We describe the topological cluster classification (TCC) algorithm. The TCC detects local structures with bond topologies similar to isolated clusters which minimise the potential energy for a number of monatomic and binary simple liquids with m ⩽ 13 particles. We detail a modified Voronoi bond detection method that optimizes the cluster detection. The method to identify each cluster is outlined, and a test example of Lennard-Jones liquid and crystal phases is considered and critically examined.

1.
J.-P.
Hansen
and
I. R.
McDonald
,
Theory of Simple Liquids
, 3rd ed. (
Academic Press
,
2006
).
2.
J. D.
Bernal
,
Nature (London)
183
,
141
(
1959
).
3.
A.
Rahman
,
J. Chem. Phys.
45
,
2585
(
1966
).
4.
J. L.
Finney
,
Proc. R. Soc. London, Ser. A
319
,
479
(
1970
).
5.
J. D.
Honeycutt
and
H. C.
Andersen
,
J. Phys. Chem.
91
,
4950
(
1987
).
6.
M.
Tanemura
,
Y.
Hiwatari
,
H.
Matsuda
,
T.
Ogawa
,
N.
Ogita
, and
A.
Ueda
,
Prog. Theor. Phys.
58
,
1079
(
1977
).
7.
H.
Jónsson
and
H.
Andersen
,
Phys. Rev. Lett.
60
,
2295
(
1988
).
8.
K.
Tsumuraya
and
M. S.
Watanabe
,
J. Chem. Phys.
92
,
4983
(
1990
).
9.
R.
Della Valle
,
D.
Gazzillo
,
R.
Frattini
, and
G.
Pastore
,
Phys. Rev. B
49
,
12625
(
1994
).
10.
N.
Bailey
,
J.
Schiøtz
, and
K.
Jacobsen
,
Phys. Rev. B
69
,
144205
(
2004
).
11.
D.
Coslovich
and
G.
Pastore
,
J. Chem. Phys.
127
,
124504
(
2007
).
12.
L. O.
Hedges
,
R. L.
Jack
,
J. P.
Garrahan
, and
D.
Chandler
,
Science
323
,
1309
(
2009
).
13.
C. S.
Hsu
and
A.
Rahman
,
J. Chem. Phys.
71
,
4974
(
1979
).
14.
W.
Swope
and
H.
Andersen
,
Phys. Rev. B
41
,
7042
(
1990
).
15.
P.
Steinhardt
,
D.
Nelson
, and
M.
Ronchetti
,
Phys. Rev. Lett.
47
,
1297
(
1981
).
16.
P.
Steinhardt
,
D.
Nelson
, and
M.
Ronchetti
,
Phys. Rev. B
28
,
784
(
1983
).
17.
A.
Mitus
,
F.
Smolej
,
H.
Hahn
, and
A.
Patashinski
,
Physica A
232
,
662
(
1996
).
18.
T.
Tomida
and
T.
Egami
,
Phys. Rev. B
52
,
3290
(
1995
).
19.
H.
Tanaka
,
T.
Kawasaki
,
H.
Shintani
, and
K.
Watanabe
,
Nature Mater.
9
,
324
(
2010
).
20.
M.
Heni
and
H.
Löwen
,
Phys. Rev. E
65
,
021501
(
2002
).
21.
K.
Wierschem
and
E.
Manousakis
,
Phys. Rev. B
83
,
214108
(
2011
).
22.
C.
Chakravarty
,
Mol. Phys.
100
,
3777
(
2002
).
23.
P. R.
Ten Wolde
,
M. J.
Ruizmontero
, and
D.
Frenkel
,
Phys. Rev. Lett.
75
,
2714
(
1995
).
24.
S.
Auer
and
D.
Frenkel
,
J. Chem. Phys.
120
,
3015
(
2004
).
25.
W.
Lechner
and
C.
Dellago
,
J. Chem. Phys.
129
,
114707
(
2008
).
26.
J. A.
van Meel
,
B.
Charbonneau
,
A.
Fortini
, and
P.
Charbonneau
,
Phys. Rev. E
80
,
061110
(
2009
).
27.
T.
Kawasaki
and
H.
Tanaka
,
Proc. Natl. Acad. Sci. U.S.A.
107
,
14036
(
2010
).
28.
J.
Russo
and
H.
Tanaka
,
Sci. Rep.
2
,
505
(
2012
).
29.
A.
van Blaaderen
and
P.
Wiltzius
,
Science
270
,
1177
(
1995
).
30.
J. C.
Crocker
and
D. G.
Grier
,
J. Colloid Interface Sci.
179
,
298
(
1996
).
31.
C. P.
Royall
,
M. E.
Leunissen
, and
A.
van Blaaderen
,
J. Phys.: Condens. Matter
15
,
S3581
(
2003
).
32.
C. P.
Royall
,
S. R.
Williams
,
T.
Ohtsuka
, and
H.
Tanaka
,
Nature Mater.
7
,
556
(
2008
).
33.
C. P.
Royall
,
D. G. A. L.
Aarts
, and
H.
Tanaka
,
Nat. Phys.
3
,
636
(
2007
).
34.
C. P.
Royall
,
S. R.
Williams
,
T.
Ohtsuka
, and
H.
Tanaka
,
AIP Conf. Proc.
982
,
97
(
2008
).
35.
C. P.
Royall
and
S. R.
Williams
,
J. Phys. Chem. B
115
,
7288
(
2011
).
36.
J.
Taffs
,
A.
Malins
,
S. R.
Williams
, and
C. P.
Royall
,
J. Phys.: Condens. Matter
22
,
104119
(
2010
).
37.
A.
Malins
,
S. R.
Williams
,
J.
Eggers
,
H.
Tanaka
, and
C. P.
Royall
,
J. Phys.: Condens. Matter
21
,
425103
(
2009
).
38.
A.
Malins
,
S. R.
Williams
,
J.
Eggers
,
H.
Tanaka
, and
C. P.
Royall
,
J. Non-Cryst. Solids
357
,
760
(
2011
).
39.
C. L.
Klix
,
K.-i.
Murata
,
H.
Tanaka
,
S. R.
Williams
,
A.
Malins
, and
C. P.
Royall
,
Sci. Rep.
3
,
2072
(
2013
).
40.
M.
Godogna
,
A.
Malins
,
S. R.
Williams
, and
C. P.
Royall
,
Mol. Phys.
109
,
1393
(
2010
).
41.
A.
Malins
,
J.
Eggers
,
C. P.
Royall
,
S. R.
Williams
, and
H.
Tanaka
,
J. Chem. Phys.
138
,
12A535
(
2013
).
42.
A.
Malins
,
J.
Eggers
,
H.
Tanaka
, and
C. P.
Royall
, “
Lifetimes and Lengthscales of structural motifs in a model glassformer
,” Faraday Discuss. (to be published).
43.
C. P.
Royall
,
A.
Malins
,
A. J.
Dunleavy
, and
R.
Pinney
, “
Geometric frustration is strong in model fragile glassformers
,”
Fragility of Glassforming Liquids
(
Hindustan Book Agency
,
New Delhi, India
,
2014
).
44.
J.
Taffs
,
S. R.
Williams
,
H.
Tanaka
, and
C. P.
Royall
,
Soft Matter
9
,
297
(
2013
).
45.
D. J.
Wales
and
J. P. K.
Doye
,
J. Phys. Chem. A
101
,
5111
(
1997
).
46.
F. C.
Frank
,
Proc. R. Soc. London, Ser. A
215
,
43
(
1952
).
47.
S.
Mossa
and
G.
Tarjus
,
J. Chem. Phys.
119
,
8069
(
2003
).
48.
G.
Voronoi
,
J. Reine Angew. Math.
1908
,
198
.
49.
50.
C. S.
Hsu
and
A.
Rahman
,
J. Chem. Phys.
70
,
5234
(
1979
).
51.
A. E.
Galashev
and
V. P.
Skripov
,
J. Struct. Chem.
21
,
158
(
1980
).
52.
N. N.
Medvedev
and
Y. I.
Naberukhin
,
J. Struct. Chem.
26
,
369
(
1985
).
53.
B.
O'Malley
, “
Molecular dynamics investigation of crystallization in the hard sphere system
,” Ph.D. thesis (
RMIT University
,
2001
).
54.
B.
O'Malley
and
I.
Snook
,
Phys. Rev. Lett.
90
,
085702
(
2003
).
55.
J. P.
Troadec
,
A.
Gervois
, and
L.
Oger
,
Europhys. Lett.
42
,
167
(
1998
).
56.
S. R.
Williams
, “
Topological Classification of Clusters in Condensed Phases
,” preprint arXiv:0705.0203 (
2007
).
57.
J. L.
Meijering
,
Philips Res. Rep.
8
,
270
(
1953
).
58.
W.
Brostow
,
J.-P.
Dussault
, and
B. L.
Fox
,
J. Comput. Phys.
29
,
81
(
1978
).
59.
N.
Medvedev
,
J. Comput. Phys.
67
,
223
(
1986
).
60.
J.
Taffs
,
A.
Malins
,
S. R.
Williams
, and
C. P.
Royall
,
J. Chem. Phys.
133
,
244901
(
2010
).
61.
62.
P.
Rein ten Wolde
,
M. J.
Ruiz-Montero
, and
D.
Frenkel
,
J. Chem. Phys.
104
,
9932
(
1996
).
63.
J. A.
van Meel
,
L.
Filion
,
C.
Valeriani
, and
D.
Frenkel
,
J. Chem. Phys.
136
,
234107
(
2012
).
64.
W.
Mickel
,
S. C.
Kapfer
,
G. E.
Schorder-Turk
, and
K.
Mecke
,
J. Chem. Phys.
138
,
044501
(
2013
).
66.
J. P. K.
Doye
,
D. J.
Wales
, and
R. S.
Berry
,
J. Chem. Phys.
103
,
4234
(
1995
).
67.
M.
Dzugutov
and
U.
Dahlborg
,
J. Non-Cryst. Solids
131–133
,
62
(
1991
).
68.
J. P. K.
Doye
,
D. J.
Wales
, and
S. I.
Simdyankin
,
Faraday Discuss.
118
,
159
(
2001
).
69.
70.
W.
Kob
and
H. C.
Andersen
,
Phys. Rev. E
51
,
4626
(
1995
).
71.
D.
Franzblau
,
Phys. Rev. B
44
,
4925
(
1991
).
72.
D. B.
Miracle
and
P.
Harrowell
,
J. Chem. Phys.
130
,
114505
(
2009
).
73.
A.
Nijenhuis
and
H. S.
Wilf
,
Combinatorial Algorithms
, 2nd ed. (
Academic Press
,
1978
) p.
302
.
74.
C. S.
Marians
and
J. K.
Burdett
,
J. Non-Cryst. Solids
124
,
1
(
1990
).
75.
J. P. K.
Doye
and
D. J.
Wales
,
J. Chem. Soc., Faraday Trans.
93
,
4233
(
1997
).
76.
N.
Arkus
,
V.
Manoharan
, and
M.
Brenner
,
Phys. Rev. Lett.
103
,
118303
(
2009
).
77.
G.
Meng
,
N.
Arkus
,
M. P.
Brenner
, and
V. N.
Manoharan
,
Science
327
,
560
(
2010
).
78.
F.
Stillinger
and
R.
LaViolette
,
Phys. Rev. B
34
,
5136
(
1986
).
79.
N. N.
Medvedev
,
V. P.
Voloshin
, and
Y. I.
Naberukhin
,
J. Struct. Chem.
27
,
581
(
1987
).
80.
R.
LaViolette
,
Phys. Rev. B
41
,
8526
(
1990
).
81.
A.
Jackson
,
A.
Bruce
, and
G.
Ackland
,
Phys. Rev. E
65
,
036710
(
2002
).
82.
T.
Speck
,
A.
Malins
, and
C. P.
Royall
,
Phys. Rev. Lett.
109
,
195703
(
2012
).
You do not currently have access to this content.