Ice nucleation plays a significant role in a large number of natural and technological processes, but it is challenging to investigate experimentally because of the small time scales (ns) and short length scales (nm) involved. On the other hand, conventional molecular simulations struggle to cope with the relatively long time scale required for critical ice nuclei to form. One way to tackle this issue is to take advantage of free energy or path sampling techniques. Unfortunately, these are computationally costly. Seeded molecular dynamics is a much less demanding alternative that has been successfully applied already to study the homogeneous freezing of water. However, in the case of heterogeneous ice nucleation, nature’s favourite route to form ice, an array of suitable interfaces between the ice seeds and the substrate of interest has to be built, and this is no trivial task. In this paper, we present a Heterogeneous SEEDing (HSEED) approach which harnesses a random structure search framework to tackle the ice-substrate challenge, thus enabling seeded molecular dynamics simulations of heterogeneous ice nucleation on crystalline surfaces. We validate the HSEED framework by investigating the nucleation of ice on (i) model crystalline surfaces, using the coarse-grained mW model, and (ii) cholesterol crystals, employing the fully atomistic TIP4P/ice water model. We show that the HSEED technique yields results in excellent agreement with both metadynamics and forward flux sampling simulations. Because of its computational efficiency, the HSEED method allows one to rapidly assess the ice nucleation ability of whole libraries of crystalline substrates—a long-awaited computational development in, e.g., atmospheric science.

1.
P.
Mazur
, “
Cryobiology: The freezing of biological systems
,”
Science
168
(
3934
),
939
949
(
1970
).
2.
A.
Lintunen
,
T.
Hölttä
, and
M.
Kulmala
, “
Anatomical regulation of ice nucleation and cavitation helps trees to survive freezing and drought stress
,”
Sci. Rep.
3
,
2031
(
2013
).
3.
K. A.
Pratt
,
P. J.
DeMott
,
J. R.
French
,
Z.
Wang
,
D. L.
Westphal
,
A. J.
Heymsfield
,
C. H.
Twohy
,
A. J.
Prenni
, and
K. A.
Prather
, “
In situ detection of biological particles in cloud ice-crystals
,”
Nat. Geosci.
2
(
6
),
398
401
(
2009
).
4.
B. J.
Murray
,
D.
O’Sullivan
,
J. D.
Atkinson
, and
M. E.
Webb
, “
Ice nucleation by particles immersed in supercooled cloud droplets
,”
Chem. Soc. Rev.
41
,
6519
6554
(
2012
).
5.
T.
Bartels-Rausch
, “
Chemistry: Ten things we need to know about ice and snow
,”
Nature
494
(
7435
),
27
29
(
2013
).
6.
R. Y.
Tam
,
C. N.
Rowley
,
I.
Petrov
,
T.
Zhang
,
N. A.
Afagh
,
T. K.
Woo
, and
R. N.
Ben
, “
Solution conformation of c-linked antifreeze glycoprotein analogues and modulation of ice recrystallization
,”
J. Am. Chem. Soc.
131
(
43
),
15745
15753
(
2009
).
7.
C. A.
Koh
, “
Towards a fundamental understanding of natural gas hydrates
,”
Chem. Soc. Rev.
31
(
3
),
157
167
(
2002
).
8.
B. J.
Murray
,
S. L.
Broadley
, and
G. J.
Morris
, “
Supercooling of water droplets in jet aviation fuel
,”
Fuel
90
(
1
),
433
435
(
2011
).
9.
G. C.
Sosso
,
J.
Chen
,
S. J.
Cox
,
M.
Fitzner
,
P.
Pedevilla
,
A.
Zen
, and
A.
Michaelides
, “
Crystal nucleation in liquids: Open questions and future challenges in molecular dynamics simulations
,”
Chem. Rev.
116
(
12
),
7078
7116
(
2016
).
10.
S. A.
Zielke
,
A. K.
Bertram
, and
G. N.
Patey
, “
A molecular mechanism of ice nucleation on model AgI surfaces
,”
J. Phys. Chem. B
119
(
29
),
9049
9055
(
2015
).
11.
X.
Zhang
,
M.
Chen
, and
M.
Fu
, “
Impact of surface nanostructure on ice nucleation
,”
J. Chem. Phys.
141
(
12
),
124709
(
2014
).
12.
A.
Reinhardt
and
J. P. K.
Doye
, “
Effects of surface interactions on heterogeneous ice nucleation for a monatomic water model
,”
J. Chem. Phys.
141
(
8
),
084501
(
2014
).
13.
G.
Fraux
and
J. P. K.
Doye
, “
Heterogeneous ice nucleation on silver-iodide-like surfaces
,”
J. Chem. Phys.
141
(
21
),
216101
(
2014
).
14.
A.
Kiselev
,
F.
Bachmann
,
P.
Pedevilla
,
S. J.
Cox
,
A.
Michaelides
,
D.
Gerthsen
, and
T.
Leisner
, “
Active sites in heterogeneous ice nucleation—the example of k-rich feldspars
,”
Science
355
(
6323
),
367
371
(
2017
).
15.
Y.
Bi
,
B.
Cao
, and
T.
Li
, “
Enhanced heterogeneous ice nucleation by special surface geometry
,”
Nat. Commun.
8
,
15372
(
2017
).
16.
L.
Lupi
,
A.
Hudait
,
B.
Peters
,
M.
Grünwald
,
R. G.
Mullen
,
A. H.
Nguyen
, and
V.
Molinero
, “
Role of stacking disorder in ice nucleation
,”
Nature
551
(
7679
),
218
222
(
2017
).
17.
A.
Hudait
and
V.
Molinero
, “
What determines the ice polymorph in clouds?
,”
J. Am. Chem. Soc.
138
(
28
),
8958
8967
(
2016
).
18.
V.
Molinero
and
E. B.
Moore
, “
Water modeled as an intermediate element between carbon and silicon
,”
J. Phys. Chem. B
113
,
4008
(
2008
).
19.
G. M.
Torrie
and
J. P.
Valleau
, “
Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling
,”
J. Comput. Phys.
23
(
2
),
187
199
(
1977
).
20.
A.
Warmflash
,
P.
Bhimalapuram
, and
A. R.
Dinner
, “
Umbrella sampling for nonequilibrium processes
,”
J. Chem. Phys.
127
(
15
),
154112
(
2007
).
21.
P. R.
Ten Wolde
,
M. J.
Ruiz-Montero
, and
D.
Frenkel
, “
Numerical calculation of the rate of crystal nucleation in a Lennard-Jones system at moderate undercooling
,”
J. Chem. Phys.
104
(
24
),
9932
9947
(
1996
).
22.
S.
Auer
and
D.
Frenkel
, “
Prediction of absolute crystal-nucleation rate in hard-sphere colloids
,”
Nature
409
(
6823
),
1020
1023
(
2001
).
23.
R.
Radhakrishnan
and
B. L.
Trout
, “
Nucleation of hexagonal ice (Ih) in liquid water
,”
J. Am. Chem. Soc.
125
(
25
),
7743
7747
(
2003
).
24.
A.
Laio
and
M.
Parrinello
, “
Escaping free-energy minima
,”
Proc. Natl. Acad. Sci. U. S. A.
99
(
20
),
12562
12566
(
2002
).
25.
F.
Trudu
,
D.
Donadio
, and
M.
Parrinello
, “
Freezing of a Lennard-Jones fluid: From nucleation to spinodal regime
,”
Phys. Rev. Lett.
97
(
10
),
105701
(
2006
), cited by 139.
26.
M.
Salvalaglio
,
P.
Tiwary
,
G. M.
Maggioni
,
M.
Mazzotti
, and
M.
Parrinello
, “
Overcoming time scale and finite size limitations to compute nucleation rates from small scale well tempered metadynamics simulations
,”
J. Chem. Phys.
145
(
21
),
211925
(
2016
).
27.
P. G.
Bolhuis
,
D.
Chandler
,
C.
Dellago
, and
P. L.
Geissler
, “
Transition path sampling: Throwing ropes over rough mountain passes, in the dark
,”
Annu. Rev. Phys. Chem.
53
,
291
318
(
2002
).
28.
W.
Lechner
,
C.
Dellago
, and
P. G.
Bolhuis
, “
Role of the prestructured surface cloud in crystal nucleation
,”
Phys. Rev. Lett.
106
(
8
),
085701
(
2011
).
29.
C.
Valeriani
,
E.
Sanz
, and
D.
Frenkel
, “
Rate of homogeneous crystal nucleation in molten NaCl
,”
J. Chem. Phys.
122
(
19
),
194501
(
2005
).
30.
L.
Filion
,
M.
Hermes
,
R.
Ni
, and
M.
Dijkstra
, “
Crystal nucleation of hard spheres using molecular dynamics, umbrella sampling, and forward flux sampling: A comparison of simulation techniques
,”
J. Chem. Phys.
133
(
24
),
244115
(
2010
).
31.
T.
Li
,
D.
Donadio
,
G.
Russo
, and
G.
Galli
, “
Homogeneous ice nucleation from supercooled water
,”
Phys. Chem. Chem. Phys.
13
,
19807
(
2011
).
32.
A.
Haji-Akbari
and
P. G.
Debenedetti
, “
Direct calculation of ice homogeneous nucleation rate for a molecular model of water
,”
Proc. Natl. Acad. Sci. U. S. A.
112
(
34
),
10582
10588
(
2015
).
33.
G. C.
Sosso
,
T.
Li
,
D.
Donadio
,
G. A.
Tribello
, and
A.
Michaelides
, “
Microscopic mechanism and kinetics of ice formation at complex interfaces: Zooming in on kaolinite
,”
J. Phys. Chem. Lett.
7
(
13
),
2350
2355
(
2016
).
34.
V.
Kalikmanov
,
Nucleation Theory
(
Springer
,
Dordrecht, The Netherlands
,
2013
).
35.
J. R.
Espinosa
,
C.
Vega
,
C.
Valeriani
, and
E.
Sanz
, “
Seeding approach to crystal nucleation
,”
J. Chem. Phys.
144
(
3
),
034501
(
2016
).
36.
T. L.
Malkin
,
B. J.
Murray
,
C. G.
Salzmann
,
V.
Molinero
,
S. J.
Pickering
, and
T. F.
Whale
, “
Stacking disorder in ice I
,”
Phys. Chem. Chem. Phys.
17
,
60
76
(
2015
).
37.
B.
Emily Moore
and
V.
Molinero
, “
Is it cubic? Ice crystallization from deeply supercooled water
,”
Phys. Chem. Chem. Phys.
13
,
20008
20016
(
2011
).
38.
A.
Zaragoza
,
M. M.
Conde
,
J. R.
Espinosa
,
C.
Valeriani
,
C.
Vega
, and
E.
Sanz
, “
Competition between ices Ih and Ic in homogeneous water freezing
,”
J. Chem. Phys.
143
(
13
),
134504
(
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
(
2010
).
40.
L.
Lupi
,
A.
Hudait
, and
V.
Molinero
, “
Heterogeneous nucleation of ice on carbon surfaces
,”
J. Am. Chem. Soc.
136
,
3156
(
2014
).
41.
S. J.
Cox
,
S. M.
Kathmann
,
B.
Slater
, and
A.
Michaelides
, “
Molecular simulations of heterogeneous ice nucleation. II. Peeling back the layers
,”
J. Chem. Phys.
142
(
18
),
184705
(
2015
).
42.
S. J.
Cox
,
S. M.
Kathmann
,
B.
Slater
, and
A.
Michaelides
, “
Molecular simulations of heterogeneous ice nucleation. I. Controlling ice nucleation through surface hydrophilicity
,”
J. Chem. Phys.
142
(
18
),
184704
(
2015
).
43.
M.
Fitzner
,
G. C.
Sosso
,
S. J.
Cox
, and
A.
Michaelides
, “
The many faces of heterogeneous ice nucleation: Interplay between surface morphology and hydrophobicity
,”
J. Am. Chem. Soc.
137
(
42
),
13658
13669
(
2015
).
44.
Y.
Bi
,
R.
Cabriolu
, and
T.
Li
, “
Heterogeneous ice nucleation controlled by the coupling of surface crystallinity and surface hydrophilicity
,”
J. Phys. Chem. C
120
(
3
),
1507
1514
(
2016
).
45.
L.
Lupi
,
B.
Peters
, and
V.
Molinero
, “
Pre-ordering of interfacial water in the pathway of heterogeneous ice nucleation does not lead to a two-step crystallization mechanism
,”
J. Chem. Phys.
145
(
21
),
211910
(
2016
).
46.
O.
Björneholm
,
M. H.
Hansen
,
A.
Hodgson
,
L.-M.
Liu
,
D. T.
Limmer
,
A.
Michaelides
,
P.
Pedevilla
,
J.
Rossmeisl
,
H.
Shen
,
G.
Tocci
,
E.
Tyrode
,
M.-M.
Walz
,
J.
Werner
, and
H.
Bluhm
, “
Water at interfaces
,”
Chem. Rev.
116
(
13
),
7698
7726
(
2016
).
47.
R.
Cabriolu
and
T.
Li
, “
Ice nucleation on carbon surface supports the classical theory for heterogeneous nucleation
,”
Phys. Rev. E
91
,
052402
(
2015
).
48.
G. C.
Sosso
,
G. A.
Tribello
,
A.
Zen
,
P.
Pedevilla
, and
A.
Michaelides
, “
Ice formation on kaolinite: Insights from molecular dynamics simulations
,”
J. Chem. Phys.
145
,
211927
(
2016
).
49.
G. C.
Sosso
,
T. F.
Whale
,
P.
Pedevilla
, and
A.
Michaelides
, “
Unraveling the origins of ice nucleation on organic crystals
” (unpublished).
50.
P.
Pedevilla
,
S. J.
Cox
,
B.
Slater
, and
A.
Michaelides
, “
Can ice-like structures form on non-ice-like substrates? The example of the K-feldspar microcline
,”
J. Phys. Chem. C
120
(
12
),
6704
6713
(
2016
).
51.
S. J.
Cox
,
S. M.
Kathmann
,
J. A.
Purton
,
M. J.
Gillan
, and
A.
Michaelides
, “
Non-hexagonal ice at hexagonal surfaces: The role of lattice mismatch
,”
Phys. Chem. Chem. Phys.
14
(
22
),
7944
7949
(
2012
).
52.
G. C.
Sosso
, Hseed-(heterogeneous) seeded molecular dynamics, https://github.com/gcsosso/HSeed.git,
2018
.
53.
J.
Nocedal
, “
Updating quasi-Newton matrices with limited storage
,”
Math. Comput.
35
,
773
782
, (
1980
).
54.
E.
Sanz
,
C.
Vega
,
J. R.
Espinosa
,
R.
Caballero-Bernal
,
J. L. F.
Abascal
, and
C.
Valeriani
, “
Homogeneous ice nucleation at moderate supercooling from molecular simulation
,”
J. Am. Chem. Soc.
135
(
40
),
15008
15017
(
2013
).
55.
M.
Fitzner
,
G. C.
Sosso
,
F.
Pietrucci
,
S.
Pipolo
, and
A.
Michaelides
, “
Pre-critical fluctuations and what they disclose about heterogeneous crystal nucleation
,”
Nat. Commun.
8
(
1
),
2257
(
2017
).
56.
P.
Pedevilla
,
M.
Fitzner
, and
A.
Michaelides
, “
What makes a good descriptor for heterogeneous ice nucleation on OH-patterned surfaces
,”
Phys. Rev. B
96
,
115441
(
2017
).
57.
A.
Barducci
,
G.
Bussi
, and
M.
Parrinello
, “
Well-tempered metadynamics: A smoothly converging and tunable free-energy method
,”
Phys. Rev. Lett.
100
(
2
),
020603
(
2008
).
58.
A.
Grégoire Gallet
and
F.
Pietrucci
, “
Structural cluster analysis of chemical reactions in solution
,”
J. Chem. Phys.
139
(
7
),
074101
(
2013
).
59.
G. J.
Martyna
,
M. L.
Klein
, and
M.
Tuckerman
, “
Nosé-Hoover chains: The canonical ensemble via continuous dynamics
,”
J. Chem. Phys.
97
(
4
),
2635
2643
(
1992
).
60.
S.
Plimpton
, “
Fast parallel algorithms for short-range molecular dynamics
,”
J. Comput. Phys.
117
(
1
),
1
19
(
1995
).
61.
B. M.
Craven
, “
Crystal structure of cholesterol monohydrate
,”
Nature
260
(
5553
),
727
729
(
1976
).
62.
J. L. F.
Abascal
,
E.
Sanz
,
R.
García Fernández
, and
C.
Vega
, “
A potential model for the study of ices and amorphous water: Tip4p/Ice
,”
J. Chem. Phys.
122
(
23
),
234511
(
2005
).
63.
B.
Hess
,
C.
Kutzner
,
D.
van der Spoel
, and
E.
Lindahl
, “
GROMACS 4: Algorithms for highly efficient, load-balanced, and scalable molecular simulations
,”
J. Chem. Theory Comput.
4
(
3
),
435
447
(
2008
).
64.
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
).
65.
P.
Bjelkmar
,
P.
Larsson
,
M. A.
Cuendet
,
B.
Hess
, and
E.
Lindahl
, “
Implementation of the CHARMM force field in GROMACS: Analysis of protein stability effects from correction maps, virtual interaction sites, and water models
,”
J. Chem. Theory Comput.
6
(
2
),
459
466
(
2010
).
66.
J. B.
Lim
,
B.
Rogaski
, and
J. B.
Klauda
, “
Update of the cholesterol force field parameters in CHARMM
,”
J. Phys. Chem. B
116
(
1
),
203
210
(
2011
).
67.
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
(
19
),
8577
8593
(
1995
).
68.
G.
Bussi
,
D.
Donadio
, and
M.
Parrinello
, “
Canonical sampling through velocity rescaling
,”
J. Chem. Phys.
126
(
1
),
014101
(
2007
).
69.
S.
Miyamoto
and
P. A.
Kollman
, “
Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models
,”
J. Comput. Chem.
13
(
8
),
952
962
(
1992
).
70.
B.
Hess
,
H.
Bekker
,
H. J. C.
Berendsen
, and
J. G. E. M.
Fraaije
, “
LINCS: A linear constraint solver for molecular simulations
,”
J. Comput. Chem.
18
(
12
),
1463
1472
(
1997
).
71.
B.
Hess
, “
P-LINCS: A parallel linear constraint solver for molecular simulation
,”
J. Chem. Theory Comput.
4
(
1
),
116
122
(
2008
).
72.
S. J.
Cox
,
Z.
Raza
,
S. M.
Kathmann
,
B.
Slater
, and
A.
Michaelides
, “
The microscopic features of heterogeneous ice nucleation may affect the macroscopic morphology of atmospheric ice crystals
,”
Faraday Discuss.
167
,
389
403
(
2013
).
73.
S. A.
Zielke
,
A. K.
Bertram
, and
G. N.
Patey
, “
Simulations of ice nucleation by kaolinite (001) with rigid and flexible surfaces
,”
J. Phys. Chem. B
120
,
1726
1734
(
2015
).
74.
N.
Fukuta
and
B. J.
Mason
, “
Epitaxial growth of ice on organic crystals
,”
J. Phys. Chem. Solids
24
(
6
),
715
718
(
1963
).
75.
R. J.
Allen
,
C.
Valeriani
, and
P. R.
ten Wolde
, “
Forward flux sampling for rare event simulations
,”
J. Phys.: Condens. Matter
21
(
46
),
463102
(
2009
).
76.
P.
Raiteri
,
A.
Laio
,
F.
Luigi Gervasio
,
C.
Micheletti
, and
M.
Parrinello
, “
Efficient reconstruction of complex free energy landscapes by multiple walkers metadynamics
,”
J. Phys. Chem. B
110
(
8
),
3533
3539
(
2006
).
77.
B.
Wang
,
D. A.
Knopf
,
S.
China
,
B. W.
Arey
,
T. H.
Harder
,
M. K.
Gilles
, and
A.
Laskin
, “
Direct observation of ice nucleation events on individual atmospheric particles
,”
Phys. Chem. Chem. Phys.
18
(
43
),
29721
29731
(
2016
).
You do not currently have access to this content.