The quantum nature of nuclei plays an important role in the accurate modelling of light atoms such as hydrogen, but it is often neglected in simulations due to the high computational overhead involved. It has recently been shown that zero-point energy effects can be included comparatively cheaply in simulations of harmonic and quasiharmonic systems by augmenting classical molecular dynamics with a generalized Langevin equation (GLE). Here we describe how a similar approach can be used to accelerate the convergence of path integral (PI) molecular dynamics to the exact quantum mechanical result in more strongly anharmonic systems exhibiting both zero point energy and tunnelling effects. The resulting PI-GLE method is illustrated with applications to a double-well tunnelling problem and to liquid water.

1.
J. A.
Morrone
and
R.
Car
,
Phys. Rev. Lett.
101
,
017801
(
2008
).
2.
D.
Chandler
and
P. G.
Wolynes
,
J. Chem. Phys.
74
,
4078
(
1981
).
3.
R. P.
Feynman
and
A. R.
Hibbs
,
Quantum Mechanics and Path Integrals
(
McGraw-Hill
,
New York
,
1965
).
4.
T. E.
Markland
and
D. E.
Manolopoulos
,
J. Chem. Phys.
129
,
024105
(
2008
).
5.
T. E.
Markland
and
D. E.
Manolopoulos
,
Chem. Phys. Lett.
464
,
256
(
2008
).
6.
G. S.
Fanourgakis
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
131
,
094102
(
2009
).
8.
M.
Ceriotti
,
G.
Bussi
, and
M.
Parrinello
,
J. Chem. Theory Comput.
6
,
1170
(
2010
).
9.
M.
Ceriotti
,
M.
Parrinello
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
133
,
124104
(
2010
).
10.
M.
Ceriotti
,
G.
Bussi
, and
M.
Parrinello
,
Phys. Rev. Lett.
103
,
030603
(
2009
).
11.
J. A.
Barker
,
J. Chem. Phys.
70
,
2914
(
1979
).
12.
M.
Parrinello
and
A.
Rahman
, in
Monte Carlo Methods in Quantum Problems
, edited by
M. H.
Kalos
(
Reidel
,
Dordrecht
,
1984
), p.
105
.
13.
M.
Parrinello
and
A.
Rahman
,
J. Chem. Phys.
80
,
860
(
1984
).
14.
D. M.
Ceperley
,
Rev. Mod. Phys.
67
,
279
(
1995
).
15.
L. S.
Schulman
,
Techniques and Applications of Path Integration
(
Dover
,
New York
,
2005
).
16.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
100
,
5106
(
1994
).
17.
S.
Jang
and
G. A.
Voth
,
J. Chem. Phys.
111
,
2371
(
1999
).
18.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
121
,
3368
(
2004
).
19.
B. J.
Braams
and
D. E.
Manolopoulos
,
J. Chem. Phys.
125
,
124105
(
2006
).
20.
R.
Zwanzig
,
Nonequilibrium Statistical Mechanics
(
Oxford University Press
,
Oxford
,
2001
).
21.
C. W.
Gardiner
,
Handbook of Stochastic Methods
, ed. (
Springer
,
Berlin
,
2003
).
22.
S.
Habershon
and
D. E.
Manolopoulos
,
J. Chem. Phys.
131
,
244518
(
2009
).
23.
R. Z.
Khaliullin
,
H.
Eshet
,
T. D.
Kühne
,
J.
Behler
, and
M.
Parrinello
,
Phys. Rev. B
81
,
100103
(
2010
).
24.
M.
Ceriotti
,
G.
Miceli
,
A.
Pietropaolo
,
D.
Colognesi
,
A.
Nale
,
M.
Catti
,
M.
Bernasconi
, and
M.
Parrinello
,
Phys. Rev. B
82
,
174306
(
2010
).
25.
The GLE parameters we have used in the present study and our solutions gP(x) of the functional equation (13) may be downloaded from http://gle4md.berlios.de.
26.
M.
Ceriotti
,
G.
Bussi
, and
M.
Parrinello
,
Phys. Rev. Lett.
102
,
020601
(
2009
).
27.
L.
Lin
,
J. A.
Morrone
,
R.
Car
, and
M.
Parrinello
,
Phys. Rev. Lett.
105
,
110602
(
2010
).
28.
M. E.
Tuckerman
,
B. J.
Berne
, and
G. J.
Martyna
,
J. Chem. Phys.
97
,
1990
(
1992
).
29.
M. E.
Tuckerman
,
B. J.
Berne
,
G. J.
Martyna
, and
M. L.
Klein
,
J. Chem. Phys.
99
,
2796
(
1993
).
30.
D. M.
Endres
and
J. E.
Schindelin
,
IEEE Trans. Inf. Theory
49
,
1858
(
2003
).
31.
S.
Habershon
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
131
,
024501
(
2009
).
32.
G.
Bussi
,
D.
Donadio
, and
M.
Parrinello
,
J. Chem. Phys.
126
,
014101
(
2007
).
33.
M.
Shiga
and
W.
Shinoda
,
J. Chem. Phys.
123
,
134502
(
2005
).
34.
M.
Takahashi
and
M.
Imada
,
J. Phys. Soc. Japn.
53
,
3765
(
1984
).
35.
36.
S.
Jang
,
S.
Jang
, and
G. A.
Voth
,
J. Chem. Phys.
115
,
7832
(
2001
).
37.
T. M.
Yamamoto
,
J. Chem. Phys.
123
,
104101
(
2005
).
You do not currently have access to this content.