The important role of liquid water in many areas of science from chemistry, physics, biology, geology to climate research, etc., has motivated numerous theoretical studies of its structure and dynamics. The significance of quantum effects on the properties of water, however, has not yet been fully resolved. In this paper we focus on quantum dynamical effects in liquid water based on the linearized semiclassical initial value representation (LSC-IVR) with a quantum version of the simple point charge/flexible (q-SPC/fw) model [Paesani et al., J. Chem. Phys.125, 184507 (2006)] for the potential energy function. The infrared (IR) absorption spectrum and the translational diffusion constants have been obtained from the corresponding thermal correlation functions, and the effects of intermolecular and intramolecular correlations have been studied. The LSC-IVR simulation results are compared with those predicted by the centroid molecular dynamics (CMD) approach. Although the LSC-IVR and CMD results agree well for the broadband for hindered motions in liquid water, the intramolecular bending and O–H stretching peaks predicted by the LSC-IVR are blueshifted from those given by CMD; reasons for this are discussed. We also suggest that the broadband in the IR spectrum corresponding to restricted translation and libration gives more information than the diffusion constant on the nature of quantum effects on translational and rotational motions and should thus receive more attention in this regard.

1.
W. H.
Miller
,
Adv. Chem. Phys.
25
,
69
(
1974
).
2.
W. H.
Miller
,
Adv. Chem. Phys.
30
,
77
(
1976
).
3.
W. H.
Miller
,
J. Chem. Phys.
53
,
3578
(
1970
).
4.
R. A.
Marcus
,
J. Chem. Phys.
54
,
3965
(
1971
).
5.
R. A.
Marcus
,
J. Chem. Phys.
56
,
3548
(
1972
).
6.
E. J.
Heller
,
J. Chem. Phys.
62
,
1544
(
1975
).
7.
M. F.
Herman
and
E.
Kluk
,
Chem. Phys.
91
,
27
(
1984
).
8.
M. F.
Herman
,
Annu. Rev. Phys. Chem.
45
,
83
(
1994
).
9.
M. F.
Herman
,
J. Phys. Chem. A
109
,
9196
(
2005
).
10.
Y. H.
Wu
and
M. F.
Herman
,
J. Chem. Phys.
123
,
144106
(
2005
).
11.
Y. H.
Wu
and
M. F.
Herman
,
J. Chem. Phys.
125
,
154116
(
2006
).
12.
Y. H.
Wu
and
M. F.
Herman
,
J. Chem. Phys.
127
,
044109
(
2007
).
13.
M. F.
Herman
and
Y. H.
Wu
,
J. Chem. Phys.
128
,
114105
(
2008
).
14.
E. J.
Heller
,
J. Chem. Phys.
95
,
9431
(
1991
).
15.
E. J.
Heller
,
J. Chem. Phys.
94
,
2723
(
1991
).
16.
K. G.
Kay
,
J. Chem. Phys.
100
,
4377
(
1994
).
17.
K. G.
Kay
,
J. Chem. Phys.
100
,
4432
(
1994
).
19.
G.
Campolieti
and
P.
Brumer
,
Phys. Rev. A
50
,
997
(
1994
).
20.
J.
Wilkie
and
P.
Brumer
,
Phys. Rev. A
61
,
064101
(
2000
).
21.
D. J.
Tannor
and
S.
Garashchuk
,
Annu. Rev. Phys. Chem.
51
,
553
(
2000
).
22.
W. H.
Miller
,
Faraday Discuss.
110
,
1
(
1998
).
23.
H.
Wang
,
M.
Thoss
, and
W. H.
Miller
,
J. Chem. Phys.
112
,
47
(
2000
).
24.
M.
Thoss
,
H.
Wang
, and
W. H.
Miller
,
J. Chem. Phys.
114
,
9220
(
2001
).
25.
W. H.
Miller
,
J. Phys. Chem. A
105
,
2942
(
2001
).
26.
T.
Yamamoto
,
H. B.
Wang
, and
W. H.
Miller
,
J. Chem. Phys.
116
,
7335
(
2002
).
27.
M.
Thoss
and
H. B.
Wang
,
Annu. Rev. Phys. Chem.
55
,
299
(
2004
).
28.
W. H.
Miller
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
6660
(
2005
).
29.
W. H.
Miller
,
J. Chem. Phys.
125
,
132305
(
2006
).
30.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
125
,
224104
(
2006
).
31.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
126
,
234110
(
2007
).
32.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
127
,
114506
(
2007
).
33.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
128
,
144511
(
2008
).
34.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
129
,
124111
(
2008
).
35.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
131
,
074113
(
2009
).
36.
N.
Ananth
,
C.
Venkataraman
, and
W. H.
Miller
,
J. Chem. Phys.
127
,
084114
(
2007
).
37.
W. H.
Miller
,
J. Phys. Chem. A
113
,
1405
(
2009
).
38.
G.
Tao
and
W. H.
Miller
,
J. Chem. Phys.
130
,
184108
(
2009
).
39.
A.
Nakayama
and
N.
Makri
,
J. Chem. Phys.
119
,
8592
(
2003
).
40.
N.
Makri
,
A.
Nakayama
, and
N.
Wright
,
J. Theor. Comput. Chem.
3
,
391
(
2004
).
41.
A.
Nakayama
and
N.
Makri
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
4230
(
2005
).
42.
J.
Liu
and
N.
Makri
,
Chem. Phys.
322
,
23
(
2006
).
43.
J.
Liu
,
A.
Nakayama
, and
N.
Makri
,
Mol. Phys.
104
,
1267
(
2006
).
44.
B. B.
Issack
and
P. N.
Roy
,
J. Chem. Phys.
126
,
024111
(
2007
).
45.
B. B.
Issack
and
P. N.
Roy
,
J. Chem. Phys.
127
,
144306
(
2007
).
46.
B. B.
Issack
and
P. N.
Roy
,
J. Chem. Phys.
127
,
054105
(
2007
).
47.
Q.
Shi
and
E.
Geva
,
J. Phys. Chem. A
107
,
9059
(
2003
).
48.
Q.
Shi
and
E.
Geva
,
J. Phys. Chem. A
107
,
9070
(
2003
).
49.
B. J.
Ka
,
Q.
Shi
, and
E.
Geva
,
J. Phys. Chem. A
109
,
5527
(
2005
).
50.
B. J.
Ka
and
E.
Geva
,
J. Phys. Chem. A
110
,
9555
(
2006
).
51.
I.
Navrotskaya
and
E.
Geva
,
J. Phys. Chem. A
111
,
460
(
2007
).
52.
B. R.
McQuarrie
,
D. G.
Abrashkevich
, and
P.
Brumer
,
J. Chem. Phys.
119
,
3606
(
2003
).
53.
S.
Bonella
,
D.
Montemayor
, and
D. F.
Coker
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
6715
(
2005
).
54.
S. M.
Gruenbaum
and
R. F.
Loring
,
J. Chem. Phys.
128
,
124106
(
2008
).
55.
C. M.
Goletz
and
F.
Grossmann
,
J. Chem. Phys.
130
,
244107
(
2009
).
56.
M.
Ceotto
,
S.
Atahan
,
G. F.
Tantardini
, and
A.
Aspuru-Guzik
,
J. Chem. Phys.
130
,
234113
(
2009
).
57.
E.
Martin-Fierro
and
E.
Pollak
,
J. Chem. Phys.
125
,
164104
(
2006
).
58.
X.
Sun
and
W. H.
Miller
,
J. Chem. Phys.
106
,
916
(
1997
).
59.
H.
Wang
,
X.
Sun
, and
W. H.
Miller
,
J. Chem. Phys.
108
,
9726
(
1998
).
60.
X.
Sun
,
H.
Wang
, and
W. H.
Miller
,
J. Chem. Phys.
109
,
7064
(
1998
).
61.
R.
Hernandez
and
G. A.
Voth
,
Chem. Phys.
233
,
243
(
1998
).
62.
63.
E. J.
Heller
,
J. Chem. Phys.
65
,
1289
(
1976
).
64.
H. W.
Lee
and
M. O.
Scully
,
J. Chem. Phys.
73
,
2238
(
1980
).
65.
X.
Sun
and
W. H.
Miller
,
J. Chem. Phys.
110
,
6635
(
1999
).
66.
T.
Yamamoto
and
W. H.
Miller
,
J. Chem. Phys.
118
,
2135
(
2003
).
67.
Q.
Shi
and
E.
Geva
,
J. Chem. Phys.
119
,
9030
(
2003
).
68.
J.
Shao
and
N.
Makri
,
J. Phys. Chem. A
103
,
7753
(
1999
).
69.
J.
Shao
and
N.
Makri
,
J. Phys. Chem. A
103
,
9479
(
1999
).
70.
N.
Makri
,
J. Phys. Chem. B
106
,
8390
(
2002
).
71.
N. J.
Wright
and
N.
Makri
,
J. Chem. Phys.
119
,
1634
(
2003
).
72.
N. J.
Wright
and
N.
Makri
,
J. Phys. Chem. B
108
,
6816
(
2004
).
73.
A.
Nakayama
and
N.
Makri
,
Chem. Phys.
304
,
147
(
2004
).
74.
J.
Kegerreis
and
N.
Makri
,
J. Comput. Chem.
28
,
818
(
2007
).
75.
E.
Bukhman
and
N.
Makri
,
J. Phys. Chem. A
111
,
11320
(
2007
).
76.
J.
Chen
and
N.
Makri
,
Mol. Phys.
106
,
443
(
2008
).
77.
J.
Kegerreis
,
A.
Nakayama
, and
N.
Makri
,
J. Chem. Phys.
128
,
184509
(
2008
).
78.
E.
Bukhman
and
N.
Makri
,
J. Phys. Chem. A
113
,
7183
(
2009
).
79.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
99
,
10070
(
1993
).
80.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
100
,
5106
(
1994
).
81.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
101
,
6168
(
1994
).
82.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
101
,
6157
(
1994
).
83.
S.
Jang
and
G. A.
Voth
,
J. Chem. Phys.
111
,
2371
(
1999
).
84.
S.
Jang
and
G. A.
Voth
,
J. Chem. Phys.
111
,
2357
(
1999
).
85.
D. R.
Reichman
,
P. N.
Roy
,
S.
Jang
, and
G. A.
Voth
,
J. Chem. Phys.
113
,
919
(
2000
).
86.
T. D.
Hone
and
G. A.
Voth
,
J. Chem. Phys.
121
,
6412
(
2004
).
87.
T. D.
Hone
,
P. J.
Rossky
, and
G. A.
Voth
,
J. Chem. Phys.
124
,
154103
(
2006
).
88.
F.
Paesani
,
W.
Zhang
,
D. A.
Case
,
T. E.
Cheatham
, and
G. A.
Voth
,
J. Chem. Phys.
125
,
184507
(
2006
).
89.
F.
Paesani
,
S.
Luchi
, and
G. A.
Voth
,
J. Chem. Phys.
127
,
074506
(
2007
).
90.
F.
Paesani
and
G. A.
Voth
,
J. Chem. Phys.
129
,
194113
(
2008
).
91.
F.
Paesani
and
G. A.
Voth
,
J. Phys. Chem. B
113
,
5702
(
2009
).
92.
F.
Paesani
,
S. S.
Xantheas
, and
G. A.
Voth
,
J. Phys. Chem. B
113
,
13118
(
2009
).
93.
K.
Kinugawa
,
Chem. Phys. Lett.
292
,
454
(
1998
).
94.
K.
Kinugawa
,
H.
Nagao
, and
K.
Ohta
,
J. Chem. Phys.
114
,
1454
(
2001
).
95.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
121
,
3368
(
2004
).
96.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
122
,
084106
(
2005
).
97.
I. R.
Craig
and
D. E.
Manolopoulos
,
Chem. Phys.
322
,
236
(
2006
).
98.
T. F.
Miller
and
D. E.
Manolopoulos
,
J. Chem. Phys.
123
,
154504
(
2005
).
99.
T. F.
Miller
and
D. E.
Manolopoulos
,
J. Chem. Phys.
122
,
184503
(
2005
).
100.
B. J.
Braams
and
D. E.
Manolopoulos
,
J. Chem. Phys.
125
,
124105
(
2006
).
101.
S.
Habershon
,
B. J.
Braams
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
127
,
174108
(
2007
).
102.
R.
Collepardo-Guevara
,
I. R.
Craig
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
128
,
144502
(
2008
).
103.
T. E.
Markland
,
S.
Habershon
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
128
,
194506
(
2008
).
104.
A.
Witt
,
S. D.
Ivanov
,
M.
Shiga
,
H.
Forbert
, and
D.
Marx
,
J. Chem. Phys.
130
,
194510
(
2009
).
105.
S.
Habershon
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
131
,
024501
(
2009
).
106.
R. A.
Kuharski
and
P. J.
Rossky
,
J. Chem. Phys.
82
,
5164
(
1985
).
107.
A.
Wallqvist
and
B. J.
Berne
,
Chem. Phys. Lett.
117
,
214
(
1985
).
108.
J.
Lobaugh
and
G. A.
Voth
,
J. Chem. Phys.
106
,
2400
(
1997
).
109.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
Proc. Natl. Acad. Sci. U.S.A.
102
,
6709
(
2005
).
110.
L.
Hernández de la Peña
and
P. G.
Kusalik
,
J. Chem. Phys.
121
,
5992
(
2004
).
111.
L.
Hernández de la Peña
and
P. G.
Kusalik
,
J. Am. Chem. Soc.
127
,
5246
(
2005
).
112.
L.
Hernández de la Pena
and
P. G.
Kusalik
,
J. Chem. Phys.
125
,
054512
(
2006
).
113.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Chem. Theory Comput.
2
,
1482
(
2006
).
114.
B. J.
Berne
and
G. D.
Harp
,
Adv. Chem. Phys.
17
,
63
(
1970
).
115.
W. H.
Miller
,
S. D.
Schwartz
, and
J. W.
Tromp
,
J. Chem. Phys.
79
,
4889
(
1983
).
116.
R.
Kubo
,
M.
Toda
, and
N.
Hashitsume
,
Statistical Physics II: Nonequilibrium Statistical Mechanics
, 2nd ed. (
Springer-Verlag
,
Berlin
,
1991
).
117.
E. J.
Wigner
,
Trans. Faraday Soc.
34
,
29
(
1938
).
118.
E.
Pollak
and
J. L.
Liao
,
J. Chem. Phys.
108
,
2733
(
1998
).
119.
Q.
Shi
and
E.
Geva
,
J. Chem. Phys.
118
,
8173
(
2003
).
120.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Chem. Phys.
119
,
12179
(
2003
).
121.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Phys. Chem. B
108
,
19799
(
2004
).
122.
Of course, versatile as the LSC-IVR method is, one can also calculate the standard version of the above correlation functions. As we have investigated (not shown in the paper), both the Kubo-transformed version and the standard one actually give almost identical results, except slight difference in the low-frequency regime. We use the Kubo-transformed version for the convenience to directly compare with the CMD results (i.e., also Kubo-transformed version) and for the reason given in the note (Ref. 119) in Ref. 33.
123.
D. A.
Case
,
T. E.
Cheatham
,
T.
Darden
,
H.
Gohlke
,
R.
Luo
,
K. M.
Merz
,
A.
Onufriev
,
C.
Simmerling
,
B.
Wang
, and
R. J.
Woods
,
J. Comput. Chem.
26
,
1668
(
2005
).
125.
T.
Darden
,
D.
York
, and
L.
Pedersen
,
J. Chem. Phys.
98
,
10089
(
1993
).
126.
U.
Essmann
,
L.
Perera
,
M. L.
Berkowitz
,
T.
Darden
,
H.
Lee
, and
L. G.
Pedersen
,
J. Chem. Phys.
103
,
8577
(
1995
).
127.
H. G.
Petersen
,
J. Chem. Phys.
103
,
3668
(
1995
).
128.
G. J.
Martyna
,
A.
Hughes
, and
M.
Tuckerman
,
J. Chem. Phys.
110
,
3275
(
1999
).
129.
G. J.
Martyna
,
M. L.
Klein
, and
M.
Tuckerman
,
J. Chem. Phys.
97
,
2635
(
1992
).
130.
M. P.
Allen
and
D. J.
Tildesley
,
Computer Simulations of Liquids
(
Oxford University Press
,
Oxford
,
1987
).
131.
D.
Frenkel
and
B.
Smit
,
Understanding Molecular Simulation: From Algorithms to Applications
(
Academic
,
New York
,
2002
).
132.
J. E.
Bertie
and
Z. D.
Lan
,
Appl. Spectrosc.
50
,
1047
(
1996
).
133.
When the vibrational frequency is high (i.e., the O–H stretch is much higher than the thermal energy at room temperature or below), the centrifugal force from the rotation correction is actually negligible. In such a high-frequency limit, the 3D problem reduces to a 1D problem. In general, the shifted 3D harmonic oscillator is a nonlinear system. However, in the high frequency limit, it is effectively a linear model, even though the center is shifted. However, we also point out that the accuracy of the LSC-IVR for anharmonic stretches (i.e., Morse potentials) should be investigated too.
134.
G. S.
Fanourgakis
and
S. S.
Xantheas
,
J. Chem. Phys.
128
,
074506
(
2008
).
135.
S.
Habershon
,
G. S.
Fanourgakis
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
129
,
074501
(
2008
).
136.
K.
Krynicki
,
C. D.
Green
, and
D. W.
Sawyer
,
Faraday Discuss.
66
,
199
(
1978
).
137.
D. E.
Manolopoulos
, private communication (
2009
).
138.
J. L. F.
Abascal
and
C.
Vega
,
J. Chem. Phys.
123
,
234505
(
2005
).
You do not currently have access to this content.