We investigate the temperature dependence of nuclear quantum effects (NQEs) on structural and dynamic properties of liquid water by training a neural network force field using first-principles molecular dynamics (FPMD) based on the strongly constrained and appropriately normed meta-generalized gradient approximation exchange-correlation approximation. The FPMD simulation based on density functional theory has become a powerful computational approach for studying a wide range of condensed phase systems. However, its large computational cost makes it difficult to incorporate NQEs in the simulation and investigate temperature dependence of various properties. To circumvent this difficulty, we use an artificial neural network model and employ the thermostatted ring polymer MD approach for studying the temperature dependence of NQEs on various properties. The NQEs generally bring the radial distribution functions closer to the experimental measurements. Translational diffusivity and rotational dynamics of water molecules are both slowed down by the NQEs. The competing inter-molecular and intra-molecular quantum effects on hydrogen bonds, as discussed by Habershon, Markland, and Manolopoulos [J. Chem. Phys. 131(2), 024501 (2019)], can explain the observed temperature dependence of the NQEs on the dynamical properties in our simulation.
REFERENCES
1.
J.
Cheng
and M.
Sprik
, “Aligning electronic energy levels at the TiO2/H2O interface
,” Phys. Rev. B
82
(8
), 081406
(2010
).2.
M. W.
Denny
, Air and Water: The Biology and Physics of Life’s Media
(Princeton University Press
, 1993
).3.
D. V.
Esposito
, J. B.
Baxter
, J.
John
, N. S.
Lewis
, T. P.
Moffat
, T.
Ogitsu
, G. D.
O’Neil
, T. A.
Pham
, A. A.
Talin
, J. M.
Velazquez
, and B. C.
Wood
, “Methods of photoelectrode characterization with high spatial and temporal resolution
,” Energy Environ. Sci.
8
(10
), 2863
–2885
(2015
).4.
T.
Ikeshoji
, M.
Otani
, I.
Hamada
, and Y.
Okamoto
, “Reversible redox reaction and water configuration on a positively charged platinum surface: First principles molecular dynamics simulation
,” Phys. Chem. Chem. Phys.
13
(45
), 20223
–20227
(2011
).5.
T. A.
Pham
, D.
Lee
, E.
Schwegler
, and G.
Galli
, “Interfacial effects on the band edges of functionalized Si surfaces in liquid water
,” J. Am. Chem. Soc.
136
(49
), 17071
–17077
(2014
).6.
K. G.
Reeves
and Y.
Kanai
, “Electronic excitation dynamics in liquid water under proton irradiation
,” Sci. Rep.
7
, 40379
(2017
).7.
K. G.
Reeves
, Y.
Yao
, and Y.
Kanai
, “Electronic stopping power in liquid water for protons and α particles from first principles
,” Phys. Rev. B
94
(4
), 041108
(2016
).8.
B. C.
Wood
, E.
Schwegler
, W. I.
Choi
, and T.
Ogitsu
, “Hydrogen-bond dynamics of water at the interface with InP/GaP(001) and the implications for photoelectrochemistry
,” J. Am. Chem. Soc.
135
(42
), 15774
–15783
(2013
).9.
B. C.
Wood
, E.
Schwegler
, W. I.
Choi
, and T.
Ogitsu
, “Surface chemistry of GaP(001) and InP(001) in contact with water
,” J. Phys. Chem. C
118
(2
), 1062
–1070
(2014
).10.
Y.
Yao
, Y.
Kanai
, and M. L.
Berkowitz
, “Role of charge transfer in water diffusivity in aqueous ionic solutions
,” J. Phys. Chem. Lett.
5
(15
), 2711
–2716
(2014
).11.
Y.
Yao
, M. L.
Berkowitz
, and Y.
Kanai
, “Communication: Modeling of concentration dependent water diffusivity in ionic solutions: Role of intermolecular charge transfer
,” J. Chem. Phys.
143
(24
), 241101
(2015
).12.
E.
Duboué-Dijon
and D.
Laage
, “Characterization of the local structure in liquid water by various order parameters
,” J. Phys. Chem. B
119
(26
), 8406
–8418
(2015
).13.
M.
Chen
, H.-Y.
Ko
, R. C.
Remsing
, M. F.
Calegari Andrade
, B.
Santra
, Z.
Sun
, A.
Selloni
, R.
Car
, M. L.
Klein
, J. P.
Perdew
, and X.
Wu
, “Ab initio theory and modeling of water
,” Proc. Natl. Acad. Sci. U. S. A.
114
(41
), 10846
–10851
(2017
).14.
L.
Zheng
, M.
Chen
, Z.
Sun
, H.-Y.
Ko
, B.
Santra
, P.
Dhuvad
, and X.
Wu
, “Structural, electronic, and dynamical properties of liquid water by ab initio molecular dynamics based on SCAN functional within the canonical ensemble
,” J. Chem. Phys.
148
(16
), 164505
(2018
).15.
J. C.
Grossman
, E.
Schwegler
, E. W.
Draeger
, F.
Gygi
, and G.
Galli
, “Towards an assessment of the accuracy of density functional theory for first principles simulations of water
,” J. Chem. Phys.
120
(1
), 300
–311
(2004
).16.
E.
Schwegler
, J. C.
Grossman
, F.
Gygi
, and G.
Galli
, “Towards an assessment of the accuracy of density functional theory for first principles simulations of water. II
,” J. Chem. Phys.
121
(11
), 5400
–5409
(2004
).17.
D.
Lu
, F.
Gygi
, and G.
Galli
, “Dielectric properties of ice and liquid water from first-principles calculations
,” Phys. Rev. Lett.
100
(14
), 147601
(2008
).18.
M. V.
Fernández-Serra
, G.
Ferlat
, and E.
Artacho
, “Two exchange-correlation functionals compared for first-principles liquid water
,” Mol. Simul.
31
(5
), 361
–366
(2005
).19.
B.
Chen
, I.
Ivanov
, M. L.
Klein
, and M.
Parrinello
, “Hydrogen bonding in water
,” Phys. Rev. Lett.
91
(21
), 215503
(2003
).20.
C.
Zhang
, D.
Donadio
, F.
Gygi
, and G.
Galli
, “First principles simulations of the infrared spectrum of liquid water using hybrid density functionals
,” J. Chem. Theory Comput.
7
(5
), 1443
–1449
(2011
).21.
M.
Del Ben
, M.
Schönherr
, J.
Hutter
, and J.
VandeVondele
, “Bulk liquid water at ambient temperature and pressure from MP2 theory
,” J. Phys. Chem. Lett.
4
(21
), 3753
–3759
(2013
).22.
I.-F. W.
Kuo
, C. J.
Mundy
, M. J.
McGrath
, J. I.
Siepmann
, J.
VandeVondele
, M.
Sprik
, J.
Hutter
, B.
Chen
, M. L.
Klein
, F.
Mohamed
, M.
Krack
, and M.
Parrinello
, “Liquid water from first Principles: Investigation of different sampling approaches
,” J. Phys. Chem. B
108
(34
), 12990
–12998
(2004
).23.
K.
Laasonen
, M.
Sprik
, M.
Parrinello
, and R.
Car
, ““Ab initio” liquid water
,” J. Chem. Phys.
99
(11
), 9080
–9089
(1993
).24.
P. L.
Silvestrelli
and M.
Parrinello
, “Structural, electronic, and bonding properties of liquid water from first principles
,” J. Chem. Phys.
111
(8
), 3572
–3580
(1999
).25.
M.
Sprik
, J.
Hutter
, and M.
Parrinello
, “Ab initio molecular dynamics simulation of liquid water: Comparison of three gradient-corrected density functionals
,” J. Chem. Phys.
105
(3
), 1142
–1152
(1996
).26.
H.-S.
Lee
and M. E.
Tuckerman
, “Dynamical properties of liquid water from ab initio molecular dynamics performed in the complete basis set limit
,” J. Chem. Phys.
126
(16
), 164501
(2007
).27.
H.-S.
Lee
and M. E.
Tuckerman
, “Structure of liquid water at ambient temperature from ab initio molecular dynamics performed in the complete basis set limit
,” J. Chem. Phys.
125
(15
), 154507
(2006
).28.
A.
Bankura
, A.
Karmakar
, V.
Carnevale
, A.
Chandra
, and M. L.
Klein
, “Structure, dynamics, and spectral diffusion of water from first-principles molecular dynamics
,” J. Phys. Chem. C
118
(50
), 29401
–29411
(2014
).29.
A.
Zen
, Y.
Luo
, G.
Mazzola
, L.
Guidoni
, and S.
Sorella
, “Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo
,” J. Chem. Phys.
142
(14
), 144111
(2015
).30.
D.
Prendergast
and G.
Galli
, “X-ray absorption spectra of water from first principles calculations
,” Phys. Rev. Lett.
96
(21
), 215502
(2006
).31.
Z.
Sun
, L.
Zheng
, M.
Chen
, M. L.
Klein
, F.
Paesani
, and X.
Wu
, “Electron-hole theory of the effect of quantum nuclei on the X-ray absorption spectra of liquid water
,” Phys. Rev. Lett.
121
(13
), 137401
(2018
).32.
T.
Morawietz
, O.
Marsalek
, S. R.
Pattenaude
, L. M.
Streacker
, D.
Ben-Amotz
, and T. E.
Markland
, “The interplay of structure and dynamics in the Raman spectrum of liquid water over the full frequency and temperature range
,” J. Phys. Chem. Lett.
9
(4
), 851
–857
(2018
).33.
T.
Morawietz
, A.
Singraber
, C.
Dellago
, and J.
Behler
, “How van der Waals interactions determine the unique properties of water
,” Proc. Natl. Acad. Sci. U. S. A.
113
(30
), 8368
–8373
(2016
).34.
M. J.
Gillan
, D.
Alfè
, and A.
Michaelides
, “Perspective: How good is DFT for water?
,” J. Chem. Phys.
144
(13
), 130901
(2016
).35.
I.-C.
Lin
, A. P.
Seitsonen
, I.
Tavernelli
, and U.
Rothlisberger
, “Structure and dynamics of liquid water from ab initio molecular dynamics—Comparison of BLYP, PBE, and revPBE density functionals with and without van der Waals corrections
,” J. Chem. Theory Comput.
8
(10
), 3902
–3910
(2012
).36.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, “Generalized gradient approximation made simple
,” Phys. Rev. Lett.
77
(18
), 3865
–3868
(1996
).37.
M.
Ceriotti
, W.
Fang
, P. G.
Kusalik
, R. H.
McKenzie
, A.
Michaelides
, M. A.
Morales
, and T. E.
Markland
, “Nuclear quantum effects in water and aqueous systems: Experiment, theory, and current challenges
,” Chem. Rev.
116
(13
), 7529
–7550
(2016
).38.
J. A.
Morrone
and R.
Car
, “Nuclear quantum effects in water
,” Phys. Rev. Lett.
101
(1
), 017801
(2008
).39.
M.
Ceriotti
, J.
Cuny
, M.
Parrinello
, and D. E.
Manolopoulos
, “Nuclear quantum effects and hydrogen bond fluctuations in water
,” Proc. Natl. Acad. Sci. U. S. A.
110
(39
), 15591
–15596
(2013
).40.
S.
Raugei
and M. L.
Klein
, “Nuclear quantum effects and hydrogen bonding in liquids
,” J. Am. Chem. Soc.
125
(30
), 8992
–8993
(2003
).41.
F.
Paesani
, S.
Yoo
, H. J.
Bakker
, and S. S.
Xantheas
, “Nuclear quantum effects in the reorientation of water
,” J. Phys. Chem. Lett.
1
(15
), 2316
–2321
(2010
).42.
O.
Marsalek
and T. E.
Markland
, “Quantum dynamics and spectroscopy of ab initio liquid water: The interplay of nuclear and electronic quantum effects
,” J. Phys. Chem. Lett.
8
(7
), 1545
–1551
(2017
).43.
F.
Paesani
, W.
Zhang
, D. A.
Case
, T. E.
Cheatham III
, and G. A.
Voth
, “An accurate and simple quantum model for liquid water
,” J. Chem. Phys.
125
(18
), 184507
(2006
).44.
F.
Paesani
, S.
Iuchi
, and G. A.
Voth
, “Quantum effects in liquid water from an ab initio-based polarizable force field
,” J. Chem. Phys.
127
(7
), 074506
(2007
).45.
L.
Hernández de la Peña
and P. G.
Kusalik
, “Temperature dependence of quantum effects in liquid water
,” J. Am. Chem. Soc.
127
(14
), 5246
–5251
(2005
).46.
S.
Fritsch
, R.
Potestio
, D.
Donadio
, and K.
Kremer
, “Nuclear quantum effects in water: A multiscale study
,” J. Chem. Theory Comput.
10
(2
), 816
–824
(2014
).47.
T.
Spura
, C.
John
, S.
Habershon
, and T. D.
Kühne
, “Nuclear quantum effects in liquid water from path-integral simulations using an ab initio force-matching approach
,” Mol. Phys.
113
(8
), 808
–822
(2015
).48.
L.
Wang
, M.
Ceriotti
, and T. E.
Markland
, “Quantum fluctuations and isotope effects in ab initio descriptions of water
,” J. Chem. Phys.
141
(10
), 104502
(2014
).49.
S.
Habershon
, T. E.
Markland
, and D. E.
Manolopoulos
, “Competing quantum effects in the dynamics of a flexible water model
,” J. Chem. Phys.
131
(2
), 024501
(2009
).50.
T. E.
Markland
and B. J.
Berne
, “Unraveling quantum mechanical effects in water using isotopic fractionation
,” Proc. Natl. Acad. Sci. U. S. A.
109
(21
), 7988
–7991
(2012
).51.
L.
Hernández de la Peña
and P. G.
Kusalik
, “Quantum effects in light and heavy liquid water: A rigid-body centroid molecular dynamics study
,” J. Chem. Phys.
121
(12
), 5992
–6002
(2004
).52.
T. F.
Miller
III and D. E.
Manolopoulos
, “Quantum diffusion in liquid water from ring polymer molecular dynamics
,” J. Chem. Phys.
123
(15
), 154504
(2005
).53.
L.
Hernández de la Peña
and P. G.
Kusalik
, “Quantum effects in liquid water and ice: Model dependence
,” J. Chem. Phys.
125
(5
), 054512
(2006
).54.
T. E.
Markland
and M.
Ceriotti
, “Nuclear quantum effects enter the mainstream
,” Nat. Rev. Chem.
2
, 0109
(2018
).55.
T. A.
Pham
, T.
Ogitsu
, E. Y.
Lau
, and E.
Schwegler
, “Structure and dynamics of aqueous solutions from PBE-based first-principles molecular dynamics simulations
,” J. Chem. Phys.
145
(15
), 154501
(2016
).56.
L.
Ruiz Pestana
, O.
Marsalek
, T. E.
Markland
, and T.
Head-Gordon
, “The quest for accurate liquid water properties from first principles
,” J. Phys. Chem. Lett.
9
(17
), 5009
–5016
(2018
).57.
M. A.
Morales
, J. R.
Gergely
, J.
McMinis
, J. M.
McMahon
, J.
Kim
, and D. M.
Ceperley
, “Quantum Monte Carlo benchmark of exchange-correlation functionals for bulk water
,” J. Chem. Theory Comput.
10
(6
), 2355
–2362
(2014
).58.
J. P.
Perdew
, “Climbing the ladder of density functional approximations
,” MRS Bull.
38
(9
), 743
(2013
).59.
M. G.
Medvedev
, I. S.
Bushmarinov
, J.
Sun
, J. P.
Perdew
, and K. A.
Lyssenko
, “Density functional theory is straying from the path toward the exact functional
,” Science
355
(6320
), 49
–52
(2017
).60.
J. P.
Perdew
, A.
Ruzsinszky
, J.
Tao
, V. N.
Staroverov
, G. E.
Scuseria
, and G. I.
Csonka
, “Prescription for the design and selection of density functional approximations: More constraint satisfaction with fewer fits
,” J. Chem. Phys.
123
(6
), 062201
(2005
).61.
J.
Sun
, A.
Ruzsinszky
, and J. P.
Perdew
, “Strongly constrained and appropriately normed semilocal density functional
,” Phys. Rev. Lett.
115
(3
), 036402
(2015
).62.
J.
Sun
, R. C.
Remsing
, Y.
Zhang
, Z.
Sun
, A.
Ruzsinszky
, H.
Peng
, Z.
Yang
, A.
Paul
, U.
Waghmare
, X.
Wu
, M. L.
Klein
, and J. P.
Perdew
, “Accurate first-principles structures and energies of diversely bonded systems from an efficient density functional
,” Nat. Chem.
8
, 831
(2016
).63.
A.
Tkatchenko
and M.
Scheffler
, “Accurate molecular van der Waals interactions from ground-state electron density and free-atom reference data
,” Phys. Rev. Lett.
102
(7
), 073005
(2009
).64.
W.
Dawson
and F.
Gygi
, “Equilibration and analysis of first-principles molecular dynamics simulations of water
,” J. Chem. Phys.
148
(12
), 124501
(2018
).65.
G.
Pranami
and M. H.
Lamm
, “Estimating error in diffusion coefficients derived from molecular dynamics simulations
,” J. Chem. Theory Comput.
11
(10
), 4586
–4592
(2015
).66.
N.
Luehr
, T. E.
Markland
, and T. J.
Martínez
, “Multiple time step integrators in ab initio molecular dynamics
,” J. Chem. Phys.
140
(8
), 084116
(2014
).67.
O.
Marsalek
and T. E.
Markland
, “Ab initio molecular dynamics with nuclear quantum effects at classical cost: Ring polymer contraction for density functional theory
,” J. Chem. Phys.
144
(5
), 054112
(2016
).68.
M.
Ceriotti
, G. A. R.
Brain
, O.
Riordan
, and D. E.
Manolopoulos
, “The inefficiency of re-weighted sampling and the curse of system size in high-order path integration
,” Proc. R. Soc. A
468
(2137
), 2
–17
(2012
).69.
T. M.
Yamamoto
, “Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators
,” J. Chem. Phys.
123
(10
), 104101
(2005
).70.
S.
Jang
, S.
Jang
, and G. A.
Voth
, “Applications of higher order composite factorization schemes in imaginary time path integral simulations
,” J. Chem. Phys.
115
(17
), 7832
–7842
(2001
).71.
V.
Kapil
, J.
Behler
, and M.
Ceriotti
, “High order path integrals made easy
,” J. Chem. Phys.
145
(23
), 234103
(2016
).72.
I.
Poltavsky
and A.
Tkatchenko
, “Modeling quantum nuclei with perturbed path integral molecular dynamics
,” Chem. Sci.
7
(2
), 1368
–1372
(2016
).73.
J. E.
Cuervo
, P.-N.
Roy
, and M.
Boninsegni
, “Path integral ground state with a fourth-order propagator: Application to condensed helium
,” J. Chem. Phys.
122
(11
), 114504
(2005
).74.
M.
Ceriotti
, D. E.
Manolopoulos
, and M.
Parrinello
, “Accelerating the convergence of path integral dynamics with a generalized Langevin equation
,” J. Chem. Phys.
134
(8
), 084104
(2011
).75.
M.
Ceriotti
and D. E.
Manolopoulos
, “Efficient first-principles calculation of the quantum kinetic energy and momentum distribution of nuclei
,” Phys. Rev. Lett.
109
(10
), 100604
(2012
).76.
Y.
Yao
and Y.
Kanai
, “Plane-wave pseudopotential implementation and performance of SCAN meta-GGA exchange-correlation functional for extended systems
,” J. Chem. Phys.
146
(22
), 224105
(2017
).77.
T.
Morawietz
, Efficient Simulations of Water with Ab Initio Accuracy
Ph.D. Dissertation (Ruhr University Bochum, Bochum
, 2016
).78.
T.
Morawietz
and J.
Behler
, “A density-functional theory-based neural network potential for water clusters including van der Waals corrections
,” J. Phys. Chem. A
117
(32
), 7356
–7366
(2013
).79.
T.
Morawietz
, V.
Sharma
, and J.
Behler
, “A neural network potential-energy surface for the water dimer based on environment-dependent atomic energies and charges
,” J. Chem. Phys.
136
(6
), 064103
(2012
).80.
Y.
Yao
, Advancing Molecular Dynamics Simulations of Aqueous Ionic Solutions
(The University of North Carolina at Chapel Hill
, 2018
).81.
M.
Rossi
, M.
Ceriotti
, and D. E.
Manolopoulos
, “How to remove the spurious resonances from ring polymer molecular dynamics
,” J. Chem. Phys.
140
(23
), 234116
(2014
).82.
M.
Rossi
, H.
Liu
, F.
Paesani
, J.
Bowman
, and M.
Ceriotti
, “Communication: On the consistency of approximate quantum dynamics simulation methods for vibrational spectra in the condensed phase
,” J. Chem. Phys.
141
(18
), 181101
(2014
).83.
J.
Cao
and G. A.
Voth
, “The formulation of quantum statistical mechanics based on the Feynman path centroid density. II. Dynamical properties
,” J. Chem. Phys.
100
(7
), 5106
–5117
(1994
).84.
S.
Jang
and G. A.
Voth
, “A derivation of centroid molecular dynamics and other approximate time evolution methods for path integral centroid variables
,” J. Chem. Phys.
111
(6
), 2371
–2384
(1999
).85.
I. R.
Craig
and D. E.
Manolopoulos
, “Quantum statistics and classical mechanics: Real time correlation functions from ring polymer molecular dynamics
,” J. Chem. Phys.
121
(8
), 3368
–3373
(2004
).86.
S.
Habershon
, D. E.
Manolopoulos
, T. E.
Markland
, and T. F.
Miller
III, “Ring-polymer molecular dynamics: Quantum effects in chemical dynamics from classical trajectories in an extended phase space
,” Annu. Rev. Phys. Chem.
64
(1
), 387
–413
(2013
).87.
N.
Artrith
and A.
Urban
, “An implementation of artificial neural-network potentials for atomistic materials simulations: Performance for TiO2
,” Comput. Mater. Sci.
114
, 135
–150
(2016
).88.
R.
Car
and M.
Parrinello
, “Unified approach for molecular dynamics and density-functional theory
,” Phys. Rev. Lett.
55
(22
), 2471
–2474
(1985
).89.
A.
Hjorth Larsen
, J.
Jørgen Mortensen
, J.
Blomqvist
, I. E.
Castelli
, R.
Christensen
, M.
Dułak
, J.
Friis
, M. N.
Groves
, B.
Hammer
, C.
Hargus
, E. D.
Hermes
, P. C.
Jennings
, P.
Bjerre Jensen
, J.
Kermode
, J. R.
Kitchin
, E.
Leonhard Kolsbjerg
, J.
Kubal
, K.
Kaasbjerg
, S.
Lysgaard
, J.
Bergmann Maronsson
, T.
Maxson
, T.
Olsen
, L.
Pastewka
, A.
Peterson
, C.
Rostgaard
, J.
Schiøtz
, O.
Schütt
, M.
Strange
, K. S.
Thygesen
, T.
Vegge
, L.
Vilhelmsen
, M.
Walter
, Z.
Zeng
, and K. W.
Jacobsen
, “The atomic simulation environment—A Python library for working with atoms
,” J. Phys.: Condens. Matter
29
(27
), 273002
(2017
).90.
M.
Ceriotti
, J.
More
, and D. E.
Manolopoulos
, “i-PI: A Python interface for ab initio path integral molecular dynamics simulations
,” Comput. Phys. Commun.
185
(3
), 1019
–1026
(2014
).91.
M.
Ceriotti
, M.
Parrinello
, T. E.
Markland
, and D. E.
Manolopoulos
, “Efficient stochastic thermostatting of path integral molecular dynamics
,” J. Chem. Phys.
133
(12
), 124104
(2010
).92.
H. J. C.
Berendsen
, J. R.
Grigera
, and T. P.
Straatsma
, “The missing term in effective pair potentials
,” J. Phys. Chem.
91
(24
), 6269
–6271
(1987
).93.
D.
Van Der Spoel
, E.
Lindahl
, B.
Hess
, G.
Groenhof
, A. E.
Mark
, and H. J. C.
Berendsen
, “GROMACS: Fast, flexible, and free
,” J. Comput. Chem.
26
(16
), 1701
–1718
(2005
).94.
A. K.
Soper
and C. J.
Benmore
, “Quantum differences between heavy and light water
,” Phys. Rev. Lett.
101
(6
), 065502
(2008
).95.
J. A.
Morrone
, V.
Srinivasan
, D.
Sebastiani
, and R.
Car
, “Proton momentum distribution in water: An open path integral molecular dynamics study
,” J. Chem. Phys.
126
(23
), 234504
(2007
).96.
J.
Wiktor
, F.
Ambrosio
, and A.
Pasquarello
, “Note: Assessment of the SCAN+rVV10 functional for the structure of liquid water
,” J. Chem. Phys.
147
(21
), 216101
(2017
).97.
M. D.
LaCount
and F.
Gygi
, “Ensemble first-principles molecular dynamics simulations of water using the SCAN meta-GGA density functional
,” J. Chem. Phys.
151
(16
), 164101
(2019
).98.
P.
Gasparotto
, A. A.
Hassanali
, and M.
Ceriotti
, “Probing defects and correlations in the hydrogen-bond network of ab initio water
,” J. Chem. Theory Comput.
12
(4
), 1953
–1964
(2016
).99.
G. R.
Medders
, V.
Babin
, and F.
Paesani
, “Development of a “first-principles” water potential with flexible monomers. III. Liquid phase properties
,” J. Chem. Theory Comput.
10
(8
), 2906
–2910
(2014
).100.
D. H.
Brookes
and T.
Head-Gordon
, “Family of oxygen–oxygen radial distribution functions for water
,” J. Phys. Chem. Lett.
6
(15
), 2938
–2943
(2015
).101.
L. B.
Skinner
, C.
Huang
, D.
Schlesinger
, L. G. M.
Pettersson
, A.
Nilsson
, and C. J.
Benmore
, “Benchmark oxygen-oxygen pair-distribution function of ambient water from x-ray diffraction measurements with a wide Q-range
,” J. Chem. Phys.
138
(7
), 074506
(2013
).102.
L. B.
Skinner
, C. J.
Benmore
, J. C.
Neuefeind
, and J. B.
Parise
, “The structure of water around the compressibility minimum
,” J. Chem. Phys.
141
(21
), 214507
(2014
).103.
A. K.
Soper
, “The radial distribution functions of water as derived from radiation total scattering experiments: Is there anything we can say for sure?
,” ISRN Phys. Chem.
2013
, 1
–67
; available at https://www.hindawi.com/journals/isrn/2013/279463/ .104.
H.
Peng
, Z.-H.
Yang
, J. P.
Perdew
, and J.
Sun
, “Versatile van der Waals density functional based on a meta-generalized gradient approximation
,” Phys. Rev. X
6
(4
), 041005
(2016
).105.
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
(2
), 785
–789
(1988
).106.
F.
Paesani
, “Water: Many-body potential from first principles (from the gas to the liquid phase)
,” in Handbook of Materials Modeling: Methods: Theory and Modeling
, edited by W.
Andreoni
and S.
Yip
(Springer International Publishing
, Cham
, 2020
), pp. 635
–660
.107.
K.
Modig
, B. G.
Pfrommer
, and B.
Halle
, “Temperature-dependent hydrogen-bond geometry in liquid water
,” Phys. Rev. Lett.
90
(7
), 075502
(2003
).108.
P. S.
Tofts
, D.
Lloyd
, C. A.
Clark
, G. J.
Barker
, G. J. M.
Parker
, P.
McConville
, C.
Baldock
, and J. M.
Pope
, “Test liquids for quantitative MRI measurements of self-diffusion coefficient in vivo
,” Magn. Reson. Med.
43
(3
), 368
–374
(2000
).109.
T. E.
Markland
and D. E.
Manolopoulos
, “An efficient ring polymer contraction scheme for imaginary time path integral simulations
,” J. Chem. Phys.
129
(2
), 024105
(2008
).110.
J.
Lobaugh
and G. A.
Voth
, “A quantum model for water: Equilibrium and dynamical properties
,” J. Chem. Phys.
106
(6
), 2400
–2410
(1997
).111.
I.-C.
Yeh
and G.
Hummer
, “System-size dependence of diffusion coefficients and viscosities from molecular dynamics simulations with periodic boundary conditions
,” J. Phys. Chem. B
108
(40
), 15873
–15879
(2004
).112.
I. D.
Zaytsev
and G. G.
Aseyev
, Properties of Aqueous Solutions of Electrolytes
(CRC Press
, 1992
).113.
N.
Galamba
, “Water’s structure around hydrophobic solutes and the iceberg model
,” J. Phys. Chem. B
117
(7
), 2153
–2159
(2013
).114.
N.
Giovambattista
, P. G.
Debenedetti
, F.
Sciortino
, and H. E.
Stanley
, “Structural order in glassy water
,” Phys. Rev. E
71
(6
), 061505
(2005
).115.
M.
Paolantoni
, N. F.
Lago
, M.
Albertí
, and A.
Laganà
, “Tetrahedral ordering in water: Raman profiles and their temperature dependence
,” J. Phys. Chem. A
113
(52
), 15100
–15105
(2009
).116.
F.
Sedlmeier
, D.
Horinek
, and R. R.
Netz
, “Spatial correlations of density and structural fluctuations in liquid water: A comparative simulation study
,” J. Am. Chem. Soc.
133
(5
), 1391
–1398
(2011
).117.
Z.
Yan
, S. V.
Buldyrev
, P.
Kumar
, N.
Giovambattista
, P. G.
Debenedetti
, and H. E.
Stanley
, “Structure of the first- and second-neighbor shells of simulated water: Quantitative relation to translational and orientational order
,” Phys. Rev. E
76
(5
), 051201
(2007
).118.
A.
Luzar
and D.
Chandler
, “Hydrogen-bond kinetics in liquid water
,” Nature
379
(6560
), 55
–57
(1996
).119.
S. Y.
Willow
, X. C.
Zeng
, S. S.
Xantheas
, K. S.
Kim
, and S.
Hirata
, “Why is MP2-water “cooler” and “denser” than DFT-water?
,” J. Phys. Chem. Lett.
7
(4
), 680
–684
(2016
).120.
M.
Del Ben
, J.
Hutter
, and J.
VandeVondele
, “Probing the structural and dynamical properties of liquid water with models including non-local electron correlation
,” J. Chem. Phys.
143
(5
), 054506
(2015
).121.
H.-S.
Tan
, I. R.
Piletic
, and M. D.
Fayer
, “Orientational dynamics of water confined on a nanometer length scale in reverse micelles
,” J. Chem. Phys.
122
(17
), 174501
(2005
).122.
Y. L. A.
Rezus
and H. J.
Bakker
, “On the orientational relaxation of HDO in liquid water
,” J. Chem. Phys.
123
(11
), 114502
(2005
).123.
C. P.
Lawrence
and J. L.
Skinner
, “Vibrational spectroscopy of HOD in liquid D2O. III. Spectral diffusion, and hydrogen-bonding and rotational dynamics
,” J. Chem. Phys.
118
(1
), 264
–272
(2003
).124.
K.
Winkler
, J.
Lindner
, H.
Bürsing
, and P.
Vöhringer
, “Ultrafast Raman-induced Kerr-effect of water: Single molecule versus collective motions
,” J. Chem. Phys.
113
(11
), 4674
–4682
(2000
).© 2020 Author(s).
2020
Author(s)
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