Fast evolution of modern society stimulates intense development of new materials with novel functionalities in energy and environmental applications. Due to rapid progress of computer science, computational design of materials with target properties has recently attracted a lot of interest. Accurate and efficient calculation of fundamental thermodynamic properties, including redox potentials, acidity constants, and solvation free energies, is of great importance for selection and design of desirable materials. Free energy calculation based on ab initio molecular dynamics (AIMD) can predict these properties with high accuracy at complex environments, however, they are being impeded by high computational costs. To address this issue, this work develops an automated scheme that combines iterative training of machine learning potentials (MLPs) and free energy calculation and demonstrates that these thermodynamic properties can be computed by ML accelerated MD with ab initio accuracy and a much longer time scale at cheaper costs, improving poor statistics and convergence of numerical integration by AIMD. Our automated scheme lays the foundation for computational chemistry-assisted materials design.
REFERENCES
1.
J.
Blumberger
, “Recent advances in the theory and molecular simulation of biological electron transfer reactions
,” Chem. Rev.
115
, 11191
–11238
(2015
).2.
P.
Wardman
, “Reduction potentials of one-electron couples involving free radicals in aqueous solution
,” J. Phys. Chem. Ref. Data
18
, 1637
–1755
(1989
).3.
D. R.
Weinberg
, C. J.
Gagliardi
, J. F.
Hull
, C. F.
Murphy
, C. A.
Kent
, B. C.
Westlake
, A.
Paul
, D. H.
Ess
, D. G.
McCafferty
, and T. J.
Meyer
, “Proton-coupled electron transfer
,” Chem. Rev.
112
, 4016
–4093
(2012
).4.
P.
Arévalo-Cid
, P.
Dias
, A.
Mendes
, and J.
Azevedo
, “Redox flow batteries: A new frontier on energy storage
,” Sustainable Energy Fuels
5
, 5366
–5419
(2021
).5.
S. J.
Mora
, E.
Odella
, G. F.
Moore
, D.
Gust
, T. A.
Moore
, and A. L.
Moore
, “Proton-coupled electron transfer in artificial photosynthetic systems
,” Acc. Chem. Res.
51
, 445
–453
(2018
).6.
G. S.
Pokrovski
, A. Y.
Borisova
, and A. Y.
Bychkov
, “Speciation and transport of metals and metalloids in geological vapors
,” Rev. Mineral. Geochem.
76
, 165
–218
(2013
).7.
J.
Cheng
, X.
Liu
, J.
VandeVondele
, M.
Sulpizi
, and M.
Sprik
, “Redox potentials and acidity constants from density functional theory based molecular dynamics
,” Acc. Chem. Res.
47
, 3522
–3529
(2014
).8.
E.
Hruska
, A.
Gale
, and F.
Liu
, “Bridging the experiment-calculation divide: Machine learning corrections to redox potential calculations in implicit and explicit solvent models
,” J. Chem. Theory Comput.
18
, 1096
–1108
(2022
).9.
C. M.
Sterling
and R.
Bjornsson
, “Multistep explicit solvation protocol for calculation of redox potentials
,” J. Chem. Theory Comput.
15
, 52
–67
(2018
).10.
O.
Allam
, R.
Kuramshin
, Z.
Stoichev
, B. W.
Cho
, S. W.
Lee
, and S. S.
Jang
, “Molecular structure–redox potential relationship for organic electrode materials: Density functional theory–machine learning approach
,” Mater. Today Energy
17
, 100482
(2020
).11.
J.
Yu
, T.-S.
Zhao
, and D.
Pan
, “Tuning the performance of aqueous organic redox flow batteries via first-principles calculations
,” J. Phys. Chem. Lett.
11
, 10433
–10438
(2020
).12.
J.
Tomasi
, B.
Mennucci
, and R.
Cammi
, “Quantum mechanical continuum solvation models
,” Chem. Rev.
105
, 2999
–3094
(2005
).13.
K.
Leung
, “Predicting the voltage dependence of interfacial electrochemical processes at lithium-intercalated graphite edge planes
,” Phys. Chem. Chem. Phys.
17
, 1637
–1643
(2015
).14.
F.
Costanzo
, M.
Sulpizi
, R. G.
Della Valle
, and M.
Sprik
, “The oxidation of tyrosine and tryptophan studied by a molecular dynamics normal hydrogen electrode
,” J. Chem. Phys.
134
, 244508
(2011
).15.
M.
Sulpizi
and M.
Sprik
, “Acidity constants from DFT-based molecular dynamics simulations
,” J. Phys.: Condens. Matter
22
, 284116
(2010
).16.
M.
Mangold
, L.
Rolland
, F.
Costanzo
, M.
Sprik
, M.
Sulpizi
, and J.
Blumberger
, “Absolute pKa values and solvation structure of amino acids from density functional based molecular dynamics simulation
,” J. Chem. Theory Comput.
7
, 1951
–1961
(2011
).17.
X.
Liu
, M.
Sprik
, and J.
Cheng
, “Hydration, acidity and metal complexing of polysulfide species: A first principles molecular dynamics study
,” Chem. Phys. Lett.
563
, 9
–14
(2013
).18.
X.
Zhang
, X.
Liu
, M.
He
, Y.
Zhang
, Y.
Sun
, and X.
Lu
, “A molecular dynamics simulation study of KF and NaF ion pairs in hydrothermal fluids
,” Fluid Phase Equilib.
518
, 112625
(2020
).19.
P.
Schienbein
and D.
Marx
, “Assessing the properties of supercritical water in terms of structural dynamics and electronic polarization effects
,” Phys. Chem. Chem. Phys.
22
, 10462
–10479
(2020
).20.
M.
DelloStritto
, J.
Xu
, X.
Wu
, and M. L.
Klein
, “Aqueous solvation of the chloride ion revisited with density functional theory: Impact of correlation and exchange approximations
,” Phys. Chem. Chem. Phys.
22
, 10666
–10675
(2020
).21.
A.
Yamaguchi
, K.
Kobayashi
, Y.
Takahashi
, M.
Machida
, and M.
Okumura
, “Hydration structures of barium ions: Ab initio molecular dynamics simulations using the SCAN meta-GGA density functional and EXAFS spectroscopy studies
,” Chem. Phys. Lett.
780
, 138945
(2021
).22.
G.
King
and A.
Warshel
, “Investigation of the free energy functions for electron transfer reactions
,” J. Chem. Phys.
93
, 8682
–8692
(1990
).23.
J.
Cheng
, M.
Sulpizi
, and M.
Sprik
, “Redox potentials and pKa for benzoquinone from density functional theory based molecular dynamics
,” J. Chem. Phys.
131
, 154504
(2009
).24.
J.
Blumberger
, I.
Tavernelli
, M. L.
Klein
, and M.
Sprik
, “Diabatic free energy curves and coordination fluctuations for the aqueous Ag+/Ag2+ redox couple: A biased Born-Oppenheimer molecular dynamics investigation
,” J. Chem. Phys.
124
, 064507
(2006
).25.
C.
Adriaanse
, J.
Cheng
, V.
Chau
, M.
Sulpizi
, J.
VandeVondele
, and M.
Sprik
, “Aqueous redox chemistry and the electronic band structure of liquid water
,” J. Phys. Chem. Lett.
3
, 3411
–3415
(2012
).26.
X.-H.
Yang
, A.
Cuesta
, and J.
Cheng
, “Computational Ag/AgCl reference electrode from density functional theory-based molecular dynamics
,” J. Phys. Chem. B
123
, 10224
–10232
(2019
).27.
K.
Leung
and C. M.
Tenney
, “Toward first principles prediction of voltage dependences of electrolyte/electrolyte interfacial processes in lithium ion batteries
,” J. Phys. Chem. C
117
, 24224
–24235
(2013
).28.
J.
Cheng
and J.
VandeVondele
, “Calculation of electrochemical energy levels in water using the random phase approximation and a double hybrid functional
,” Phys. Rev. Lett.
116
, 086402
(2016
).29.
N. Q.
Su
and X.
Xu
, “The XYG3 type of doubly hybrid density functionals
,” Wiley Interdiscip. Rev.: Comput. Mol. Sci.
6
, 721
–747
(2016
).30.
N. Q.
Su
, Z.
Zhu
, and X.
Xu
, “Doubly hybrid density functionals that correctly describe both density and energy for atoms
,” Proc. Natl. Acad. Sci. U. S. A.
115
, 2287
–2292
(2018
).31.
I. Y.
Zhang
, J.
Wu
, and X.
Xu
, “Accurate heats of formation of polycyclic saturated hydrocarbons predicted by using the XYG3 type of doubly hybrid functionals
,” J. Comput. Chem.
40
, 1113
–1122
(2019
).32.
A. P.
Thompson
, L. P.
Swiler
, C. R.
Trott
, S. M.
Foiles
, and G. J.
Tucker
, “Spectral neighbor analysis method for automated generation of quantum-accurate interatomic potentials
,” J. Comput. Phys.
285
, 316
–330
(2015
).33.
T. D.
Huan
, R.
Batra
, J.
Chapman
, S.
Krishnan
, L.
Chen
, and R.
Ramprasad
, “A universal strategy for the creation of machine learning-based atomistic force fields
,” npj Comput. Mater.
3
, 37
(2017
).34.
J.
Behler
and M.
Parrinello
, “Generalized neural-network representation of high-dimensional potential-energy surfaces
,” Phys. Rev. Lett.
98
, 146401
(2007
).35.
J.
Behler
, “Perspective: Machine learning potentials for atomistic simulations
,” J. Chem. Phys.
145
, 170901
(2016
).36.
A. P.
Bartók
, M. C.
Payne
, R.
Kondor
, and G.
Csányi
, “Gaussian approximation potentials: The accuracy of quantum mechanics, without the electrons
,” Phys. Rev. Lett.
104
, 136403
(2010
).37.
M.
Rupp
, A.
Tkatchenko
, K.-R.
Müller
, and O. A.
von Lilienfeld
, “Fast and accurate modeling of molecular atomization energies with machine learning
,” Phys. Rev. Lett.
108
, 058301
(2012
).38.
L.
Zhang
, J.
Han
, H.
Wang
, R.
Car
, and W.
E
, “Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics
,” Phys. Rev. Lett.
120
, 143001
(2018
).39.
H.
Wang
, L.
Zhang
, J.
Han
, and W.
E
, “DeePMD-kit: A deep learning package for many-body potential energy representation and molecular dynamics
,” Comput. Phys. Commun.
228
, 178
–184
(2018
).40.
S.
Chmiela
, A.
Tkatchenko
, H. E.
Sauceda
, I.
Poltavsky
, K. T.
Schütt
, and K. R.
Müller
, “Machine learning of accurate energy-conserving molecular force fields
,” Sci. Adv.
3
, e1603015
(2017
).41.
K. T.
Schütt
, F.
Arbabzadah
, S.
Chmiela
, K. R.
Müller
, and A.
Tkatchenko
, “Quantum-chemical insights from deep tensor neural networks
,” Nat. Commun.
8
, 13890
(2017
).42.
L.
Zhang
, D.-Y.
Lin
, H.
Wang
, R.
Car
, and W.
E
, “Active learning of uniformly accurate interatomic potentials for materials simulation
,” Phys. Rev. Mater.
3
, 023804
(2019
).43.
Y.
Zhang
, H.
Wang
, W.
Chen
, J.
Zeng
, L.
Zhang
, H.
Wang
, and W.
E
, “DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models
,” Comput. Phys. Commun.
253
, 107206
(2020
).44.
J. G.
Kirkwood
, “Statistical mechanics of fluid mixtures
,” J. Chem. Phys.
3
, 300
–313
(1935
).45.
J.
Behler
and M.
Parrinello
, “Generalized neural-network representation of high-dimensional potential-energy surfaces
,” Phys. Rev. Lett.
98
, 146401
(2007
).46.
L.
Zhang
, H.
Wang
, and W.
E
, “Adaptive coupling of a deep neural network potential to a classical force field
,” J. Chem. Phys.
149
, 154107
(2018
).47.
J.
VandeVondele
, M.
Krack
, F.
Mohamed
, M.
Parrinello
, T.
Chassaing
, and J.
Hutter
, “QUICKSTEP: Fast and accurate density functional calculations using a mixed Gaussian and plane waves approach
,” Comput. Phys. Commun.
167
, 103
–128
(2005
).48.
A. D.
Becke
, “Density-functional exchange-energy approximation with correct asymptotic behavior
,” Phys. Rev. A
38
, 3098
–3100
(1988
).49.
C.
Lee
, W.
Yang
, and R. G.
Parr
, “Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
,” Phys. Rev. B
37
, 785
–789
(1988
).50.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, “A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu
,” J. Chem. Phys.
132
, 154104
(2010
).51.
C.
Hartwigsen
, S.
Goedecker
, and J.
Hutter
, “Relativistic separable dual-space Gaussian pseudopotentials from H to Rn
,” Phys. Rev. B
58
, 3641
–3662
(1998
).52.
S.
Goedecker
, M.
Teter
, and J.
Hutter
, “Separable dual-space Gaussian pseudopotentials
,” Phys. Rev. B
54
, 1703
–1710
(1996
).53.
J.
VandeVondele
and J.
Hutter
, “Gaussian basis sets for accurate calculations on molecular systems in gas and condensed phases
,” J. Chem. Phys.
127
, 114105
(2007
).54.
L.
Zhang
, J.
Han
, H.
Wang
, W.
Saidi
, R.
Car
, and W.
E
, “End-to-end symmetry preserving inter-atomic potential energy model for finite and extended systems
,” in Advances in Neural Information Processing Systems
, edited by S.
Bengio
, H.
Wallach
, H.
Larochelle
, K.
Grauman
, N.
Cesa-Bianchi
, and R.
Garnett
(Curran Associates, Inc.
, 2018
), Vol. 31, pp. 4436
–4446
.55.
M.
Sulpizi
and M.
Sprik
, “Acidity constants from vertical energy gaps: Density functional theory based molecular dynamics implementation
,” Phys. Chem. Chem. Phys.
10
, 5238
–5249
(2008
).56.
E.
Hruska
, A.
Gale
, X.
Huang
, and F.
Liu
, “AutoSolvate: A toolkit for automating quantum chemistry design and discovery of solvated molecules
,” J. Chem. Phys.
156
, 124801
(2022
).© 2022 Author(s). Published under an exclusive license by AIP Publishing.
2022
Author(s)
You do not currently have access to this content.
