Two of the most successful methods that are presently available for simulating the quantum dynamics of condensed phase systems are centroid molecular dynamics (CMD) and ring polymer molecular dynamics (RPMD). Despite their conceptual differences, practical implementations of these methods differ in just two respects: the choice of the Parrinello-Rahman mass matrix and whether or not a thermostat is applied to the internal modes of the ring polymer during the dynamics. Here, we explore a method which is halfway between the two approximations: we keep the path integral bead masses equal to the physical particle masses but attach a Langevin thermostat to the internal modes of the ring polymer during the dynamics. We justify this by showing analytically that the inclusion of an internal mode thermostat does not affect any of the established features of RPMD: thermostatted RPMD is equally valid with respect to everything that has actually been proven about the method as RPMD itself. In particular, because of the choice of bead masses, the resulting method is still optimum in the short-time limit, and the transition state approximation to its reaction rate theory remains closely related to the semiclassical instanton approximation in the deep quantum tunneling regime. In effect, there is a continuous family of methods with these properties, parameterised by the strength of the Langevin friction. Here, we explore numerically how the approximation to quantum dynamics depends on this friction, with a particular emphasis on vibrational spectroscopy. We find that a broad range of frictions approaching optimal damping give similar results, and that these results are immune to both the resonance problem of RPMD and the curvature problem of CMD.

1.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
100
,
5106
(
1994
).
2.
S.
Jang
and
G. A.
Voth
,
J. Chem. Phys.
111
,
2371
(
1999
).
3.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
121
,
3368
(
2004
).
4.
B. J.
Braams
and
D. E.
Manolopoulos
,
J. Chem. Phys.
125
,
124105
(
2006
).
5.
R. P.
Feynman
and
A. R.
Hibbs
,
Quantum Mechanics and Path Integrals
(
McGraw-Hill
,
New York
,
1965
).
6.
D.
Chandler
and
P. G.
Wolynes
,
J. Chem. Phys.
74
,
4078
(
1981
).
7.
G. A.
Voth
,
Adv. Chem. Phys.
93
,
135
(
1996
).
8.
S.
Habershon
,
D. E.
Manolopoulos
,
T. E.
Markland
, and
T. F.
Miller
 III
,
Annu. Rev. Phys. Chem.
64
,
387
(
2013
).
9.
M.
Pavese
and
G. A.
Voth
,
Chem. Phys. Lett.
249
,
231
(
1996
).
10.
J.
Lobaugh
and
G. A.
Voth
,
J. Chem. Phys.
106
,
2400
(
1997
).
11.
Y.
Yonetani
and
K.
Kinugawa
,
J. Chem. Phys.
119
,
9651
(
2003
).
12.
T. D.
Hone
and
G. A.
Voth
,
J. Chem. Phys.
121
,
6412
(
2004
).
13.
T. F.
Miller
 III
and
D. E.
Manolopoulos
,
J. Chem. Phys.
122
,
184503
(
2005
).
14.
T. F.
Miller
 III
and
D. E.
Manolopoulos
,
J. Chem. Phys.
123
,
154504
(
2005
).
15.
T. D.
Hone
,
P. J.
Rossky
, and
G. A.
Voth
,
J. Chem. Phys.
124
,
154103
(
2006
).
16.
T. E.
Markland
,
S.
Habershon
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
128
,
194506
(
2008
).
17.
T. F.
Miller
 III
,
J. Chem. Phys.
129
,
194502
(
2008
).
18.
S.
Habershon
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
131
,
024501
(
2009
).
19.
A. R.
Menzeleev
and
T. F.
Miller
 III
,
J. Chem. Phys.
132
,
034106
(
2010
).
20.
T. E.
Markland
,
J. A.
Morrone
,
B. J.
Berne
,
K.
Miyazaki
,
E.
Rabani
, and
D. R.
Reichman
,
Nat. Phys.
7
,
134
(
2011
).
21.
G. A.
Voth
,
J. Phys. Chem.
97
,
8365
(
1993
).
22.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
105
,
6856
(
1996
).
23.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
106
,
1769
(
1997
).
24.
S.
Jang
and
G. A.
Voth
,
J. Chem. Phys.
112
,
8747
(
2000
).
25.
E.
Geva
,
Q.
Shi
, and
G. A.
Voth
,
J. Chem. Phys.
115
,
9209
(
2001
).
26.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
122
,
084106
(
2005
).
27.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
123
,
034102
(
2005
).
28.
R.
Collepardo-Guevara
,
I. R.
Craig
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
128
,
144502
(
2008
).
29.
R.
Collepardo-Guevara
,
Y. V.
Suleimanov
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
130
,
174713
(
2009
).
30.
Y. V.
Suleimanov
,
R.
Collepardo-Guevara
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
134
,
044131
(
2011
).
31.
A. R.
Menzeleev
,
N.
Ananth
, and
T. F.
Miller
 III
,
J. Chem. Phys.
135
,
074106
(
2011
).
32.
N.
Boekelheide
,
R.
Salomon-Ferrer
, and
T. F.
Miller
 III
,
Proc. Natl. Acad. Sci. U.S.A.
108
,
16159
(
2011
).
33.
R.
Perez de Tudela
,
F. J.
Aoiz
,
Y. V.
Suleimanov
, and
D. E.
Manolopoulos
,
J. Phys. Chem. Lett.
3
,
493
(
2012
).
34.
J. W.
Allen
,
W. H.
Green
,
Y.
Li
,
H.
Guo
, and
Y. V.
Suleimanov
,
J. Chem. Phys.
138
,
221103
(
2013
).
35.
Y.
Li
,
Y. V.
Suleimanov
, and
H.
Guo
,
J. Phys. Chem. Lett.
5
,
700
(
2014
).
36.
A. R.
Menzeleev
,
F.
Bell
, and
T. F.
Miller
 III
,
J. Chem. Phys.
140
,
064103
(
2014
).
37.
B. J.
Braams
,
T. F.
Miller
 III
, and
D. E.
Manolopoulos
,
Chem. Phys. Lett.
418
,
179
(
2006
).
38.
S.
Habershon
,
B. J.
Braams
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
127
,
174108
(
2007
).
39.
A.
Perez
,
M. E.
Tuckerman
, and
M. H.
Muser
,
J. Chem. Phys.
130
,
184105
(
2009
).
40.
M.
Shiga
and
A.
Nakayama
,
Chem. Phys. Lett.
451
,
175
(
2008
).
41.
S.
Habershon
,
G. S.
Fanourgakis
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
129
,
074501
(
2008
).
42.
A.
Witt
,
S. D.
Ivanov
,
M.
Shiga
,
H.
Forbert
, and
D.
Marx
,
J. Chem. Phys.
130
,
194510
(
2009
).
43.
S. D.
Ivanov
,
A.
Witt
,
M.
Shiga
, and
D.
Marx
,
J. Chem. Phys.
132
,
031101
(
2010
).
44.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
101
,
6168
(
1994
).
45.
R.
Kubo
,
J. Phys. Soc. Jpn.
12
,
570
(
1957
).
46.
J. O.
Richardson
and
S. C.
Althorpe
,
J. Chem. Phys.
131
,
214106
(
2009
).
47.
T. J. H.
Hele
and
S. C.
Althorpe
,
J. Chem. Phys.
138
,
084108
(
2013
).
48.
S. C.
Althorpe
and
T. J. H.
Hele
,
J. Chem. Phys.
139
,
084115
(
2013
).
49.
T. J. H.
Hele
and
S. C.
Althorpe
,
J. Chem. Phys.
139
,
084116
(
2013
).
50.
A.
Horikoshi
and
K.
Kinugawa
,
J. Chem. Phys.
122
,
174104
(
2005
).
51.
S.
Jang
,
A. V.
Sinitskiy
, and
G. A.
Voth
,
J. Chem. Phys.
140
,
154103
(
2014
).
52.
R.
Zwanzig
,
Nonequilibrium Statistical Mechanics
(
Oxford University Press
,
New York
,
2001
), pp.
42
and
.
53.
M.
Parrinello
and
A.
Rahman
,
J. Chem. Phys.
80
,
860
(
1984
).
54.
J.
Cao
and
G. A.
Voth
,
J. Chem. Phys.
101
,
6157
(
1994
).
55.
M.
Ceriotti
,
G.
Bussi
, and
M.
Parrinello
,
J. Chem. Theory Comput.
6
,
1170
(
2010
).
56.
M.
Ceriotti
,
M.
Parrinello
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
133
,
124104
(
2010
).
57.
K. P.
Huber
and
G.
Herzberg
,
Molecular Spectra and Molecular Structure IV. Constants of Diatomic Molecules
(
Van Nostrand Reinhold
,
New York
,
1979
), p.
508
.
58.
X.
Huang
,
B. J.
Braams
, and
J. M.
Bowman
,
J. Chem. Phys.
122
,
044308
(
2005
).
59.
O.
Vendrell
,
F.
Gatti
, and
H.-D.
Meyer
,
J. Chem. Phys.
127
,
184303
(
2007
).
60.
G.
Niedner-Schatteburg
,
Angew. Chem., Int. Ed.
47
,
1008
(
2008
).
61.
X.
Huang
,
S.
Habershon
, and
J. M.
Bowman
,
Chem. Phys. Lett.
450
,
253
(
2008
).
62.
M.
Kaledin
,
A. L.
Kaledin
,
J. M.
Bowman
,
J.
Ding
, and
K. D.
Jordan
,
J. Phys. Chem. A
113
,
7671
(
2009
).
63.
M.
Baer
,
D.
Marx
, and
G.
Mathias
,
Angew. Chem., Int. Ed.
49
,
7346
(
2010
).
64.
F.
Agostini
,
R.
Vuilleumier
, and
G.
Ciccotti
,
J. Chem. Phys.
134
,
084302
(
2011
).
65.
L. I.
Yeh
,
M.
Okumura
,
J. D.
Meyers
,
J. M.
Price
, and
Y. T.
Lee
,
J. Chem. Phys.
91
,
7319
(
1989
).
66.
K. R.
Asmis
,
N. L.
Pivonka
,
G.
Santambrogio
,
M.
Brümmer
,
C.
Kaposta
,
D. M.
Neumark
, and
L.
Wöste
,
Science
299
,
1375
(
2003
).
67.
T. D.
Fridgen
,
T. B.
McMahon
,
L.
MacAleese
,
J.
Lemaire
, and
P.
Maitre
,
J. Phys. Chem. A
108
,
9008
(
2004
).
68.
N. I.
Hammer
,
E. G.
Diken
,
J. R.
Roscoli
,
M. A.
Johnson
,
E. M.
Myshakin
,
K. D.
Jordan
,
A. B.
McCoy
,
X.
Huang
,
J. M.
Bowman
, and
S.
Carter
,
J. Chem. Phys.
122
,
244301
(
2005
).
69.
T. L.
Guasco
,
M. A.
Johnson
, and
A. B.
McCoy
,
J. Phys. Chem. A
115
,
5847
(
2011
).
70.
M.
Ceriotti
,
J.
More
, and
D. E.
Manolopoulos
,
Comput. Phys. Commun.
185
,
1019
(
2014
).
71.
S.
Plimpton
,
J. Comput. Phys.
117
,
1
(
1995
).
72.
R. W.
Hall
and
B. J.
Berne
,
J. Chem. Phys.
81
,
3641
(
1984
).
73.
J. E.
Bertie
and
Z.
Lan
,
Appl. Spectrosc.
50
,
1047
(
1996
).
74.
G. S.
Fanourgakis
and
S. S.
Xantheas
,
J. Chem. Phys.
128
,
074506
(
2008
).
75.
F.
Paesani
and
G. A.
Voth
,
J. Chem. Phys.
132
,
014105
(
2010
).
76.
Y.
Wang
and
J. M.
Bowman
,
J. Chem. Phys.
134
,
154510
(
2011
).
77.
H.
Liu
,
Y.
Wang
, and
J. M.
Bowman
,
J. Phys. Chem. Lett.
3
,
3671
(
2012
).
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