Thermodynamical and structural properties of neon in the liquid and supercritical
states obtained from ab initio calculations and molecular dynamics simulations
Rolf Eggenberger, Stefan Gerber, Hanspeter Huber, Debra Searles, and Marc Welker
Citation: The Journal of Chemical Physics 99, 9163 (1993); doi: 10.1063/1.465530
View online: http://dx.doi.org/10.1063/1.465530
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/99/11?ver=pdfcov
Published by the AIP Publishing
Articles you may be interested in
Molecular simulation of the thermodynamic, structural, and vapor-liquid equilibrium properties of neon
J. Chem. Phys. 145, 104501 (2016); 10.1063/1.4961682
Ab initio calculations of the phonon frequencies and related properties of crystalline Ne under pressure
Low Temp. Phys. 35, 815 (2009); 10.1063/1.3253406
Ab initio calculation of interatomic decay rates of excited doubly ionized states in clusters
J. Chem. Phys. 129, 244102 (2008); 10.1063/1.3043437
Intermolecular interactions of H 2 S with rare gases from molecular beam scattering in the glory regime and
from ab initio calculations
J. Chem. Phys. 125, 133111 (2006); 10.1063/1.2218513
Intermolecular potential energy surfaces and spectra of Ne–HCN complex from ab initio calculations
J. Chem. Phys. 114, 764 (2001); 10.1063/1.1331101
Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 130.102.82.2 On: Tue, 18
Oct 2016 06:36:54
Thermodynamical and structural properties of neon in the liquid
and supercritical states obtained from ab initio calculations
and molecular dynamics simulations
Rolf Eggenberger,a) Stefan Gerber, Hanspeter Huber, Debra Searles,b) and Marc Welker
Institut for Physikalische Chemie der Universitiit Basel, Klingelbergstrasse 80,
CH-4056 Basel, Switzerland
(Received 26 April 1993; accepted 23 August 1993)
Thermodynamical and structural properties including the equation of state, the second virial
coefficient, the enthalpy and internal energy, the molar heat capacity, the speed of sound, the
thermal expansion and pressure coefficients, the compressibility, and the pair distribution
function are calculated in an ab initio approach for supercritical and liquid neon. The neon
climer potential energy curve has been obtained previously from ab initio calculations and is
applied in classical molecular dynamics simulations. Care was taken to eliminate all possible
errors thus reducing the remaining error in the supercritical state at higher temperatures to two
sources, namely, the inaccuracies in the quantum chemical potential curve and the two particle
approximation in the simulation. At lower temperatures, there is in addition an error due to the
classical simulation. The calculated properties will be used as benchmarks in future work to
investigate the influence of an improved potential curve and of an inclusion of the three particle
potential in the simulation.
I. INTRODUCTION
Although molecular dynamics simulations of liquids
with empirical potentials have been performed now for several decades, applying potentials from quantum chemical
calculations to simulations started only about ten years ago
mainly by the pioneering work of Clementi (Ref. 1 and
references therein) on water. Since this time, several
groups have investigated molecular liquids with potentials
obtained fully or at least partially from ab initio calculations. However, most of the previous simulations of liquids
were aiming towards chemically important liquids, such as
water, the goal of our work on neon is to analyze the errors
made in this approach and to find out where the greatest
effort is justified to improve the quality of this approach. It
is still at the limits oftoday's feasibilities to obtain accurate
atomic potential curves, even more so to obtain potential
surfaces for molecular simulations. In addition it is not
easy in the molecular case to find a simple analytical function which fits the quantum chemical information without
loosing accuracy. If even three-particle interactions have to
be considered, the approach soon becomes unfeasible. This
paper is the fifth in a series of papers2- 5 with the goal of
establishing benchmark data obtained with a good ab initio
potential for many liquid properties of neon. Similarly, an
accurate potential for the argon dimer was obtained by
McLean et al. 6 In contrast to McLean's work, we employed molecular dynamics simulations to calculate many
liquid properties. Care was taken not to lose any accuracy
in fitting the quantum chemical information to an analytical curve and in using appropriate parameters in the sim-
ulations. Therefore, the remaining errors, at temperatures
high enough that quantum effects can be neglected, are due
to the quantum chemical approximations for the potential
and to the two-particle approximation. Further work is in
progress to calculate a more accurate two-particle potential
on one hand, which, applied in the same simulations, will
show the improvement of each individual liquid property
due to the quantum chemical improvement, and to obtain
a three-particle potential surface at the present level of
-160
'--_~_...J....._~_---'-_~
2.5
4.5
6.5
_ _<-....J
8.5
r/(80)
·)Present address: Biosym Technologies Inc., 9685 Scranton Road, San
Diego, California 92121-2777.
b)Present address: Research School of Chemistry, GPO Box 4, Canberra,
ACT 2601 Australia.
FIG. 1. Potential energy curves of the neon dimer from Aziz and Slaman
(HFD-B,-), from Kortbeek and Schouten (exp-6,-' '-' '-), and the
ab initio potential (ai,---). Note the logarithmic scale for positive energies.
J. Chern.content
Phys. is
99subject
(11), 1toDecember
0021-9606/93/99(11 )/9163/7/$6.00 © 1993 American
Institute
of Physics
9163
Reuse of AIP Publishing
the terms:1993
https://publishing.aip.org/authors/rights-and-permissions.
Downloaded
to IP:
130.102.82.2
On: Tue, 18
Oct 2016 06:36:54
9164
Eggenberger et al.: Thermodynamical and structural properties of neon
accuracy on the other hand, which will show the error of
each individual liquid property due to the two-particle approximation. Since in the first paper2 of this series the potential was established, the next three discussed results
for three transport properties, the thermal conductivity, 3
the shear viscosity,4 and the diffusion coefficient. 5 Here we
present thermodynamical and structural properties of
neon, in particular, the equation of state; the second virial
coefficient; the enthalpy and internal energy; the molar
heat capacity; the speed of sound; the thermal expansion
and pressure coefficients; the compressibility; and the pair
distribution function.
II. METHOD AND CALCULATIONS
The potential was taken from our previous work. 2 It
was obtained from ab initio calculations with an
14slOp4dIJ basis set contracted to 7s6p4dIJ applying
M011er-Plesset perturbation theory to fourth order including all excitations up to quadruple excitations, i.e.,
MP4(SDTQ). The basis set superposition error was corrected by the full counterpoise correction and much care
was taken not to lose any accuracy converting the data into
an analytical function. The potential curve is shown in Fig.
1 together with the HFD-B potential by Aziz and Slaman/'s which is at the moment the most accurate empirical two-particle potential, and with an effective potential
TABLE I. Compressibility factor z.
T(K)
vm (l0-6 m3 mol- 1)
298
298
298
298
298
298
298
298
298
298
298
54.24
37.78
25.19
20.78
18.38
16.84
15.63
14.93
14.27
13.74
13.27
100
100
100
100
100
P (MPa)
Zsim
.
exp-6 by Kortbeek and Schouten, 9 which was obtained by
fits to the sound velocities in the supercritical state under
similar pressures as applied in this work.
All molecular dynamics equilibrium simulations were
performed with the above ab initio potential in a constantNVE ensemble. Programs were written in standard
FORTRAN 77, partially using the code from Allen and Tildesley.1O Using little random access memory (RAM) as
well as disk space, the programs can run on very different
machines. 3, 11
The Verlet leap frog algorithm for a cubic box with
periodic boundary conditions and the minimum image
convention was used throughout. Long range corrections
were applied with a shifted potential for pressure and potential energy. On scalar computers, Verlet neighbor lists
were used. The simulations were started from a facecentered-cubic (fcc) lattice with Gaussian distributed velocities scaled to correspond to the desired temperatures.
Tests indicating when the equilibrium is reached were built
into the program. At the beginning, the time step is increased for faster melting until the order parameter falls
short of a given limit. Then the simulation is continued
automatically with the normal time step until the temperature is constant and equal to the desired value. During
this procedure, the temperature is rescaled every few time
steps. Starting from a fcc state, it usually took about 800
Zcxp
b
Error (%)
1.308
1.525
2.034
2.516
2.967
3.399
3.785
4.217
4.608
4.990
5.355
2.9
4.3
6.6
7.4
8.2
8.6
11.2
9.3
9.3
9.6
10.2
1.495 (1.497)
1.519( 1.521)
1000
1.351
1.590 ( 1.592)
2.168
2.702
3.212
3.692
4.207
4.612
5.037
5.469
5.901 (5.883)
5.130(5.121)
5.267 (5.255)
44.88
28.68
23.79
21.28
19.66
20
40
60
80
100
1.186
1.585
1.994
2.388
2.804(2.826 )
1.080
1.380
1.717
2.048
2.365
9.9
14.9
16.1
16.6
18.6
2.162(2.203 )
2.371 (2.413)
200
200
200
200
200
93.11
52.61
39.35
32.79
28.86
20
40
60
80
100
1.149
1.324
1.506
1.691
1.873( 1.877)
1.120
1.265
1.420
1.578
1.735
2.6
4.6
6.1
7.2
7.9
400
500
600
68.63
82.78
96.82
60
60
60
1.268
1.216
1.180
1.238
1.195
1.164
2.4
1.8
1.3
400
500
600
46.45
55.01
63.51
100
100
100
1.447 ( 1.448)
1.357( 1.357)
1.297 (1.297)
1.397
1.323
1.273
3.6
2.6
1.9
28
15.74
20
2.497 (3.374)
1.352
84.7
-0.681(0.729)
0.665 ( 1.817)
60
100
200
300
400
500
600
700
800
900
'Values in parentheses include the first quantum correction for temperature and pressure.
bCalculated from Ref. 22.
J. Chem. Phys., Vol. 99, No. 11, 1 December 1993
Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 130.102.82.2 On: Tue, 18
Oct 2016 06:36:54
Eggenberger et al.: Thermodynamical and structural properties of neon
z
l
0
5.0
0
•
0
0
•
0
0
3.0
0
•
•
o
+
•
i
i
i
i
i
II
ot
+
Ol!
zsim
zexp
-30
<tx
-40
600
t
~
Of-
-20
0
400
t
o
0
~
Oli
a
200
0
.....
I'Q
•
0
10
~
•
•0
•
20
-10
•
1.0
•
9165
800
-50
1000
P/MPa
•
+
•x
0
B exp
B this work
+ BEXP-6
0
x
100
200
300
B HFD-B
sao
400
600
T/K
FIG. 2. The experimental and simulated (ai) compressibility factor
of supercritica1 neon at 298 K as a function of pressure.
Z= PV".I RT
steps to reach the equilibrium. The equilibrium simulations
for the transport properties3- S were carried out in batches
of 33 600 steps. They were also used to obtain the compressibility factor, the energy and enthalpy, the molar heat
capacity at constant volume, and the pair distribution
function. To obtain the quantum corrections for the temperature and the pressure and the remaining properties, the
simulations were continued after a change in the program
for at least 15 000 steps and longer in cases with large
statistical errors.
We used the following parameters for the final runs:
500 particles, time step length !1t 10 fs, cut-off radius 2.5 0'
[0' taken as the distance where the potential energy is zero
(see Fig. 1)], and list radius 2.9 0'.
III. RESULTS AND DISCUSSION
A. The compressibility factor
A basic test for the ab initio approach applied here is
how well the equation of state is reproduced. We discuss it
with the help of the compressibility factor z=PVmIRT,
which gives the deviation from the ideal gas behavior. Values obtained over a large range in the supercritical state
together with one point in the liquid phase are tabulated in
Table I and where available compared to experimental values. Figure 2 shows the z dependence on pressure at room
temperature (298 K) in comparison with experiment. The
simulated results are always too large, at the highest pres-
FIG. 3. The second virial coefficient B of neon as a function of temperature. Experimental values in comparison with values obtained from different potentials.
sure by about 10%. In a simple picture, this can be attributed to an excessively high actual volume of the atoms
which again would mean that the "radius" of the atoms
has been calculated to be about 3% too long. This is in fair
agreement with the deviation between the calculated
(6.00 aD) and the experimental (S.86±O.09 aD) equilibrium distance in the neon dimer and also with the small
parallel shift to longer distances of our potential in the
repulsive region compared to the experimental potential by
Aziz and Slaman as shown in Fig. 1.
In the liquid phase, the simulated compressibility factor deviates much more from the experimental value than
in the supercritical states (see Table I). However, compared to deviations in molecular liquids (see, e.g., the wellknown potentials for water 12,13), the error of 85% is still
small. Nevertheless, it is clear that the potential is still
unable to predict thermodynamical liquid properties for
practical purposes. This failure is only partially due to the
too shallow well of the potential since pure pair potentials
as accurate as the HFD-B potential fail as badly. Clearly,
only more sophisticated effective pair potentials are able to
reproduce the liquid range (see the following discussion).
First quantum corrections of temperature 14,15 and
pressure 16,17 were calculated for some state points. The corrections are very small compared to the deviation from the
experiment for all points in the supercritical region,
whereas in the liquid phase, its size is similar to the devi-
TABLE II. Second virial coefficients (cm 3 mol-I).
T(K)
44
50
60
70
80
100
125
150
200
250
300
350
400
450
500
550
-36.3
-34.0
-41.5
-47.9
_46.1<
-27.6
-25.8
-32.4
-37.5
-35.4<
-17.6
-16.4
-21.9
-25.8
-24.9<
-11.0
-10.1
-14.8
-17.9
_17.1<
-6.3
-5.5
-9.7
-12.3
_12.8d
0.0
0.5
-3.0
-5.0
-6.0d
4.6
5.0
2.0
0.5
_O.4d
7.5
7.8
5.2
4.0
3.2d
10.8
11.0
8.8
7.9
7.7d
12.5
12.7
10.8
10.1
13.6
13.7
12.0
11.4
l1.3 d
14.2
14.3
12.7
12.2
12.1 d
14.6
14.7
13.2
12.7
12.7d
14.8
14.9
13.6
13.1
13.1 d
15.0
15.1
13.8
13.4
13.4d
15.1
15.1
13.9
13.6
13.7d
Potential
Hu4dl,r
Hu4dl/,
exp-6b
HFD-Bb
Experiment
1O.~
aHu4dlf is the potential obtained from the (14slOp4dlf)/[7s6p4dlf] basis set (see the text).
blnc1uding the first quantum correction calculated according to Ref. 27.
~rom Ref. 28.
dFrom Ref. 29. The experimental uncertainty is 1 cm3 mol-I.
Reuse of AIP Publishing content is subject to the terms:
https://publishing.aip.org/authors/rights-and-permissions.
Downloaded to IP: 130.102.82.2 On: Tue, 18
J. Chem.
Phys., Vol. 99, No. 11, 1 December 1993
Oct 2016 06:36:54
Eggenberger et al.: Thermodynamical and structural properties of neon
9166
TABLE III. Enthalpy H and energy U (J/mol).
T(K)
P (MPa)
298
60
100
200
300
400
500
60
100
400
18436
26472
39693
48118
54411
59367
14571
21527
Error (%)
U,im
4.4
5.5
8.1
7.7
8.9
9.5
2.7
4.8
3613
3550
3577
3605
3743
3876
4928
4968
6695
7110
8310
9542
10763
11 932
8900
9370
6990
7498
8986
10276
11725
13 067
9143
9818
Error (%)
3460
3372
3281
(3269)
(3289)
(3324)
4801
4745
4.4
5.3
9.0
10.3
13.8
16.6
2.6
4.7
'Interpolated with data from Refs. 18 and 19.
bInterpolated and extrapolated (in parentheses) with data from Ref. 18.
ation from experiment, but makes the result even worse.
Evidently, the main defects are due to the potential and the
two particle potential approximation and not due to the
classical simulation.
For a few points, simulations were performed with the
HFD-B potential by Aziz and Slaman and the exp-6 potential by Kortbeek and Schouten. In general, the last performs best, which is not very surprising as it was calibrated
under similar conditions (high pressures) as applied here.
Comparing the values from the three different potentials at
the liquid state point suggests that the approximation of a
two particle potential and the overly shallow well in the
potential are compensating partially.
B. The second vlrlal coefficient
Table II and Fig. 3 show the second virial coefficient at
different temperatures from 550 K down to the critical
point. In contrast to our previous paper, 2 the data here are
calculated from the analytical form of the potential. This is
TABLE IV. Several simulated properties."
c
ap
(ms- I )
(10- 3 K- I )
f3s
(GPa- l )
627(602)
724(693)
930(891)
1097(1053)
1224( 1177)
1341 (1289)
1461 (1389)
1543(1489)
1619(1561 )
1712(1636)
1786(1706)
2.43
2.07
1.59
1.31
1.17
1.06
0.92
0.85
0.84
0.73
0.69
6.85
11.29
5.79(6.52)
3.57(3.85)
1.44 ( 1.57) 2.27(2.57)
1.31( 1.48)
0.86(0.94)
0.61 (0.66) 0.91 (1.01)
0.46(0.50) 0.69(0.75)
0.36(0.41 ) 0.52(0.59)
0.31(0.34) 0.44(0.49)
0.27(0.29) 0.38(0.41)
0.23(0.25) 0.32(0.36)
0.21(0.23) 0.28(0.31)
13.2( 13.2)
13.7( 13.6)
14.6(14.5)
15.4( 15.2)
16.1
16.7
17.3
17.7
18.1
18.5
18.8
21.8(22.6)
22.2(23.0)
23.1 (23.6)
23.6(24.0)
24.2
24.8
24.8
25.1
25.8
25.6
25.5
20
40
60
80
100
13.8
14.7
15.5
16.1
16.8
27.2(30.0)
28.3(30.0)
27.5(29.2)
26.7(28.9)
29.3(28.8)
386
514
629
724
783(735)
9.39
7.03
5.10
3.98
4.18
14.95
5.37
2.98
2.01
1.59
29.57
10.34
5.26
3.31
2.77
0.32
0.68
0.98
1.22
1.51
93.11
52.61
39.35
32.79
28.86
20
40
60
80
100
12.9
13.3
13.7
14.0
14.4
22.4(22.9)
23.3(24.0)
23.9(24.5)
24.7(24.8)
24.0(24.9)
443
514
582
647
712(677)
4.56
4.03
3.60
3.36
2.79
23.55
9.88
5.75
3.89
2.82
40.88
17.25
10.03
6.85
4.71
0.11
0.23
0.36
0.49
0.59
400
500
600
68.63
82.78
96.82
60
60
60
13.0( 12.8)
12.9
12.8
21.5(21.7)
21.2
21.0
666(634)
711
754
1.97
1.63
1.39
7.66
8.12
8.45
12.62
13.34
13.83
0.16
0.12
0.10
400
500
600
46.45
55.01
63.51
100
100
100
13.4(13.1 )
13.2
13.1
22.9(21.9)
21.3
21.1
739(711)
787
822
1.93
1.45
1.26
4.21
4.40
4.65
7.24
7.12
7.51
0.27
0.20
0.17
28
15.74b
20
22.7(17.7)
39.7(38.4)
770(581)
9.40(15.4)
1.32(2.52)
2.30(5.49)
4.09(2.83)
298
298
298
298
298
298
298
298
298
298
298
54.24
37.78
25.19
20.78
18.38
16.84
15.63
14.93
14.27
13.74
13.27
60
100
200
300
400
500
600
700
800
900
1000
100
100
100
100
100
44.88
28.68
23.79
21.29
19.66
200
200
200
200
200
1.62( 1.70)
1.58( 1.63)
1.53( 1.58)
1.50 ( 1.53)
1.49 ( 1.49)
1.43 ( 1.46)
1.42 ( 1.44)
1.43 ( 1.42)
1.38 ( 1.40)
1.36( 1.38)
1.75(2.17)
0.22
0.36
0.70
1.00
1.28
1.53
1.77
1.95
2.17
2.31
2.46
"Experimental values in parentheses, where available from Refs. 18, 21, and 22.
"The experimental values at 16.95:>< 10- 6 m 3 mol-I from Ref. 30, which is on the saturation curve; on the melting curve (15.57X 10- 6 m J mol-I),
a Cp,m value of 34.7 J mol-I K- I is given in Ref. 22.
J. Chem. Phys., Vol. 99, No. 11, 1 December 1993
Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 130.102.82.2 On: Tue, 18
Oct 2016 06:36:54
Eggenberger et al.: Thermodynamical and structural properties of neon
consistent with the use of the analytical potential in the
simulations. The values including the first quantum correction show that quantum effects are of smaller or comparable size to the experimental error ( ± 1 cm 3mol- 1 ) down to
about 60 K. The calculated values deviate from the experimental values over the whole range with the same sign, the
deviation becoming quite large with decreasing temperatures. This can be attributed to the well being too shallow
in the calculated potential. Also shown in Table II are the
second virial coefficients calculated with the exp-6 potential of Kortbeek and Schouten9 and with the HFD-B potential. As Slaman and Aziz showed7 and as a comparison
with the experimental data in Table II confirms, the
HFD-B potential yields virtually exact virial coefficients.
The effective potential of Kortbeek and Schouten, which
was obtained from experiments at high pressure, gives very
accurate values at higher temperatures, but deviates at
lower temperatures, although less than our potential. This
might be interpreted as reflecting the overly shallow potential, which is responsible for deviations at low temperatures, and the correct behavior in the repulsive area which
is more important at the higher temperatures.
9167
3.0
42K
2.0
0
exp
sim
-.::-
C;
1.0
.
~
~
<f
0.0
36K
A
2.0
-.::-
C;
1.0
9<\
<>
exp
sim
<>
exp
sim
i
<E
c. Enthalpy H and energy U
Table III lists the enthalpy H and internal energy U for
a few points at two different temperatures and pressures up
to 500 MPa, where we found experimental values for comparison. 18•19 The experimental values given relative to O·C
were changed by /liIz, CJ!.T= 20.786 JIK mol· (-25 K)
= -520 J/mol (Ref. 20) (reference 273 K) to 298 K and
with .a6-ng=6197 J/mol (reference 298 K) to absolute
values (Le., 5677 J/mol were added). Similarly, we added
3406 J/mol to the experimental energy U to give it relative
to 0 K. The errors in the simulated energies due to the
inaccuracy of the temperature are less than 1%, i.e., the
tabulated error is due mainly to the quantum chemical
inaccuracies and assumptions used in the simulation (e.g.,
two particle potential). The simulated values are all too
large by 5% to 10%.
D. Molar heat capacities Cv,m and Cp,m. speed of
sound c, thermal expansion coefficient ap,
compresslblllties 13r and Ps, and thermal
pressure coefficient yv
The results are summarized in Table IV. Whereas the
statistical error for most properties is reasonably small,
e.g., for C V,m about 0.1 J Imol K, it is much larger for CP,m'
typically about I J/mol K. In general, the agreement is
good (typically z, 5%) for all properties in the supercritical phase, but is rather poor in the liquid. In the liquid, at
least the unusually large ratio Cp,mlCV,m is reproduced
qUalitatively correctly. Although only a limited number of
experimental data are available 18,21,22 in the supercritical
phase, we might assume from the interdependence with the
other properties and the equation of state that all simulated
properties are accurate to better than 10%. In addition to
the properties in the table, we also calculated the thermal
Joule-Thomson coefficient. Because its statistical error was
1000
r/pm
FIG. 4. The simulated (ai) pair distribution functions at different points
along the liquid-vapor coexistence line in comparison with experiment.
in general very large, we did not include it in the table. For
the state point at 298 K and 300 MPa, where we performed
a longer simulation, we obtained a value of -0.53 K/MPa
compared to an experimental value of -0.50 K/MPa.
E. Structure
Recent neutron diffraction measurements of liquid
neon along the coexistence line by Bellissent-Funel et al. 23
yielded pair distribution functions at three different state
points which were used for a comparison with our simulated functions. Figure 4 shows the experimental and simulated curves at the three points. In Table V, the maxima
and minima are tabulated for all three temperatures. The
agreement between experimental and calculated values is
good in the r axis, the deviations being within accuracy.
However, the calculated curves show too much structure.
Bellissent-Funel et aL state that contributions from quantum effects are certainly lower than 2%, which means that
the deviations of our simulated curves are due mainly to
the inaccurate potential shape and the two-particle potential approximation.
Reuse of AIP Publishing content is subject to the terms:
https://publishing.aip.org/authors/rights-and-permissions.
Downloaded to IP: 130.102.82.2 On: Tue, 18
J. Chern.
Phys., Vol. 99, No. 11, 1 December 1993
Oct 2016 06:36:54
Eggenberger et sl.: Thermodynamical and structural properties of neon
9168
3.0 ,--------~_------__,
TABLE V. Maxima and minima of the pair distribution function in liquid
neon.
T (K)
p/(mol m- J )
rsim (pm)
rexp (pm)'
g,im(r)
gexp(r)a
26.1
60 459
309
440
589
712
843
986
1110
307
450
605
737
868
1016
310
464
610
752
310
440
578
713
841
989
1093
309
449
585
723
848
1003
310
445
578
760
2.86
0.57
1.23
0.81
1.06
0.90
1.01
2.40
0.74
1.16
0.93
1.04
0.98
2.13
0.82
1.03
0.97
2.47
0.66
1.21
0.89
1.06
0.96
1.02
2.15
0.77
1.12
0.95
1.03
0.98
2.04
0.83
1.09
0.98
36.4
42.2
50548
41 132
"Experimental data from Ref. 23; the r values have an accuracy of only
about 5-15 pm, the latter value being valid for the shallow peaks at
greater distances.
Table VI gives the predicted first maxima of the pair
distribution functions at room temperature as a function of
pressure. It shows nicely the shift with pressure from a
more gas-like to a more liquid-like state. At 1000 MPa (see
Fig. 5), the function has about as much structure as in the
liquid, but the shell radius is shifted from 310 pm in the
liquid to 275 pm only in the supercritical state. In other
words, whereas in the liquid the first shell is in a distance
which corresponds to the equilibrium distance (the atoms
being caught in the potential well and subjected to the laws
of quantum mechanics), in the supercritical state at high
pressure, a similar dense shell is obtained because the atoms are pressed towards the repulsive wall of the potential
(the motion closely following the laws of classical mechanics).
Thermodynamical and structural properties of neon
were obtained for the first time from a purely nonempirical
TABLE VI. First maximum of the simulated pair distribution function in
the supercritical state as a function of pressure at 298 K.
60
100
200
300
400
500
600
700
800
900
1000
"Experimental pressure.
1.0
0.00~---·1L----~---------::-::1000
r/pm
FIG. 5. Simulated pair distribution functions of points in the liquid and
in the supercritical phases at very high pressures. Both curves show similar structure, however, the shell radius for the liquid is close to the
minimum of the potential well, whereas the one of the supercritical state
is at the repUlsive wall of the potential.
approach, applying a two-particle potential obtained from
quantum chemical ab initio calculations in classical molecular dynamical simulations. Wherever experimental results
were available, these were compared with simulated results, the deviations being typically below 20% in the supercritical phase. This work is part of a systematic study
with the goal to find out in which part of the approach
(quantum chemical approximations, two particle approximation, etc.) the greatest effort is needed to improve the
results for different properties of the condensed phase. Calculations to improve the pair potential and to construct a
three particle potential are underway to be applied in the
same approach. They could give an independent theoretical confirmation of Barker's hypothesis 24-26 that properties
of rare gases are well described by pair interactions together with three-body triple-dipole interactions.
ACKNOWLEDGMENTS
IV. CONCLUSIONS
P (MPa)"
2.0
300 K /1 OOOMPa
42K/liquid
r,im (pm)
g,im(r)
306
300
293
289
286
283
280
279
277
276
275
1.26
1.32
1.47
1.57
1.66
1.73
1.81
1.86
1.91
1.97
2.02
This investigation is part of the project 20-32284.91 of
the Schweizerischer Nationalfonds zur F6rderung der Wissenschaften. We thank the staff of the university computer
center for their assistance and the HLR-Rat for a grant of
computer time on the national supercomputers. We also
would like to thank Professor Alessandra Filabozzi for
supplying us with files of the pair distribution functions.
Clementi, Modern Techniques in Computational Chemistry:
MOTECC-90 (Escom, Leiden, 1990).
2R. Eggenberger, S. Gerber, H. Huber, and D. Searles, Chern. Phys. 156,
395 (1991).
JR. Eggenberger, S. Gerber, H. Huber, D. Searles, and M. Welker, Mol.
Phys.76, 1213 (1992).
4R. Eggenberger, S. Gerber, H. Huber, D. Searles, and M. Welker,
Chern. Phys. 164, 321 (1992).
5R. Eggenberger, S. Gerber, H. Huber, D. Searles, and M. Welker, J.
Phys. Chern. 97, 1980 (1993).
6 A. D. McLean, B. Liu, and J. A. Barker, J. Chern. Phys. 89, 6339
(1988).
7M. J. Siaman and R. A. Aziz, Chern. Eng. Commun. 104, 139 (1991).
1 E.
J. Chem. Phys., Vol. 99, No. 11, 1 December 1993
Reuse of AIP Publishing content is subject to the terms: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 130.102.82.2 On: Tue, 18
Oct 2016 06:36:54
Eggenberger et sl.: Thermodynamical and structural properties of neon
SR. A. Aziz and M. J. S1aman, Chem. Phys. 130, 187 (1989).
9p. J. Kortbeek and J. A. Schouten, Mol. Phys. 69,981 (1990).
10M. P. Allen and D. J. Tildesley, Computer Simulation of Liquids (Clarendon, Oxford, 1987).
11 R. Eggenberger and H. Huber, Chimia 46, 227 (1992).
12 0. Matsuoka, E. Clementi, and M. Yoshimine, J. Chem. Phys. 64,1351
( 1976).
BU. Niesar, G. Corongiu, M.-J. Huang, M. Dupuis, and E. Clementi, Int.
J. Quantum Chern., Quantum Chern. Symp. 23, 421 (1989).
14W. C. Kerr and K. S. Singwi, Phys. Rev. A 7, 1043 (1973).
I$J. P. Hansen and J. J. Weis, Phys. Rev. 188, 314 (1969).
16F. H. Ree, J. Phys. Chern. 87, 2846 (1983).
17J. A. Barker, R. A. Fisher, and R. O. Watts, Mol. Phys. 21, 657 (1971).
11 A. Michels, T. Wassenaar, and G. J. Wolkers, Physica 31,237 (1965).
19y. Y. Maslennikova, A. N. Egorov, and D. S. Tsikiis, Sov. Phys. DokI.
21,440(1976).
2OD. D. Wagman, W. H. Evans, Y. B. Parker, R. H. Schu=, I. Halow,
9169
S. M. Bailey, K. L. Chumey and R. L. Nuttall, J. Phys. Chern. Ref.
Data 11, Suppl. 2, 1-392 (1982).
21 P. J. Kortbeek, S. N. Biswas, and J. A. Schouten, Int. J. Thermophys.
9, 803 (1988).
ny. A. Rabinovich, A. A. Yasserman, Y. I. Nedostup, and L. S. Veksler,
Thermophysical Properties of Neon, Argon, Krypton, and Xenon (Hemisphere, Washington, D.C., 1988).
23M. C. Bellissent-Funel, U. Buontempo, A. Filabozzi, C. Petrillo, and F.
P. Ricci, Phys. Rev. B 45, 4605 (1992).
24J. A. Barker, Mol. Phys. 57, 755 (1986).
25 J. A. Barker, Phys. Rev. Lett. 57, 230 (1986).
26J. A. Barker, NATO ASI Ser., Ser. B 186, 341 (1989).
27 J. O. HirschfeIder, C. F. Curtiss, and R. B. Bird, Molecular Theory of
Gases and Liquids (Wiley, New York, 1954).
28R. M. Gibbons, Cryogenics 9, 251 (1969).
29 J. H. Dymond and E. B. Smith, The Virial Coefficients of Gases, A
Critical Compilation (Clarendon, Oxford, 1969).
30D. G. Naugle, J. Chern. Phys. 56, 5730 (1972).
J. https://publishing.aip.org/authors/rights-and-permissions.
Chem. Phys., Vol. 99, No. 11, 1 December 1993
Reuse of AIP Publishing content is subject to the terms:
Downloaded to IP: 130.102.82.2 On: Tue, 18 Oct
2016 06:36:54