The dynamic structure factor of liquid para-hydrogen and ortho-deuterium in corresponding thermodynamic states (T = 20.0 K, n = 21.24 nm−3) and (T = 23.0 K, n = 24.61 nm−3), respectively, has been computed by both the Feynman-Kleinert linearized path-integral (FK-LPI) and Ring-Polymer Molecular Dynamics (RPMD) methods and compared with Inelastic X Ray Scattering spectra. The combined use of computational and experimental methods enabled us to reduce experimental uncertainties in the determination of the true sample spectrum. Furthermore, the refined experimental spectrum of para-hydrogen and ortho-deuterium is consistently reproduced by both FK-LPI and RPMD results at momentum transfers lower than 12.8 nm−1. At larger momentum transfers the FK-LPI results agree with experiment much better for ortho-deuterium than for para-hydrogen. More specifically we found that for k ∼ 20.0 nm−1para-hydrogen provides a test case for improved approximations to quantum dynamics.

1.
When referring to quantum effects it is customary to distinguish between those related to the non-commutative character of the operators describing dynamical variables and those connected with the quantum character of particle statistics (Bose-Einstein or Fermi- Dirac). While the latter are relevant in strongly quantum fluids (as, e.g., superfluid 4He, degenerate fluid 3He, and jellium), these seem to play no significant role for the semi-quantum fluids considered in the present work, whose properties can be consistently described using Maxwell-Boltzmann statistics.
2.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Chem. Phys.
119
,
12179
(
2003
).
3.
I. R.
Craig
and
D. E.
Manolopoulos
,
J. Chem. Phys.
121
,
3368
(
2004
).
4.
E. J.
Heller
,
J. Chem. Phys.
65
,
1289
(
1976
).
5.
H.
Wang
,
X.
Sun
, and
W. H.
Miller
,
J. Chem. Phys.
108
,
9726
(
1998
).
6.
Q.
Shi
and
E.
Geva
,
J. Chem. Phys.
118
,
8173
(
2003
).
7.
S.
Habershon
,
D. E.
Manolopoulos
,
T. E.
Markland
, and
T. F.
Miller
 III
,
Annu. Rev. Phys. Chem.
64
,
387
(
2013
).
8.
I. R.
Craig
and
D. E.
Manolopoulos
,
Chem. Phys.
322
,
236
(
2006
).
9.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
126
,
234110
(
2007
).
10.
J.
Liu
and
W. H.
Miller
,
J. Chem. Phys.
128
,
144511
(
2008
).
11.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Phys. Chem. B
108
,
19799
(
2004
).
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.
D. R.
Reichman
and
E.
Rabani
,
J. Chem. Phys.
116
,
6279
(
2002
).
15.
F. J.
Mompean
,
M.
Garcia-Hernandez
,
F. J.
Bermejo
, and
S. M.
Bennington
,
Phys. Rev. B
54
,
970
(
1996
).
16.
A.
Cunsolo
,
D.
Colognesi
,
M.
Sampoli
,
R.
Senesi
, and
R.
Verbeni
,
J. Chem. Phys.
123
,
114509
(
2005
).
17.
A.
Cunsolo
,
G.
Pratesi
,
D.
Colognesi
,
R.
Verbeni
,
M.
Sampoli
,
F.
Sette
,
G.
Ruocco
,
R.
Senesi
,
M. H.
Krisch
, and
M.
Nardone
,
J. Low Temp. Phys.
129
,
117
(
2002
).
18.
G. L.
Squires
,
Introduction to the Theory of Thermal Neutron Scattering
(
Cambridge University Press
,
Cambridge
,
1978
).
19.
L.
Van Hove
,
Phys. Rev.
95
,
249
(
1954
).
20.
D.
Pines
and
P.
Nozieres
,
The Theory of Quantum Liquids
(
Benjamin
,
New York
,
1966
), Vol.
I
.
21.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Phys. Chem. A
108
,
8743
(
2004
).
22.
R. P.
Feynman
and
H.
Kleinert
,
Phys. Rev. A
34
,
5080
(
1986
).
23.
H.
Kleinert
,
Path Integrals in Quantum Mechanics, Statistics, and Polymer Physics
(
World Scientific
,
Singapore
,
1995
).
24.
S.
Jang
and
G. A.
Voth
,
J. Chem. Phys.
111
,
2357
(
1999
).
25.
J. A.
Poulsen
,
G.
Nyman
, and
P. J.
Rossky
,
J. Chem. Theory Comput.
2
,
1482
(
2006
).
26.
I. F.
Silvera
and
V. V.
Goldman
,
J. Chem. Phys.
69
,
4209
(
1978
).
27.
T.
Omiyinka
and
M.
Boninsegni
,
Phys. Rev. B
88
,
024112
(
2013
).
28.
Q.
Wang
,
J. K.
Johnson
, and
J. Q.
Broughton
,
Mol. Phys.
89
,
1105
(
1996
).
29.
J. A.
Poulsen
,
J.
Scheers
,
G.
Nyman
, and
P. J.
Rossky
,
Phys. Rev. B
75
,
224505
(
2007
).
30.
C.
Kittel
,
Introduction to Solid State Physics
, 7th ed. (
Wiley
,
New York
,
1996
).
31.
T. F.
Miller
 III
,
D. E.
Manolopoulos
,
P. A.
Madden
,
M.
Konieczny
, and
H.
Oberhofer
,
J. Chem. Phys.
122
,
057101
(
2005
).
32.
P. H.
Berens
,
S. R.
White
, and
K. R.
Wilson
,
J. Chem. Phys.
75
,
515
(
1981
).
33.
M.
Ceriotti
,
M.
Parrinello
,
T. E.
Markland
, and
D. E.
Manolopoulos
,
J. Chem. Phys.
133
,
124104
(
2010
).
34.
A.
Cunsolo
, private communication (
2013
).
35.
36.
Due to a normalization issue associated with the empty container scattering contribution for H2(k = 5.5 nm−1) and H2(k = 15.3 nm−1), the use of Eq. (36) for the transmission coefficient resulted in unphysical results for the refined dynamic structure factor for these two cases. To avoid this, we treated the transmission coefficient as a free parameter for these two cases and the values used in the refinement process are shown in Table III.
37.
See supplementary material at http://dx.doi.org/10.1063/1.4851997 for tabulations of the refined experimental, FK-LPI, and RPMD dynamic structure factors in Fig. 3 as well as the non-convoluted FK-LPI and RPMD dynamic structure factors of para-hydrogen and ortho-deuterium for all of the momentum transfers considered.

Supplementary Material

You do not currently have access to this content.