.
E.
Mourad
, L.
Coustan
, P.
Lannelongue
, D.
Zigah
, A.
Mehdi
, A.
Vioux
, S. A.
Freunberger
, F.
Favier
, and O.
Fontaine
, “Biredox ionic liquids with solid-like redox density in the liquid state for high-energy supercapacitors
,” Nat. Mater.
16
, 446
–453
(2017
).72.
C.
Bodin
, E.
Mourad
, D.
Zigah
, S.
Le Vot
, S. A.
Freunberger
, F.
Favier
, and O.
Fontaine
, “Biredox ionic liquids: New opportunities toward high performance supercapacitors
,” Faraday Discuss.
206
, 393
–404
(2018
).73.
O.
Fontaine
, “A deeper understanding of the electron transfer is the key to the success of biredox ionic liquids
,” Energy Storage Mater.
21
, 240
–245
(2019
).74.
P.
Lemaire
, A.
Serva
, M.
Salanne
, G.
Rousse
, H.
Perrot
, O.
Sel
, and J.-M.
Tarascon
, “Probing the electrode—Electrolyte interface of a model K-ion battery electrode—The origin of rate capability discrepancy between aqueous and non-aqueous electrolytes
,” ACS Appl. Mater. Interfaces
14
, 20835
–20847
(2022
).75.
N.
Dubouis
, A.
Serva
, R.
Berthin
, G.
Jeanmairet
, B.
Porcheron
, E.
Salager
, M.
Salanne
, and A.
Grimaud
, “Tuning water reduction through controlled nanoconfinement within an organic liquid matrix
,” Nat. Catal.
3
, 656
–663
(2020
).76.
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
, 174704
(2020
).77.
A.
Schlaich
, D.
Jin
, L.
Bocquet
, and B.
Coasne
, “Electronic screening using a virtual Thomas–Fermi fluid for predicting wetting and phase transitions of ionic liquids at metal surfaces
,” Nat. Mater.
21
, 237
–245
(2022
).78.
P.
Clabaut
, P.
Fleurat-Lessard
, C.
Michel
, and S. N.
Steinmann
, “Ten facets, one force field: The GAL19 force field for water-noble metal interfaces
,” J. Chem. Theory Comput.
16
, 4565
–4578
(2020
).79.
M.
Ruggeri
, K.
Reeves
, T.-Y.
Hsu
, G.
Jeanmairet
, M.
Salanne
, and C.
Pierleoni
, “Multi-scale simulation of the adsorption of lithium ion on graphite surface: From quantum Monte Carlo to molecular density functional theory
,” J. Chem. Phys.
156
, 094709
(2022
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
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