Structures of liquid water are controversial not only in supercooled polyamorphism but also in stable bulk liquids in the high temperature and pressure range. Several experimental studies in bulk liquid have assumed the existence of three different liquid water structures. If indeed the three liquid water structures are different, they should be clearly distinguished by some measure other than density that characterizes the difference in structural order. In this study, whether the three different bulk liquid water structures are real or not is numerically verified based on molecular simulations using a reliable water molecular model. Since these liquid water structures have been suggested to be related to three different crystal structures (i.e., ice Ih, III, and V), liquid structures are sampled from the vicinity of the ice Ih-liquid coexistence point, the ice III-V-liquid triple point, and the ice V-VI-liquid triple point, respectively. An attempt is made to introduce local order parameters (LOPs) as an indicator to distinguish these structures. A fast and exhaustive LOP search is performed by the molecular assembly structure learning package for Identifying order parameters. The selected LOP distinguishes the molecular structures of three different stable liquid waters with high accuracy, providing numerical evidence that these structural orders differ from each other. Furthermore, regions of the liquid water structures are drawn on a phase diagram using the LOP, demonstrating their consistency with experimental studies.

1.
P.
Gallo
,
K.
Amann-Winkel
,
C. A.
Angell
,
M. A.
Anisimov
,
F.
Caupin
,
C.
Chakravarty
,
E.
Lascaris
,
T.
Loerting
,
A. Z.
Panagiotopoulos
,
J.
Russo
et al, “
Water: A tale of two liquids
,”
Chem. Rev.
116
,
7463
7500
(
2016
).
2.
E.
Brini
,
C. J.
Fennell
,
M.
Fernandez-Serra
,
B.
Hribar-Lee
,
M.
Luksic
, and
K. A.
Dill
, “
How water’s properties are encoded in its molecular structure and energies
,”
Chem. Rev.
117
,
12385
12414
(
2017
).
3.
H.
Tanaka
, “
Simple physical model of liquid water
,”
J. Chem. Phys.
112
,
799
809
(
2000
).
4.
R.
Shi
and
H.
Tanaka
, “
The anomalies and criticality of liquid water
,”
Proc. Natl. Acad. Sci. U. S. A.
117
,
26591
26599
(
2020
).
5.
P. H.
Poole
,
F.
Sciortino
,
U.
Essmann
, and
H. E.
Stanley
, “
Phase behaviour of metastable water
,”
Nature
360
,
324
328
(
1992
).
6.
O.
Mishima
,
L.
Calvert
, and
E.
Whalley
, “
‘Melting ice’ I at 77 K and 10 kbar: A new method of making amorphous solids
,”
Nature
310
,
393
395
(
1984
).
7.
O.
Mishima
, “
Reversible first-order transition between two H2O amorphs at ∼0.2 GPa and ∼135 K
,”
J. Chem. Phys.
100
,
5910
5912
(
1994
).
8.
O.
Mishima
, “
Relationship between melting and amorphization of ice
,”
Nature
384
,
546
549
(
1996
).
9.
H.
Tanaka
, “
A self-consistent phase diagram for supercooled water
,”
Nature
380
,
328
330
(
1996
).
10.
J. C.
Palmer
,
F.
Martelli
,
Y.
Liu
,
R.
Car
,
A. Z.
Panagiotopoulos
, and
P. G.
Debenedetti
, “
Metastable liquid–liquid transition in a molecular model of water
,”
Nature
510
,
385
388
(
2014
).
11.
J. C.
Palmer
,
P. H.
Poole
,
F.
Sciortino
, and
P. G.
Debenedetti
, “
Advances in computational studies of the liquid–liquid transition in water and water-like models
,”
Chem. Rev.
118
,
9129
9151
(
2018
).
12.
P. G.
Debenedetti
,
F.
Sciortino
, and
G. H.
Zerze
, “
Second critical point in two realistic models of water
,”
Science
369
,
289
292
(
2020
).
13.
K.
Bagchi
,
S.
Balasubramanian
, and
M. L.
Klein
, “
The effects of pressure on structural and dynamical properties of associated liquids: Molecular dynamics calculations for the extended simple point charge model of water
,”
J. Chem. Phys.
107
,
8561
8567
(
1997
).
14.
F. W.
Starr
,
M.-C.
Bellissent-Funel
, and
H. E.
Stanley
, “
Structure of supercooled and glassy water under pressure
,”
Phys. Rev. E
60
,
1084
(
1999
).
15.
A. M.
Saitta
and
F.
Datchi
, “
Structure and phase diagram of high-density water: The role of interstitial molecules
,”
Phys. Rev. E
67
,
020201
(
2003
).
16.
T.
Kawamoto
,
S.
Ochiai
, and
H.
Kagi
, “
Changes in the structure of water deduced from the pressure dependence of the Raman OH frequency
,”
J. Chem. Phys.
120
,
5867
5870
(
2004
).
17.
A. K.
Soper
and
M. A.
Ricci
, “
Structures of high-density and low-density water
,”
Phys. Rev. Lett.
84
,
2881
(
2000
).
18.
T.
Strässle
,
A.
Saitta
,
Y. L.
Godec
,
G.
Hamel
,
S.
Klotz
,
J.
Loveday
, and
R.
Nelmes
, “
Structure of dense liquid water by neutron scattering to 6.5 GPa and 670 K
,”
Phys. Rev. Lett.
96
,
067801
(
2006
).
19.
C.
Huang
,
K. T.
Wikfeldt
,
T.
Tokushima
,
D.
Nordlund
,
Y.
Harada
,
U.
Bergmann
,
M.
Niebuhr
,
T.
Weiss
,
Y.
Horikawa
,
M.
Leetmaa
et al, “
The inhomogeneous structure of water at ambient conditions
,”
Proc. Natl. Acad. Sci. U. S. A.
106
,
15214
15218
(
2009
).
20.
F.
Li
,
Q.
Cui
,
Z.
He
,
T.
Cui
,
J.
Zhang
,
Q.
Zhou
,
G.
Zou
, and
S.
Sasaki
, “
High pressure-temperature Brillouin study of liquid water: Evidence of the structural transition from low-density water to high-density water
,”
J. Chem. Phys.
123
,
174511
(
2005
).
21.
S.
Fanetti
,
A.
Lapini
,
M.
Pagliai
,
M.
Citroni
,
M.
Di Donato
,
S.
Scandolo
,
R.
Righini
, and
R.
Bini
, “
Structure and dynamics of low-density and high-density liquid water at high pressure
,”
J. Phys. Chem. Lett.
5
,
235
240
(
2014
).
22.
Y.
Koga
,
P.
Westh
,
K.
Yoshida
,
A.
Inaba
, and
Y.
Nakazawa
, “
Gradual crossover in molecular organization of stable liquid H2O at moderately high pressure and temperature
,”
AIP Adv.
4
,
097116
(
2014
).
23.
H.
Tanaka
, “
General view of a liquid-liquid phase transition
,”
Phys. Rev. E
62
,
6968
(
2000
).
24.
H.
Tanaka
, “
Bond orientational order in liquids: Towards a unified description of water-like anomalies, liquid-liquid transition, glass transition, and crystallization: Bond orientational order in liquids
,”
Eur. Phys. J. E
35
,
113
(
2012
).
25.
H.
Tanaka
, “
Liquid–liquid transition and polyamorphism
,”
J. Chem. Phys.
153
,
130901
(
2020
).
26.
P. J.
Steinhardt
,
D. R.
Nelson
, and
M.
Ronchetti
, “
Bond-orientational order in liquids and glasses
,”
Phys. Rev. B
28
,
784
(
1983
).
27.
W.
Lechner
and
C.
Dellago
, “
Accurate determination of crystal structures based on averaged local bond order parameters
,”
J. Chem. Phys.
129
,
114707
(
2008
).
28.
J. D.
Honeycutt
and
H. C.
Andersen
, “
Molecular dynamics study of melting and freezing of small Lennard-Jones clusters
,”
J. Phys. Chem.
91
,
4950
4963
(
1987
).
29.
E.
Maras
,
O.
Trushin
,
A.
Stukowski
,
T.
Ala-Nissila
, and
H.
Jonsson
, “
Global transition path search for dislocation formation in Ge on Si(001)
,”
Comput. Phys. Commun.
205
,
13
21
(
2016
).
30.
A.
Radhi
and
K.
Behdinan
, “
Identification of crystal structures in atomistic simulation by predominant common neighborhood analysis
,”
Comput. Mater. Sci.
126
,
182
190
(
2017
).
31.
G.
Ackland
and
A.
Jones
, “
Applications of local crystal structure measures in experiment and simulation
,”
Phys. Rev. B
73
,
054104
(
2006
).
32.
C. L.
Kelchner
,
S.
Plimpton
, and
J.
Hamilton
, “
Dislocation nucleation and defect structure during surface indentation
,”
Phys. Rev. B
58
,
11085
(
1998
).
33.
A.
Stukowski
, “
Structure identification methods for atomistic simulations of crystalline materials
,”
Modell. Simul. Mater. Sci. Eng.
20
,
045021
(
2012
).
34.
A. P.
Bartók
,
R.
Kondor
, and
G.
Csányi
, “
On representing chemical environments
,”
Phys. Rev. B
87
,
184115
(
2013
).
35.
A.
Seko
,
A.
Togo
, and
I.
Tanaka
, “
Descriptors for machine learning of materials data
,” in
Nanoinformatics
(
Springer
,
Singapore
,
2018
), pp.
3
23
.
36.
H.
Doi
,
K. Z.
Takahashi
,
K.
Tagashira
,
J.-i.
Fukuda
, and
T.
Aoyagi
, “
Machine learning-aided analysis for complex local structure of liquid crystal polymers
,”
Sci. Rep.
9
,
16370
(
2019
).
37.
P.-L.
Chau
and
A.
Hardwick
, “
A new order parameter for tetrahedral configurations
,”
Mol. Phys.
93
,
511
518
(
1998
).
38.
E.
Duboué-Dijon
and
D.
Laage
, “
Characterization of the local structure in liquid water by various order parameters
,”
J. Phys. Chem. B
119
,
8406
8418
(
2015
).
39.
E. B.
Moore
,
E.
De La Llave
,
K.
Welke
,
D. A.
Scherlis
, and
V.
Molinero
, “
Freezing, melting and structure of ice in a hydrophilic nanopore
,”
Phys. Chem. Chem. Phys.
12
,
4124
4134
(
2010
).
40.
M.
Fitzner
,
G. C.
Sosso
,
S. J.
Cox
, and
A.
Michaelides
, “
Ice is born in low-mobility regions of supercooled liquid water
,”
Proc. Natl. Acad. Sci. U. S. A.
116
,
2009
2014
(
2019
).
41.
K. Z.
Takahashi
, “
Molecular cluster analysis using local order parameters selected by machine learning
,”
Phys. Chem. Chem. Phys.
25
,
658
672
(
2023
).
42.
K. Z.
Takahashi
and
M.
Hiratsuka
, “
Local order parameters classifying water networks of ice and cyclopropane clathrate hydrates
,”
Cryst. Growth Des.
23
,
4815
(
2023
).
43.
H.
Doi
,
K. Z.
Takahashi
, and
T.
Aoyagi
, “
Mining of effective local order parameters for classifying crystal structures: A machine learning study
,”
J. Chem. Phys.
152
,
214501
(
2020
).
44.
H.
Doi
,
K. Z.
Takahashi
, and
T.
Aoyagi
, “
Searching local order parameters to classify water structures of ice Ih, Ic, and liquid
,”
J. Chem. Phys.
154
,
164505
(
2021
).
45.
H.
Doi
,
K. Z.
Takahashi
, and
T.
Aoyagi
, “
Searching for local order parameters to classify water structures at triple points
,”
J. Comput. Chem.
42
,
1720
1727
(
2021
).
46.
H.
Doi
,
K. Z.
Takahashi
, and
T.
Aoyagi
, “
Mining of effective local order parameters to classify ice polymorphs
,”
J. Phys. Chem. A
125
,
9518
9526
(
2021
).
47.
K. Z.
Takahashi
,
T.
Aoyagi
, and
J.-i.
Fukuda
, “
Multistep nucleation of anisotropic molecules
,”
Nat. Commun.
12
,
5278
(
2021
).
48.
F.
Takano
,
M.
Hiratsuka
,
T.
Aoyagi
, and
K. Z.
Takahashi
, “
Local order parameter that distinguishes crystalline and amorphous portions in polymer crystal lamellae
,”
J. Chem. Phys.
157
,
174507
(
2022
).
49.
J. L. F.
Abascal
and
C.
Vega
, “
A general purpose model for the condensed phases of water: TIP4P/2005
,”
J. Chem. Phys.
123
,
234505
(
2005
).
50.
U.
Essmann
,
L.
Perera
,
M. L.
Berkowitz
,
T.
Darden
,
H.
Lee
, and
L. G.
Pedersen
, “
A smooth particle mesh Ewald method
,”
J. Chem. Phys.
103
,
8577
8593
(
1995
).
51.
W. C.
Swope
,
H. C.
Andersen
,
P. H.
Berens
, and
K. R.
Wilson
, “
A computer simulation method for the calculation of equilibrium constants for the formation of physical clusters of molecules: Application to small water clusters
,”
J. Chem. Phys.
76
,
637
649
(
1982
).
52.
M. J.
Abraham
,
T.
Murtola
,
R.
Schulz
,
S.
Páll
,
J. C.
Smith
,
B.
Hess
, and
E.
Lindahl
, “
GROMACS: High performance molecular simulations through multi-level parallelism from laptops to supercomputers
,”
SoftwareX
1–2
,
19
25
(
2015
).
53.
F.
Pedregosa
,
G.
Varoquaux
,
A.
Gramfort
,
V.
Michel
,
B.
Thirion
,
O.
Grisel
,
M.
Blondel
,
P.
Prettenhofer
,
R.
Weiss
,
V.
Dubourg
,
J.
Vanderplas
,
A.
Passos
,
D.
Cournapeau
,
M.
Brucher
,
M.
Perrot
, and
E.
Duchesnay
, “
Scikit-learn: Machine learning in Python
,”
J. Mach. Learn. Res.
12
,
2825
2830
(
2011
); arXiv:1201.0490.
54.
A.
Jain
and
D.
Zongker
, “
Feature selection: Evaluation, application, and small sample performance
,”
IEEE Trans. Pattern Anal. Mach. Intell.
19
,
153
158
(
1997
).
55.
P. M.
Chaikin
,
T. C.
Lubensky
, and
T. A.
Witten
,
Principles of Condensed Matter Physics
(
Cambridge University Press
,
Cambridge
,
1995
), Vol.
10
.
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