Precise prediction of phase diagrams in molecular dynamics simulations is challenging due to the simultaneous need for long time and large length scales and accurate interatomic potentials. We show that thermodynamic integration from low-cost force fields to neural network potentials trained using density-functional theory (DFT) enables rapid first-principles prediction of the solid–liquid phase boundary in the model salt NaCl. We use this technique to compare the accuracy of several DFT exchange–correlation functionals for predicting the NaCl phase boundary and find that the inclusion of dispersion interactions is critical to obtain good agreement with experiment. Importantly, our approach introduces a method to predict solid–liquid phase boundaries for any material at an ab initio level of accuracy, with the majority of the computational cost at the level of classical potentials.

1.
C.
Le Brun
,
J. Nucl. Mater.
360
,
1
(
2007
).
2.
H.
Zhang
,
J.
Baeyens
,
J.
Degreve
, and
G.
Caceres
,
Renewable Sustainable Energy Rev.
22
,
466
(
2013
).
3.
W.
Grimes
,
Nucl. Appl. Technol.
8
,
137
(
1970
).
4.
A.
Kroupa
,
Comput. Mater. Sci.
66
,
3
(
2013
).
5.
N.
Metropolis
,
A.
Rosenbluth
,
M.
Rosenbluth
,
A.
Teller
, and
E.
Teller
,
J. Chem. Phys.
21
,
1087
(
1953
).
6.
B. J.
Alder
and
T. E.
Wainwright
,
J. Chem. Phys.
27
,
1208
(
1957
).
7.
L.
Verlet
,
Phys. Rev.
159
,
98
(
1967
).
8.
P.
Hohenberg
and
W.
Kohn
,
Phys. Rev.
136
,
B864
(
1964
).
9.
W.
Kohn
and
L. J.
Sham
,
Phys. Rev.
140
,
A1133
(
1965
).
10.
D. M.
Eike
,
J. F.
Brennecke
, and
E. J.
Maginn
,
J. Chem. Phys.
122
,
014115
(
2005
).
11.
J.
Anwar
,
D.
Frenkel
, and
M. G.
Noro
,
J. Chem. Phys.
118
,
728
(
2003
).
12.
E. J.
Meijer
and
F.
El Azhar
,
J. Chem. Phys.
106
,
4678
(
1997
).
13.
J.
Behler
,
J. Chem. Phys.
145
,
170901
(
2016
).
14.
R.
Lot
,
F.
Pellegrini
,
Y.
Shaidu
, and
E.
Kucukbenli
,
Comput. Phys. Commun.
256
,
107402
(
2020
); arXiv:1907.03055.
15.
K.
Lee
,
D.
Yoo
,
W.
Jeong
, and
S.
Han
,
Comput. Phys. Commun.
242
,
95
(
2019
).
16.
H.
Wang
,
L.
Zhang
,
J.
Han
, and
E.
Weinan
,
Comput. Phys. Commun.
228
,
178
(
2018
).
17.
S.-C.
Lee
,
Y.
Zhai
,
Z.
Li
,
N. P.
Walter
,
M.
Rose
,
B. J.
Heuser
, and
Y.
Z
,
J. Phys. Chem. B
125
,
10562
(
2021
).
18.
W.
Liang
,
G.
Lu
, and
J.
Yu
,
ACS Appl. Mater. Interfaces
13
,
4034
(
2021
).
19.
W.
Liang
,
G.
Lu
, and
J.
Yu
,
J. Mater. Sci. Technol.
75
,
78
(
2021
).
20.
T.
Xu
,
X.
Li
,
L.
Guo
,
F.
Wang
, and
Z.
Tang
,
Sol. Energy
209
,
568
(
2020
).
21.
Q.-J.
Li
,
E.
Küçükbenli
,
S.
Lam
,
B.
Khaykovich
,
E.
Kaxiras
, and
J.
Li
,
Cell Rep. Phys. Sci.
2
,
100359
(
2021
).
22.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
,
2nd ed.
(
Academic Press
,
2002
).
23.
J. G.
Kirkwood
,
J. Chem. Phys.
3
,
300
(
1935
).
24.
I. A.
Kruglov
,
A.
Yanilkin
,
A. R.
Oganov
, and
P.
Korotaev
,
Phys. Rev. B
100
,
174104
(
2019
).
25.
R.
Jinnouchi
,
F.
Karsai
, and
G.
Kresse
,
Phys. Rev. B
101
,
060201
(
2020
).
26.
S.
Fukushima
,
E.
Ushijima
,
H.
Kumazoe
,
A.
Koura
,
F.
Shimojo
,
K.
Shimamura
,
M.
Misawa
,
R. K.
Kalia
,
A.
Nakano
, and
P.
Vashishta
,
Phys. Rev. B
100
,
214108
(
2019
).
27.
S.
Plimpton
,
J. Comput. Phys.
117
,
1
(
1995
).
28.
F. G.
Fumi
and
M. P.
Tosi
,
J. Phys. Chem. Solids
25
,
31
(
1964
).
29.
C. J.
Fennell
and
J. D.
Gezelter
,
J. Chem. Phys.
124
,
234104
(
2006
).
30.
J.
Lu
,
S.
Yang
,
G.
Pan
,
J.
Ding
,
S.
Liu
, and
W.
Wang
,
Energies
14
,
746
(
2021
).
31.
D.
Rumelhart
,
G.
Hinton
, and
R.
Williams
,
Nature
323
,
533
(
1986
).
32.
J.
Behler
,
J. Chem. Phys.
134
,
074106
(
2011
).
33.
A.
Bartok
,
R.
Kondor
, and
G.
Csanyi
,
Phys. Rev. B
87
,
184115
(
2013
).
34.
A.
Bartok
,
M.
Payne
,
R.
Kondor
, and
G.
Csanyi
,
Phys. Rev. Lett.
104
,
136403
(
2010
).
35.
M.
Rupp
,
A.
Tkatchenko
,
K.-R.
Muller
, and
O. A.
von Lilienfeld
,
Phys. Rev. Lett.
108
,
058301
(
2012
).
36.
R.
Drautz
,
Phys. Rev. B
99
,
014104
(
2019
).
37.
W.
Jeong
,
K.
Lee
,
D.
Yoo
,
D.
Lee
, and
S.
Han
,
J. Phys. Chem. C
122
,
22790
(
2018
).
38.
J. P.
Perdew
,
K.
Burke
, and
M.
Ernzerhof
,
Phys. Rev. Lett.
77
,
3865
(
1996
).
39.
J. P.
Perdew
,
A.
Ruzsinszky
,
G. I.
Csonka
,
O. A.
Vydrov
,
G. E.
Scuseria
,
L. A.
Constantin
,
X.
Zhou
, and
K.
Burke
,
Phys. Rev. Lett.
100
,
136406
(
2008
).
40.
S.
Grimme
,
J. Comput. Chem.
27
,
1787
(
2006
).
41.
S.
Grimme
,
J.
Antony
,
S.
Ehrlich
, and
H.
Krieg
,
J. Chem. Phys.
132
,
154104
(
2010
).
42.
S.
Roy
,
M.
Brehm
,
S.
Sharma
,
F.
Wu
,
D. S.
Maltsev
,
P.
Halstenberg
,
L. C.
Gallington
,
S. M.
Mahurin
,
S.
Dai
,
A. S.
Ivanov
,
C. J.
Margulis
, and
V. S.
Bryantsev
,
J. Phys. Chem. B
125
,
5971
(
2021
).
43.
R.
Sundararaman
,
K.
Letchworth-Weaver
,
K. A.
Schwarz
,
D.
Gunceler
,
Y.
Ozhabes
, and
T. A.
Arias
,
SoftwareX
6
,
278
(
2017
).
44.
K. F.
Garrity
,
J. W.
Bennett
,
K. M.
Rabe
, and
D.
Vanderbilt
,
Comput. Mater. Sci.
81
,
446
(
2014
).
45.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulations of Liquids
,
2nd ed.
(
Oxford University Press
,
2017
).
46.
P. J.
Steinhardt
,
D. R.
Nelson
, and
M.
Ronchetti
,
Phys. Rev. B
28
,
784
(
1983
).
47.
C.
Chipot
and
A.
Pohorille
,
Free Energy Calculations: Theory and Applications in Chemistry and Biology
,
Springer Series in Chemical Physics
(
Springer
,
2007
), Vol.
86
.
48.
R.
Clausius
,
Ann. Phys. Phys. Chem.
155
,
500
(
1850
).
49.
J. L.
Aragones
,
E.
Sanz
,
C.
Valeriani
, and
C.
Vega
,
J. Chem. Phys.
137
,
104507
(
2012
).
50.
R. S.
DeFever
,
H.
Wang
,
Y.
Zhang
, and
E. J.
Maginn
,
J. Chem. Phys.
153
,
011101
(
2020
).
51.
D.
Kofke
,
Mol. Phys.
78
,
1331
(
1993
).
52.
American Institute of Physics Handbook
,
3rd ed.
, edited by
D. E.
Gray
(
McGraw-Hill
,
New York
,
1972
).
53.
P.
Brown
, A Level Born Haber Cycle Calculations Sodium Chloride Magnesium Chloride Magnesium Oxide Sodium Oxide Enthalpy Level Diagrams KS5 GCE Chemistry Revision Notes (
2000
).
54.
A.
Kirshenbaum
,
J.
Cahill
,
P.
McGonigal
, and
A.
Grosse
,
J. Inorg. Nucl. Chem.
24
,
1287
(
1962
).
55.
F.
Ullmann
,
W.
Gerhartz
,
Y. S.
Yamamoto
,
F. T.
Campbell
,
R.
Pfefferkorn
, and
J. F.
Rounsaville
,
Ullmann’s Encyclopedia of Industrial Chemistry
,
5th ed.
(
VCH
,
Weinheim, Federal Republic of Germany
,
1985
).

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