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m s 2 : A molecular simulation tool for thermodynamic properties, release 3.0

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A new version release (3.0) of the molecular simulation tool ms 2 (Deublein et al., 2011; Glass et al. 2014) is presented. Version 3.0 of ms 2 features two additional ensembles, i.e. microcanonical (NVE) and isobaric-isoenthalpic (NpH), various Helmholtz energy derivatives in the NVE ensemble, thermodynamic integration as a method for calculating the chemical potential, the osmotic pressure for calculating the activity of solvents, the six Maxwell-Stefan diffusion coefficients of quaternary mixtures, statistics for sampling hydrogen bonds, smooth-particle mesh Ewald summation as well as the ability to carry out molecular dynamics runs for an arbitrary number of state points in a single program execution. New version program summary: Program Title: ms2 Program Files doi: http://dx.doi.org/10.17632/9rcrykvkyh.1 Licensing provisions: CC by NC 3.0. Programming language: Fortran95. Supplementary material: A detailed description of the parameter setup for thermodynamic integration and hydrogen bonding is given in the supplementary material. Furthermore, all molecular force field models developed by our group are provided. Journal reference of previous versions: Deublein et al., Comput. Phys. Commun. 182 (2011) 2350 and Glass et al., Comput. Phys. Commun. 185 (2014) 3302. Does the new version supersede the previous version?: Yes. Reasons for the new version: Introduction of new features as well as enhancement of computational efficiency. Summary of revisions: Two new ensembles (NVE and NpH), new properties (Helmholtz energy derivatives, chemical potential via thermodynamic integration, activity coefficients via osmotic pressure, Maxwell-Stefan diffusion coefficients of quaternary mixtures), new functionalities (detection and statistics of hydrogen bonding, smooth-particle mesh Ewald summation, ability to carry out molecular dynamics runs for an arbitrary number of state points in a single program execution). Nature of problem: Calculation of application oriented thermodynamic properties: vapor-liquid equilibria of pure fluids and multi-component mixtures, thermal, caloric and entropic data as well as transport properties and data on microscopic structure. Solution method: Molecular dynamics, Monte Carlo, various ensembles, Grand Equilibrium method, Green-Kubo formalism, Lustig formalism, OPAS method, smooth-particle mesh Ewald summation. Restrictions: Typical problems addressed by ms2 are solved by simulating systems containing 1000 to 5000 molecules that are modeled as rigid bodies. Additional comments: Documentation is available at http://www.ms-2.de
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ms2: A molecular simulation tool for thermodynamic properties, release
3.0
abor Rutkaia, Andreas K¨ostera, Gabriela Guevara-Carriona, Tatjana Janzena, Michael
Schappalsb, Colin W. Glassc, Martin Bernreutherc, Amer Wafaic, Simon Stephanb, Maximilian
Kohnsb, Steffen Reiserb, Stephan Deubleinb, Martin Horschb, Hans Hasseb, Jadran Vrabeca,
aLehrstuhl f¨ur Thermodynamik und Energietechnik, Universit¨at Paderborn, 33098 Paderborn, Germany
bLehrstuhl f¨ur Thermodynamik, Universit¨at Kaiserslautern, 67653 Kaiserslautern, Germany
cochstleistungsrechenzentrum Universit¨at Stuttgart (HLRS), 70550 Stuttgart, Germany
Abstract
A new version release (3.0) of the molecular simulation tool ms2 [Deublein et al., Comput. Phys.
Commun. 182 (2011) 2350 and Glass et al., Comput. Phys. Commun. 185 (2014) 3302] is pre-
sented. Version 3.0 of ms2 features two additional ensembles, i.e. microcanonical (
NV E
) and
isobaric–isoenthalpic (
NpH
), various Helmholtz energy derivatives in the
NV E
ensemble, ther-
modynamic integration as a method for calculating the chemical potential, the osmotic pressure
for calculating the activity of solvents, the six Maxwell-Stefan diffusion coefficients of quaternary
mixtures, statistics for sampling hydrogen bonds, smooth-particle mesh Ewald summation as well
as the ability to carry out molecular dynamics runs for an arbitrary number of state points in a
single program execution.
Keywords: molecular simulation, molecular dynamics, Monte Carlo
New version program summary
Program Title: ms2
Operating system: Unix/Linux
Licensing provisions: Special license supplied by the authors
Programming language: Fortran95
Has the code been vectorized or parallelized:
yes (Message Passing Interface (MPI) protocol and OpenMP)
Corresponding author: Jadran Vrabec, Warburger Str. 100, 33098 Paderborn, Germany, Tel.: +49-5251/60-2420,
Email: jadran.vrabec@upb.de
Preprint submitted to Computer Physics Communications July 28, 2017
Distribution format: zip
Classification: 7.7, 7.9, 12
Catalogue identifiers of previous versions: AEJF v1 0 and AEJF v2 0
Supplementary material:
A detailed description of the parameter setup for thermodynamic integration and
hydrogen bonding is given in the supplementary material. Furthermore, all molecular force field models
developed by our group are provided
Journal reference of previous versions:
Deublein et al., Comput. Phys. Commun. 182 (2011) 2350 and
Glass et al., Comput. Phys. Commun. 185 (2014) 3302
Does the new version supersede the previous version?: Yes
Reasons for the new version:
Introduction of new features as well as enhancement of computational efficiency
Summary of revisions:
Two new ensembles (
NV E
and
NpH
), new properties (Helmholtz energy derivatives,
chemical potential via thermodynamic integration, activity coefficients via osmotic pressure, Maxwell-Stefan
diffusion coefficients of quaternary mixtures), new functionalities (detection and statistics of hydrogen
bonding, smooth-particle mesh Ewald summation, ability to carry out molecular dynamics runs for an
arbitrary number of state points in a single program execution)
Nature of problem:
Calculation of application oriented thermodynamic properties: vapor-liquid equilibria
of pure fluids and multi-component mixtures, thermal, caloric and entropic data as well as transport
properties and data on microscopic structure
Solution method:
Molecular dynamics, Monte Carlo, various ensembles, Grand Equilibrium method, Green-
Kubo formalism, Lustig formalism, OPAS method, smooth-particle mesh Ewald summation
Typical running time:
Typically from a couple of hours up to days, depending on the specific scenario
(system size, calculated properties, number of CPU cores used)
Restrictions:
Typical problems addressed by
ms
2 are solved by simulating systems containing 1000 to
5000 molecules that are modelled as rigid bodies
Documentation: Documentation is available at http://www.ms-2.de
2
1. Introduction
Due to the continuous increase in computing power, the range of possible applications of
molecular modeling and simulation has become broader over time, proceeding from qualitative
basic research in soft matter physics to quantitative applications in chemical engineering. Reaching
agreement with the available experimental data and predicting properties where experimental data
are rare or absent, molecular methods transform engineering data science [
1
,
2
]. This progress
is driven by massively-parallel high performance computing with scalable codes [
3
] and by the
concurrent execution of large numbers of simulations [
4
] or of simulations which can be decomposed
into a large number of concurrent tasks [5–7].
The program
ms
2 (molecular simulation 2) was designed to compute thermodynamic properties
of pure fluids and mixtures by Monte Carlo (MC) and molecular dynamics (MD) simulation. Licences
are available without cost for all purposes which concern academic research and teaching [
8
]. The
previous two major releases of
ms
2 [
9
,
10
] facilitate the simulation of vapor-liquid equilibria (VLE)
by Grand Equilibrium simulation and the computation of many thermodynamic bulk properties,
including linear transport coefficients, for molecular models consisting of Lennard-Jones interaction
sites, point charges and point multipoles. It has been shown that such models can reach a high
accuracy for a wide variety of thermodynamic properties for many molecular fluids [
11
16
], leading
to an increasing popularity of molecular methods in the engineering sciences [17–21].
Similar molecular simulation programs, which address multiple academic communities, include
CHARMM [
22
], DL POLY [
23
], ESPResSo [
24
], GIBBS [
25
], GROMACS [
26
], IMD [
27
], LAMMPS
[
28
],
ls
1 mardyn [
29
], NAMD [
30
], TINKER [
31
] and Towhee [
32
]. In comparison with these codes,
the aim of
ms
2 is to focus on applications of molecular modeling and simulation in fluid process
engineering, both industrial and academic. Hence, a high accuracy, short response times and the
suitability for coupling with equations of state [
4
,
33
] and rigorous model optimization approaches
[
34
36
] have been priorities in developing both the code base as well as the toolset which is provided
jointly with it. In contrast to other molecular simulation programs,
ms
2 excels in its variety of
properties that are all sampled on the fly. The present work discusses the third major release of
ms2 and its most important innovations, which are presented in detail in the following sections.
2. Microcanonical and isobaric-isoenthalpic ensembles
An ensemble is the set of all theoretically possible microscopic configurations on the molecular
level under specific macroscopic constrains. The microcanonical (
NV E
) ensemble is the set of
all configurations that fulfill the condition of having the same number of particles
N
, volume
V
and energy
E
, whereas the isobaric-isoenthalpic (
NpH
) ensemble represents a system at constant
number of particles
N
, pressure
p
and enthalpy
H
. Molecular dynamics (MD) mimics the time
evolution of a mechanical system by numerically solving Newton’s equations of motion for all
considered molecules. Because of the nature of this solution, the progress of time is discredized and
the method yields microscopic configurations at discrete and consecutive time steps. The Monte
Carlo (MC) method is the application of statistical mechanics to describe molecular systems. With
this approach, microscopic configurations are generated by random numbers that are potentially
accepted such that only relevant and physically meaningful configurations are sampled [
37
]. The
3
Table 1: Comparison of the ensembles implemented in ms2 for methyl fluoride [
41
] in terms of temperature
T
, density
ρ
, pressure
p
and potential energy
u
. Numbers in parentheses denote statistical uncertainties in the last digit that
were estimated with the block averaging method of Flyvbjerg and Petersen [42].
T ρ p u
K mol/l MPa J/mol
MD
NVT 300 1 2.090(2) -1048(3)
NpT 300 1.0015(7) 2.090 -1051(3)
NVE 300.0(1) 1 2.088(1) -1048(3)
NpH 300.0(1) 1.0003(2) 2.090 -1048(2)
MC
NVT 300 1 2.0880(2) -1051.6(2)
NpT 300 1.0019(2) 2.0880 -1053.6(3)
NVE 299.99(1) 1 2.0882(2) -1051.3(2)
NpH 300.06(2) 1.0010(1) 2.0880 -1051.7(2)
generation and acceptance of these configurations is governed by specific probabilities that are
ensemble-dependent and described in the literature for essentially every relevant ensemble. For MC
simulations, the
NV E
and
NpH
ensembles were implemented in
ms
2 release 3.0 according to Refs.
[
38
,
39
]. For MD simulations, the pressure is kept constant using Andersen’s barostat [
40
] in case of
the
NpH
ensemble. Because the solution of Newton’s equations of motion is approximate, the total
energy of the system
E
=
K
+
U
, which consists of a kinetic
K
(exclusively molecular momentum
dependent) and potential
U
(exclusively molecular position dependent) energy contribution, is not
rigorously conserved in a standard MD run mainly for numerical reasons. Therefore, the translational
and rotational momentum of every molecule is rescaled such that the total kinetic energy
K
fulfils
K
=
EU
, where the total energy
E
is specified and the potential energy
U
is calculated from the
current microscopic configuration. For a
NpH
ensemble run, the solution is analogous: Momenta
are rescaled such that the current kinetic energy
K
fulfils
K
=
HUpV
, where
H
and
p
are
specified, while
U
and
V
are dependent on the current microscopic configuration. This extends the
ensembles available in
ms
2 to five:
NV T
,
NV E
,
NpT
,
NpH
and
µV T
, where
µ
is the chemical
potential.
For verification purposes, Table 1 contains numerical results for methyl fluoride modeled by a
dipolar two-center Lennard–Jones potential [
41
] at
T
= 300 K and
ρ
= 1 mol/l. Figure 1 shows the
running averages of the calculated properties in Table 1 at the same state point.
3. Helmholtz energy derivatives in the microcanonical ensemble
The generalized calculation of the Helmholtz energy derivatives
Ar
nm = (1/T )nρmn+mfr(T, ρ)/(RT )
(1/T )n∂ρm,(1)
with molar residual Helmholtz energy
fr
, temperature
T
, density
ρ
and molar gas constant
R
was introduced in
ms
2 also for the
NV E
ensemble up to the order
n
= 3 and
m
= 2. The total
4
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Figure 1: Comparison of the ensembles implemented in ms2 for methyl fluoride [
41
] in terms of running averages for
temperature T, density ρ, pressure pand potential energy u.
5
Table 2: Comparison of the residual Helmholtz energy derivatives
Ar
nm
of methyl fluoride [
41
] at
T
= 300 K and
ρ
= 1 mol/l. Numbers in brackets denote statistical uncertainties in the last digit that were estimated with the
block averaging method of Flyvbjerg and Petersen [
42
]. Superscripts (1) and (2) indicate the two different entropy
definitions [45].
Ar
10 Ar
01 Ar
20 Ar
11 Ar
02
MD
NVT -0.420(1) -0.1620(6) -0.54(4) -0.40(2) 0.03(3)
NVE1-0.418(1) -0.1622(4) -0.55(3) -0.37(1) 0.05(3)
NVE2-0.418(1) -0.1621(4) -0.55(3) -0.37(1) 0.05(3)
MC
NVT -0.42158(8) -0.16290(8) -0.562(2) -0.391(2) 0.011(6)
NVE1-0.42149(5) -0.16280(8) -0.560(2) -0.385(3) 0.024(6)
NVE2-0.42133(5) -0.16274(8) -0.560(2) -0.385(3) 0.024(6)
reduced Helmholtz energy
f/
(
RT
) can be additively separated into an ideal
fo/
(
RT
) and a residual
contribution
fr/
(
RT
). The ideal contribution by definition corresponds to the value of
f/
(
RT
) when
no intermolecular interactions are at work [
43
].
fo/
(
RT
) consists of an exclusively temperature and
an exclusively density dependent part. The latter is the trivial term
ln
(
ρ/ρref
), whereas the former
is non-trivial. A formalism that allows for the calculation of all residual Helmholtz derivatives on
the fly from a single simulation run per state point was published by Lustig [
44
,
45
] and was already
introduced for the
NV T
ensemble in the preceding program version.
ms
2 release 3.0 now yields
these derivatives also for the
NV E
ensemble. However, in contrast to
NV T
simulations, there are
two numerical results for each calculated derivative
Anm
due to the two possible entropy definitions
in statistical mechanics [
45
]. In any case, these two different sets of results must be identical
in the thermodynamic limit (
N→ ∞
). In practice, they already agree within their statistical
uncertainty for a simulation based on around a thousand molecules. For verification purposes,
Table 2 contains numerical results for methyl fluoride [
41
]. A detailed description of the calculation
of these derivatives can be found in Ref. [
45
]. Their conversion into common thermodynamic
properties is provided in the supplementary material of release 2.0 of ms2 [10] and in Ref. [43].
4. Thermodynamic integration
The previously described method of Lustig does not allow for the direct sampling of the
chemical potential and other entropic properties like
Ar
00
. Such an effort requires techniques
based on free energy calculation, such as particle insertion and/or thermodynamic integration [
37
].
Widom’s particle insertion method [
46
] is a conceptually straightforward approach to calculate
the chemical potential at low computational cost, both for pure substances and mixtures. The
total chemical potential
µi
of species
i
can be separated into an ideal (o) and a residual (r)
contribution in the same way as the Helmholtz energy is decomposed, cf. section 2:
µi
(
T, ρ, xi
) =
µo
i
(
T
) +
RT ln
(
Ni/
(
V ρref
)) +
µr
i
(
T, ρ, xi
), where
Ni
is the number of molecules of species
i
,
ρ
=
N/V
,
xi
=
Ni/N
and
ρref
is an arbitrary reference density. The expression
µiµo
i
(
T
) is often referred to
as the configurational chemical potential
µconf
i
. Widom’s method requires the frequent insertion
of an additional (
i
=
N
+ 1) test particle into the simulation volume at a random position with
6
a random orientation. At constant temperature and constant pressure or volume, the potential
energy
Ui
of this test particle, i.e. the interaction energy with all other ”real”
N
molecules, yields
the configurational chemical potential according to
µconf
i=µiµo
i(T) = kBTln hVexp (Ui/kBT)i
hNii,(2)
where
kB
is Boltzmann’s constant. The test particle is removed immediately after the calculation of
its potential energy
Ui
, thus it does not influence the real molecules in the system in any way. In
contrast to the usual convention, the brackets
<>
have a dual meaning here: They stand for either
NV T
or
NpT
ensemble averages as well as an integral over all possible positions and orientations
of the test particles added to the system. The density of the system has a significant influence
on the accuracy of this method. For state points with a very high density, test particles almost
always overlap with real molecules, which leads to a potential energy
Ui→ ∞
and thus to a vanish-
ing contribution to Eq. (2), resulting in poor statistics and often even to complete failure of sampling.
Thermodynamic integration is one solution to overcome the limitations of Widom’s particle
insertion method. The idea behind calculating the chemical potential by thermodynamic integration
is to avoid insertion of test particles in a challenging system
A
, but rather perform it in system
B
for which this can be done without sampling problems. Because the chemical potential is a state
property, its difference
µA,i µB,i
can be calculated along any path between states
A
and
B
, which
is represented by the scalar parameter
λ
. It can be shown [
37
] that the relation between
λ
and
µA,i µB,i is
µA,i µB,i =ZA(λmax )
B(λmin)Ui(λ)
∂λ dλ. (3)
The brackets
<>
in this equation denote
NV T
or
NpT
ensemble averages and
Ui
is the potential
energy of particle
i
that must be a part of the system in the same way as the other molecules
are. The only difference between particle
i
and all other molecules is that its interaction energy
Ui
(
λ
) is scaled between states
A
(
λmax
) and
B
(
λmin
) with
λ
. As long as
∂Ui
(
λ
)
/∂λ
can be calculated
analytically and sampled during simulation, the actual way of scaling
Ui
(
λ
) with
λ
can be chosen
arbitrarily because
µi
is a state property. The integration with respect to
λ
is carried out numerically.
Assuming that
µB,i
is practically zero or at least can successfully be calculated by Widom’s particle
insertion method for state
B
using Eq.
(2)
,
µA,i
yields the configurational contribution to the
total chemical potential. The non-linear scaling
Ui
(
λ
) =
λdUi
for
λmin λ
1 =
λmax
with an
adaptive sampling technique [
47
] was implemented for MC simulations with
d
and
λmin
being input
parameters. This adaptive technique allows for the sampling of the entire range of
λmin λ
1 in
a single MC run with an arbitrary resolution for numerical integration. In addition to the standard
NV T
and
NpT
ensemble MC moves, the simulation includes changes of
λ
controlled by a proper
MC acceptance criterion, ensuring visits at each discrete
λ
value in the range
λmin λ
1. For
MD simulations, changes of
λ
are also carried out on the fly in a single simulation, but without
any acceptance criterion. A common problem related to the thermodynamic integration is the so
called ”end-point catastrophe”, i.e. the occurence of singularities at
λ
= 0 or 1 [
48
50
]. Such effects
7
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Figure 2: Comparison of the residual chemical potential
µr
of methyl fluoride [
41
] at two different state points
calculated by ms2 using either Widom’s particle insertion or thermodynamic integration (TI).
can be circumvented by the variable and non-linear scaling described above, where the exponent
d
of
λ
and
λmin
are input parameters. Furthermore, sampling at
λ
1 is improved by scaling the
fluctuating particle dynamically back and forth during simulation. A detailed description of the
parameter setup is given in the supplementary material. Figure 2 shows the running averages for
the residual chemical potential of methyl fluoride at two different state points calculated by either
Widom’s particle insertion or thermodynamic integration. For high temperatures and low densities,
the agreement between Widom’s particle insertion and thermodynamic integration is satisfactory.
Widom fails, however, for dense and strongly interacting fluids.
5. OPAS Method
The OPAS (osmotic pressure for the activity of the solvent) method was implemented in ms2.
It is an alternative to e.g. Widom’s particle insertion [
46
] or thermodynamic integration [
51
53
]
for calculating the chemical potential of the liquid phase by MD simulations. It is particularly
well-suited for studying the solvent activity of electrolyte solutions, but can in principle also be used
for mixtures of molecular species. Details and a thorough assessment of the method are presented
in Ref. [54], the method is only briefly outlined in the following.
The basic idea is a direct simulation of the osmotic equilibrium between a pure solvent phase and
a solution phase by introducing semi-permeable membranes into the simulation volume. These are
realized by an external force field that acts only on the solute molecules to keep them in the solution
phase. By sampling the total net membrane force per membrane area, the pressure difference
between the two phases, i.e. the osmotic pressure Π, is sampled. Assuming an incompressible
8
solvent, the solvent activity asis related to this osmotic pressure by
ln as=Πvs
RT ,(4)
where
vs
is the molar volume of the pure solvent at the temperature
T
, which is straightforwardly
available from separate, standard molecular simulation runs. If an electrolyte solution is considered,
the activity coefficient of the salt can be obtained by performing OPAS simulations at various salt
molalities and applying the Gibbs-Duhem equation to the results for the solvent activity.
Fig. 3 shows molecular simulation results for the water activity in aqueous NaCl solutions at
T
= 298.15 K and
p
= 1 bar. Therein, results obtained by different groups, employing different
computational approaches, are presented. Throughout, the molecular models by Joung and Cheatham
[
55
] for Na
+
and Cl
ions together with the SPC/E water model were used. It can be seen that all
simulation results, including those obtained with OPAS simulations carried out with ms2, are in
mutual agreement.
0 1 2 3 4 56
0.4
0.3
0.2
0.1
0
mNaCl /mol kg1
ln aW
Figure 3: Water activity over the salt molality for aqueous NaCl solutions at
T
= 298.15 K and
p
= 1 bar. The red
open circles are simulation results obtained with the OPAS method as implemented in ms2 [
54
]. The colored lines
represent correlations to simulation results by different groups: Free energy calculations by Benavides et al. [
56
]
(violet densely-dotted line), gradual insertion of ion pairs by Mester and Panagiotopoulos [52] (blue dashed-dotted
line) and osmotic ensemble Monte Carlo simulations by Mouˇcka et al. [
53
] (green dotted line). All simulation
results were obtained using the SPC/E + Joung-Cheatham [
55
] model combination. The black solid line shows the
correlation to experimental data by Hamer and Wu [57].
6. Quaternary Maxwell-Stefan diffusion coefficients
ms
2 employs the Green-Kubo formalism based on the net velocity correlation function to obtain
n×nphenomenological coefficients [58]
Lij =1
3NZ
0DNi
X
k=1
vi,k(0) ·
Nj
X
l=1
vj,l(t)Edt, (5)
9
in a mixture of
n
components. Here,
N
is the total number of molecules,
Ni
is the number of
molecules of species
i
and
vi,k
(
t
) denotes the center of mass velocity vector of the
k
-th molecule of
species
i
at time
t
. Note that the phenomenological coefficients given in Eq.
(5)
are constrained by
[58]
X
i
MiLij = 0 ,(6)
where Miis the molar mass of component i.
Starting from the phenomenological coefficients
Lij
, the elements of a (
n
1)
×
(
n
1) matrix
can be defined as [58]
ij = (1 xi)Lij
xj
Lin
xnxi
n
X
k=16=iLkj
xj
Lkn
xn,(7)
so that its inverse matrix
B
=
1
is related to the Maxwell-Stefan diffusion coefficients
Dij
. In
the case of a quaternary mixture, the six Maxwell-Stefan diffusion coefficients are then given by [
58
]
D14 =1
B11 + (x2/x1)B12 + (x3/x1)B13
,(8)
D24 =1
B22 + (x1/x2)B21 + (x3/x2)B23
,(9)
D34 =1
B33 + (x1/x3)B31 + (x2/x3)B32
,(10)
D12 =1
1/D24 B21/x2
,(11)
D13 =1
1/D14 B13/x1
,(12)
D23 =1
1/D24 B23/x2
.(13)
(14)
MD simulation runs for Lennard-Jones fluids were performed in order to test the validity of
the quaternary Maxwell-Stefan diffusion coefficients implementation in
ms
2. For this purpose,
a quaternary Lennard-Jones pseudo-mixture was created by giving different labels to identical
molecules, dividing them into four mole fractions (
x1
= 0.1,
x2
= 0.2,
x3
= 0.3 and
x4
= 0.4 mol
mol
1
). A system containing 800 molecules was simulated in the dense liquid state and the resulting
Maxwell-Stefan diffusion coefficients were compared with the corresponding self-diffusion coefficient
that all have to be identical in the present case.
Fig. 4 shows the development of the calculated values of the six Maxwell-Stefan diffusion
coefficients with the number of sampled time origins. As can be seen, the resulting values become
independent after around 10
4
time origins and then oscillate around their mean value. The higher
statistical uncertainties of
D12
and
D13
are due to the small number of species 1 molecules compared
with the number of molecules of the other species.
10
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







 

















Figure 4: Maxwell-Stefan diffusion coefficients
Dij
and self-diffusion coefficient
Di
as a function of time origins of a
quaternary pseudo-mixture (
=
1
=
2
=
3
=
4
and
σ
=
σ1
=
σ2
=
σ3
=
σ4
) at
kBT/
= 0.728 and
ρσ3
= 0.8442.
7. Hydrogen bonding
There is no definitive characterization of a hydrogen bond between two molecules [
59
61
].
Rather, the hydrogen (H) bond ‘is a structural motif and involves at least three atoms’ [
62
]. The
International Union of Pure and Applied Chemistry (IUPAC) defines the hydrogen bond as ‘an
attractive interaction between a hydrogen atom from a molecule or molecular fragment X–H in
which X is more electronegative than H, and an atom or a group of atoms in the same or a different
molecule, in which there is evidence of bond formation’ [61].
Energetic [
59
], geometric [
63
] and topological [
60
] hydrogen bonding criteria have been proposed
in the literature. Geometric criteria, which are not overly complex, are often based on the following
assumptions [64]:
The interaction between two hydrogen bonded sites is highly directional and short ranged.
A donor interacts at most with a single acceptor, an acceptor may interact with multiple
donors.
Accordingly, a class of geometric criteria for the evaluation of hydrogen bonding networks in fluids
was implemented in ms2. Thereby, the triangle between three charge sites, being part of two
different molecules, is evaluated to determine whether two sites constitute a hydrogen bond or not.
A molecule acts as a donor to another molecule, i.e. the acceptor, if the following conditions hold
[63–66], cf. Fig. 5:
The distance between the donor and the acceptor is smaller than a threshold distance, i.e.
`AD or `DA.
The distance between the acceptor sites of the acceptor and donor molecules is smaller than
a threshold distance, i.e. `AA.
11
The angle between the acceptor-donor axis and the acceptor-acceptor axis is smaller than a
threshold angle, i.e. ϕDAA or ϕAAD.
Therein,
`AD
,
`DA
,
`AA
,
ϕDAA
and
ϕAAD
are parameters of the implemented class of hydrogen
bonding criteria. For methanol, e.g. Haughney et al. [
63
] proposed
`AD
=
`DA
= 2
.
6
˚
A,
`AA
= 3
.
5
˚
A and
ϕAAD
=
ϕDAA
= 30
. Such geometric criteria have been applied to a variety of fluids, in
particular to water [
65
67
], methanol-water mixtures [
68
,
69
] or ethanol [
64
,
70
,
71
]. Hydrogen bonds
in sorbate-sorbent interactions can be treated analogously [
72
]. E.g., for hydrogen fluoride, a simpler
distance-based criterion can be used [
73
], which is also covered by the present implementation.
Hydrogen bonding statistics are calculated by
ms
2 on the fly during a standard simulation run which
avoids post-precessing and evaluation of trajectory files. A detailed description of the parameter
setup is given in the supplementary material.
O
H
R
O
H
R
Donor Molecule
Acceptor Molecule
Acceptor Site of Acceptor Molecule
Donor Site of Acceptor Molecule
Acceptor Site of Donor Molecule
Donor Site of Donor Molecule
AA
DA
AD
ϕDAA
ϕAAD
Figure 5: Hydrogen bonding criteria implemented in the present release version of ms2.
To test the capabilities of the hydrogen bonding statistics implemented in
ms
2, a MD simulation
run of the ternary mixture water (w) + methanol (m) + ethanol (e) (
xw
= 0.33,
xm
= 0.33,
xe
= 0.34 mol mol
1
) at
T
= 298.15 K and
p
= 0.1 MPa was carried out with 4000 molecules. All
species of this mixture can form hydrogen bonds with each other because all three molecules contain
hydroxyl groups. Thus the hydrogen atoms may act as donors and the oxygen atoms as acceptors
to form hydrogen bonds. Throughout, between like and unlike molecules, the geometric criteria of
Haughney et al. [
63
] were used. The results are listed in Table 3. The hydrogen bonding statistics
in
ms
2 not only indicates the amount of monomers (no bond), dimers (one bond), trimers (two
bonds) and tetramers (three bonds), but also provides information about which molecule species
are mutually bonded.
8. Electrostatic long range corrections
The applicability of
ms
2 was extended to electrically charged molecules or ions. The long ranged
intermolecular interactions are considered by two well established approaches, Ewald summation
and smooth-particle mesh Ewald summation (SPME). Both are well known [
37
] and are thus
introduced here only briefly.
12
Table 3: Hydrogen bonding statistics of the ternary mixture water (w) + methanol (m) + ethanol (e) (
xw
= 0.33,
xm= 0.33, xe= 0.34 mol mol1) at T= 298.15 K and p= 0.1 MPa in relative terms.
water methanol ethanol
monomer 0.1% 0.9% 1.1%
dimer 1.2% 10.6% 11.5%
bonded to (w) 0.8% 3.5% 4.1%
(m) 0.2% 3.3% 3.6%
(e) 0.2% 3.8% 3.8%
trimer 7.8% 47.7% 42.6%
bonded to (w)(w) 2.8% 2.8% 2.8%
(w)(m) 1.9% 10.5% 8.9%
(w)(e) 2.0% 12.3% 10.2%
(m)(m) 0.3% 5.0% 4.9%
(m)(e) 0.4% 11.0% 10.3%
(e)(e) 0.4% 6.1% 5.5%
tetramer 25.8% 35.9% 36.8%
bonded to (w)(w)(w) 3.9% 15.6% 12.7%
(w)(w)(m) 4.9% 7.6% 7.8%
(w)(w)(e) 5.1% 7.7% 7.6%
(w)(m)(m) 2.7% 0.7% 1.3%
(w)(m)(e) 3.8% 1.7% 2.8%
(w)(e)(e) 2.8% 0.9% 1.5%
(m)(m)(m) 0.6% 0.2% 0.4%
(m)(m)(e) 0.7% 0.6% 1.1%
(m)(e)(e) 0.6% 0.7% 1.2%
(e)(e)(e) 0.7% 0.2% 0.4%
four or more bonds 65.1% 4.9% 8.0%
13
In Ewald summation, the overall Coulombic potential acting in the simulation volume is
determined by a sum of two terms, i.e. the short range Coulombic contribution
uc,short
and the long
range Coulombic contribution uc,long
uc=uc,short +uc,long . (15)
The separation into these terms is achieved by the introduction of a fictive charge density
function ρscreen(r), which acts in the entire simulation volume.
Following the Ewald summation approach, for any configuration of molecules in the simulation
volume, each point charge of magnitude
ql
in the simulation volume is superimposed with one
countercharge of magnitude
ql
. Due to the presence of this superimposed charge, the interaction
potential decays to zero within a distance that is reasonably short for molecular simulation and
can, hence, be explicitly considered by the short range contribution of the Ewald summation.
The second term in Eq.
(15)
determines the contribution that was subtracted due to the
introduction of the fictive charge density function. This term cannot be determined explicitly by an
evaluation of pairwise interactions, since the Coulombic potential at
rlm
=
V1/3/
2, i.e. the largest
distance accessible in the molecular simulation volume
V
, is still a substantial part of the potential
energy of the system. In Ewald summation, this contribution is determined in Fourier space from
the negative charge distribution function
ρscreen
(
r
). Since
ρscreen
(
r
) depends on the molecular
positions
r
, a Fourier transformation is performed for every configurational change in the simulation
volume.
The SPME is widely considered as an improved Ewald summation method. In this approach,
the concept of splitting the long range charge-charge interactions is fully employed. The difference
between both methods lies only in the calculation of the long range contributions. In the SPME
approach, the electrostatic field of ions in the simulation volume is described by a spline function
with a given functional form. For this given spline equation, the Fourier transformation is known
and has, hence, not to be determined in each simulation step. This accelerates the calculation of
the long range contribution and reduces simulation effort and time. The accuracy of the SPME
results is assumed to be equivalent to the Ewald approach. In
ms
2 release 3.0, the SPME method
was implemented in its original form, wherein the splines are evaluated for all particles at a time,
making it specifically useful for MD simulations.
To validate the present implementation of the SPME method, otherwise identical MD simulations
with either full Ewald summation or the SPME method were carried out. For both methods, the
Debye length was set to
κ
= 5.6. In case of SPME, a grid with 35 points and a spline order of 6
were used. The simulations were equilibrated for 0
.
5
·
10
6
time steps, before sampling was carried
out over 2
.
5
·
10
6
time steps of 1.2 fs. The electrostatic cutoff was the same as the Lennard-Jones
cutoff of 15
˚
A. The studied systems were pure SPC/E water [
74
] (1000 molecules) and an aqueous
solution of NaCl in water (980 SPC/E molecules and 10 Na
+
and Cl
ions each [
75
]) at
T
= 300 K.
For a comparison of the density, simulations were carried out in the
NpT
ensemble at a pressure of
0.1 MPa. For a comparison of internal energy, simulations were carried out in the
NV T
ensemble at
a density of 55.44 mol l
1
. The results can be found in Table 4, which shows that both simulation
approaches are in mutual agreement for both studied systems. Furthermore, SPME was found to
be about 15-30% faster than full Ewald summation in the form as it is implemented in ms2.
14
Table 4: Comparison of simulation results obtained with Ewald summation and SPME, indicating the reduction of
total computation time when using SPME instead of Ewald summation.
NpT ensemble NV T ensemble
ρ/ mol l1u/ kJ mol1
System Ewald SPME Speedup Ewald SPME Speedup
SPC/E water 55.44(2) 55.41(2) 22% -46.67(3) -46.72(3) 19%
NaCl solution 55.74(2) 55.73(2) 29% -53.70(3) -53.75(3) 16%
9. Vectorization
For the vectorization of loops it is essential how accessed data are distributed in physical
memory. Deducing this information automatically from the code can be very difficult for the
compiler, especially if there is indirection. In
ms
2, many arrays are accessed via array pointers
and the order of the underlying data is therefore obfuscated. The most relevant information
is whether or not data are contiguous in physical memory. To provide this information to the
compiler directly, array pointers can be given the attribute ”contiguous”. The Fortran standard
states: ”The contiguous attribute specifies that [...] an array pointer can only be pointer associated
with a contiguous target.” This means that the array elements of a contiguous array pointer are
not separated by any other data, potentially enabling a higher degree of vectorization. In
ms
2
release 3.0, array pointers associated with contiguous targets were given the contiguous attribute.
The sequential performance gains and the resulting parallel performance gains achieved with this
optimization depend on the specific simulation scenario, but are on average very significant. For
MC and MD simulations, a suite of simulations was executed to evaluate the performance gains.
The suite covered the
NpT
and
NV T
ensembles, thermodynamic integration, Widom test particle
insertion, different thermostats, different pure fluids and mixtures. A total of 71 simulation runs
was performed. For MC simulations, the observed average reduction of runtime was more than 7%
and for MD simulations more than 20%.
10. Parallel ensemble calculations
ms
2 was already parallelized in its initial version for distributed memory architectures using the
message passing interface (MPI) [
9
,
10
]. A typical MD simulation with
N
= 1000 to 4000 particles
usually scales up to 48 cores. The present release 3.0 adds an additional level of parallelization for MD
simulations. Different ensembles are independent of each other in the sense that sampling different
state points can be done concurrently. To achieve this, the processing elements (PE) were split in
disjunct groups and each group computes the ensembles assigned to it. In principle, this allows for
the sampling of an arbitrary number of state points in the whole relevant fluid region with a single
simulation execution. The vast amount of data generated can then, e.g. be used for the development
of an equation of state. To enable this feature, the mpiEnsembleGroups option was introduced in
the input file. The default (if not set or set to 0) is to use a single ensemble group. A value of 1 will
enable the new feature and automatically set the number of ensemble groups to the minimum of
the number of ensembles and the number of PE, i.e. mpiEnsembleGroups=min(ensembles, PE).
15
Otherwise, this option will set the number of ensemble groups according to the specified integer
value. The “coloring”, i.e. the assignment of the PE to the ensemble groups, is done in continguous
blocks. This is advantageous, e.g. compared to a round robin fashion, if the processes have to be
pinned to NUMA domains.
Another change applies to the restart capability of
ms
2. A checkpoint now consists of one restart
(*.rst) file for each ensemble group that can be restarted with the ms2 -r (or --restart) option.
To illustrate the new feature, a MD program execution for three ensembles with 24 processes is
exemplarily discussed: Without the mpiEnsembleGroups option (or with mpiEnsembleGroups=0)
all 24 PE will in parallel calculate the first time step of the first ensemble, then the first time step
of the second ensemble and finally the first time step of the third one, before the second time step
is handled accordingly. Setting mpiEnsembleGroups=1 is equivalent to mpiEnsembleGroups=3 in
this example and three groups of eight PE each will calculate one ensemble in parallel concurrently.
The user may also directly specifiy the number of groups, but has to be aware that in this example
with mpiEnsembleGroups=2 one group will have to process two ensembles, while the other one
only processes a single one.
ms
2 creates a MPI communicator for each of the ensemble groups with the MPI Comm Split
command, cf. Figure 6. Another MPI communicator contains the root processes of all groups
(Communicator R including subcommunicators rank 0 processes) to ease collective communication
on a higher level among the groups.
Figure 6: MPI ranks for 24 PE in 3 MPI groups, indicating communicator hierarchy of ms2.
Even if the computation of different ensembles is embarrassingly parallel, an interaction between
the different ensemble groups through communicators remains, e.g. when the program receives a
signal to write a checkpoint and terminate. This signal may be received from an arbitrary single PE
(or non-isochronic from multiple PE). In the preceding releases of
ms
2, where ensembles were calcu-
lated consecutively with the single global communicator MPI COMM WORLD, a MPI Allreduce
spreads this information among all processes after every MD time step. This is still the case within
the ensemble groups. A collective communication of all PE beyond ensemble group boundaries for
every MD time step would implicitly synchronize all ensemble computations. However, this is not
satisfactory because computationally less intensive ensembles would be forced to wait for slower
ones to conclude their time step. The present implementation uses non-blocking communication
between the ensemble group roots through Communicator R to avoid this problem.
16
  
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
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


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

 

 
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

!
"

# 

$% 






 

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
$% 
Figure 7: Communication to distribute status information within a MD time step avoiding barriers. Thick solid
arrows indicate communication among PE (grey arrows for alternative possible receiving points). Dotted lines
between the PE indicate collective communication implicating a barrier. For mutually exclusive commands, the
second one is only executed if the first one was not triggered.
Before any MD time step iterations start, the root process executes a MPI Irecv call to receive a
potential terminate message, whereas all other processes execute a MPI Ibcast to obtain a potential
terminate message from the root, cf. Figure 7. During program execution, any process may trigger
termination by sending a message to the root, which will then broadcast the information to notify all
other processes. If no termination occurs during the iterations, the root will send a message to itself
and broadcast a non-termination message to all other processes to satisfy the outstanding receive
and broadcast (avoiding MPI Cancel). To take care of several processes sending a termination
message, a summation reduction determines the sum of all respective messages for the root process
to receive all of them. This technique can also be used hierarchically, replacing the MPI Allreduce
call within each subcommunicator. After termination, every ensemble group writes its own restart
(*.rst) file.
17
Acknowledgements
The authors gratefully acknowledge financial support by BMBF under the grant “01IH13005A
SkaSim: Skalierbare HPC-Software f¨ur molekulare Simulationen in der chemischen Industrie”,
support by the Koselleck Program under the grant HA1993/15-1 and computational support by the
High Performance Computing Center Stuttgart (HLRS) under the grant MMHBF2. Furthermore,
we gratefully acknowledge the Paderborn Center for Parallel Computing (PC
2
) for the generous
allocation of computer time on the OCuLUS cluster. The present research was conducted under
the auspices of the Boltzmann-Zuse Society of Computational Molecular Engineering (BZS). H.H.
and M.K. acknowledge support of this work by DFG under a Reinhart Koselleck grant.
18
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22
SUPPLEMENTARY INFORMATION: Hydrogen bonding
The user has to specify the geometric relations in the
*.par
file according to the simulated components
as follows: First, the keyword
NHBondCriteria = ’#h-bonds’
has to be set to the integer value
#h-bonds
according to the number of different H bonds that shall be investigated during the simulation.
This keyword has to appear under the components section in the
*.par
file.
#h-bonds
also sets the
number of lines that ms2 expects in the
*.par
file, each to have a complete set of nine parameters
that declare a certain H bond. These nine parameters are:
AccComp, AccAccSite, AccDonSite, DonComp, DonAccSite, DonDonSite, DistCrit1, DistCrit2 and
AngleCrit. The first six parameters declare which charge – charge interactions of which component
are to be considered by ms2. The acceptor and donor sites listed in the
*.par
file have to be point
charges listed in the
*.pm
file. AccComp and DonComp are the component numbers of the components
that are supposed to be the acceptor and donor of the H bond, respectively. Both have to be integer
values according to the order of the components listed in the
*.par
file. The four charge sites that
participate in the H bond have to be set by the user as AccAccSite, AccDonSite, DonAccSite and
DonDonSite. They have to be integer values according to the order of the charge sites listed in the
.*pm
file. AccAccSite and AccDonSite are the acceptor and donor charge sites in the component that
is acting as the acceptor molecule in the H bond while DonAccSite and DonDonSite are the acceptor
and donor charge-sites in the donor molecule. As mentioned, only three charge sites are needed for the
criterion, thus either the AccDonSite or the DonDonSite has to be set to
0
by the user as can be seen
in table 1. This is equivalent of defining either `DA and ϕDAA or `AD and ϕAAD.
The last three numeric parameters in table 1 are the actual geometric length
`AA
,
`AD
or
`DA
and
angles
ϕDAA
or
ϕAAD
as described in [Haughney et al., J, Chem. Phys., 91(1987) 4934–4940]. ms 2
always expects these values to be specified in
˚
Angstrom and degree, respectively, independent of the
settings of the Units keyword in the *.par file before.
DistCrit1: |`AA|= 1st Distance criterion in ˚
A
DistCrit2: |`DA|or |`AD |= 2nd Distance criterion in ˚
A
AngleCrit: ϕDAA or ϕAAD = Angle criterion in
Table 1 gives two examples for a complete parameter set to be specified in a
*.par
file. During
Table 1: Example of Parameter sets for H bonding criterion.
AccComp AccAccSite AccDonSite DonComp DonAccSite DonDonSite DistCrit1 DistCrit2 AngleCrit
1 2 0 1 2 3 3.5 2.6 30
1 2 3 1 2 0 3.5 2.6 30
simulation, ms2 lists the analysis of the H bonding in the
*.rav
file. Following the Haughney-criterion,
ms2 calculates and itemizes the number
Ni
of molecules with
i
= 0
,
1
,
2
,
3 or more hydrogen bonds. In
the
*.rav
file these numbers are listed according to the component combination. E.g. the
N3 ( 1, 2,
2, 3)
column lists the number of molecules which correspond to component 1 and are bonded twice
with component 2 and once with component 3. As usual for the
*.rav
file, these values are running
averages.
1
SUPPLEMENTARY MATERIAL to
ms2: A molecular simulation tool for thermodynamic properties, release 3.0
|`AA| ≥ |rAccAccSite rDonAccSite |(1)
|`DA| ≥ |rAccDonSite rDonAccSite |(2)
|`AD| ≥ |rAccAccSite rDonDonSite |(3)
ϕDAA arccos
(rAccDonSite rAccAccSite)·`AA
|rAccDonSite rAccAccSite|·|`AA|
(4)
ϕAAD arccos
(rDonAccSite rDonDonSite)·`AA
|rDonAccSite rDonDonSite|·|`AA|
(5)
2
SUPPLEMENTARY INFORMATION: Themodynamic Integration
There are four parameters (
LambdaMin
,
NBins
,
LambdaStepMax
and
LambdaExponent
) involved with
the present approach that the user has to specify after the entry
ChemPotMethod = ThermoInt
in the
*.par.
LambdaMin
: The lower boundary of the interval
λmin λ
1 (default value is 0.2 if not specified).
NBins
: The number of discrete
λ
–bins in the interval
λmin λ
1 used for the numerical
integration (default value is 100 if not specified). The resolution is (1
LambdaMin
)
/NBins
.
During the simulation the current bin is determined by (
λLambdaMin
)
/NBins
for the current
λ
.
LambdaStepMax
: Defines the change of
λ
during simulation. The new
λ
is the current
λ
plus a
random number between zero and ±LambdaStepMax (default value is 0.1 if not specified).
LambdaExponent
: The exponent
d
for the non-linear scaling
Uj
(
λ
) =
λdUj
(
λmin λ
1) (it
does not have to be an integer and its default value is 4.0 if not specified).
One should keep in mind when choosing these parameters that thermodynamic integration always
involves larger statistical uncertainties than the equivalent pure Widom’s particle insertion scenario for
a state point for which the latter works perfectly. In other words: The larger the contribution of the
numerical integration part as compared to the Widom contribution at
λmin
is, the higher the statistical
uncertainty of the calculated chemical potential gets. This means that setting
λmin
very low or the
exponent
d
very high (e.g. 12) might not be optimal in many systems. Moreover, high exponent
d
values
for MD simulations are not advised because the scaling with
d
at high
λ
values (where the absolute
value of
Uj
(
λ
) is close that of the non-scaled state) may result in new
Uj
(
λ
) energies (thus forces) that
non-negligibly interfere with the dynamics of the system when
λ
is changed during the simulation. For
MD simulations, a value smaller then 1.0 for dis possibly a better choice for many systems.
3
1 Potential Models in the
ms
2-distribution
1
1 Potential Models in the ms2-distribution
Filename CAS number Name Publication Model Type
Ar.pm 7440-37-1 Argon [Vrabec et al. 2001] 1 L.J. Center
Ba2+.pm 22541-12-4 Barium ion (2+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Be2+.pm 22537-20-8 Beryllium ion (2+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Br-_I.pm 24959-67-9 Bromine ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Br-_II.pm 24959-67-9 Bromine ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Br2.pm 7726-95-6 Bromine [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
C2Br2F4.pm 124-73-2 1,2-Dibromotetrafluoroethane [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
C2Cl4.pm 127-18-4 Tetrachloroethylene [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
C2ClF3.pm 79-38-9 Chlorotrifluoroethene [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2F4.pm 116-14-3 Tetrafluoroethylene [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
C2F6.pm 76-16-4 Perfluoroethane [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
C2H2.pm 74-86-2 Acetylene [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
C2H2Cl3F.pm 27154-33-2 Ethane, trichlorofluoro- [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H2Cl4_I.pm 630-20-6 1,1,1,2-Tetrachloroethane [Stoll 2004] 2 L.J. Centers & 1 Dipole
C2H2Cl4_II.pm 630-20-6 1,1,1,2-Tetrachloroethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H2F2.pm 75-38-7 1,1-Difluoroethene [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H3Cl.pm 75-01-4 Vinyl chloride [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H3Cl3_a.pm 71-55-6 Methylchloroform [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H3Cl3_b.pm 79-00-5 1,1,2-Trichloroethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H3F.pm 75-02-5 Vinyl fluoride [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H3N.pm 75-05-8 Acetonitrile [Eckl et al. 2008c] 3 L.J. Centers & 1 Dipole & 1 Quadrupole
C2H3N_m6.pm 75-05-8 Acetonitrile [Deublein et al. 2013] 3 L.J. Centers & 1 Dipole
C2H3N_m8.pm 75-05-8 Acetonitrile [Deublein et al. 2013] 3 L.J. Centers & 1 Dipole
C2H4.pm 74-85-1 Ethylene [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
C2H4Br2.pm 106-93-4 Ethylene dibromide [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
C2H4Br3.pm 557-91-5 1,1-Dibromoethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H4Cl2.pm 75-34-3 1,1-Dichloroethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H4O_I.pm 75-21-8 Ethylene oxide [Eckl et al. 2008b] 3 L.J. Centers & 1 Dipole
C2H5Br.pm 74-96-4 Ethyl bromide [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H5F.pm 353-36-6 Fluoroethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
C2H6_I.pm 74-84-0 Ethane [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
C2H6_II.pm 74-84-0 Ethane [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
C2H6O.pm 64-17-5 Ethanol [Schnabel et al. 2005] 3 L.J. Centers & 3 Charges
C2H6O2.pm 107-21-1 Ethylene glycol [Huang et al. 2012] 4 L.J. Centers & 6 Charges
C2H6S_I.pm 75-18-3 Dimethyl sulfide [Eckl et al. 2008c] 3 L.J. Centers & 1 Dipole & 2 Quadrupoles
C2H8N2.pm 57-14-7 1,1-Dimethylhydrazine [Elts et al. 2012] 4 L.J. Centers & 3 Charges
C2HCl3.pm 79-01-6 Trichloroethylene [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
Continued on next page
2
1 Potential Models in the ms2-distribution
Filename CAS number Name Publication Model Type
C2N2.pm 460-19-5 Cyanogen [Miroshnichenko et al. 2013] 4 L.J. Centers & 1 Quadrupole
C3H4.pm 463-49-0 Propadiene [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
C3H6_a.pm 115-07-1 Propylene [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
C3H6_b.pm 75-19-4 Cyclopropane [Munoz-Munoz et al. 2015] 3 L.J. Centers
C4F10.pm 355-25-9 Perfluorobutane [Köster et al. 2012] 14 L.J. Centers & 14 Charges
C4H10.pm 75-28-5 Isobutane [Eckl et al. 2008c] 4 L.J. Centers & 1 Dipole & 1 Quadrupole
C4H4S_I.pm 110-02-1 Thiophene [Eckl et al. 2008c] 5 L.J. Centers & 1 Dipole & 1 Quadrupole
C4H8.pm 287-23-0 Cyclobutane [Munoz-Munoz et al. 2015] 4 L.J. Centers
C5H10_dfg.pm 287-92-3 Cyclopentane [Munoz-Munoz et al. 2015] 5 L.J. Centers
C5H10_diff.pm 287-92-3 Cyclopentane [Munoz-Munoz et al. 2015] 5 L.J. Centers
C6H10O.pm 108-94-1 Cyclohexanone [Merker et al. 2012] 7 L.J. Centers & 1 Dipole
C6H12_dfg.pm 110-82-7 Cyclohexane [Munoz-Munoz et al. 2015] 6 L.J. Centers
C6H12_diff.pm 110-82-7 Cyclohexane [Munoz-Munoz et al. 2015] 6 L.J. Centers
C6H12_I.pm 110-82-7 Cyclohexane [Eckl et al. 2008c] 6 L.J. Centers & 1 Quadrupole
C6H12_II.pm 110-82-7 Cyclohexane [Merker et al. 2012] 6 L.J. Centers
C6H12O_II.pm 108-93-0 Cyclohexanol [Merker et al. 2009] 7 L.J. Centers & 3 Charges 1 Quadrupole
C6H4Cl2.pm 95-50-1 ortho-Dichlorobenzene [Huang et al. 2011] 8 L.J. Centers & 1 Dipole & 4 Quadrupoles
C6H5Cl.pm 108-90-7 Chlorobenzene [Huang et al. 2011] 7 L.J. Centers & 1 Dipole & 5 Quadrupoles
C6H6_I.pm 71-43-2 Benzene [Guevara-Carrion et al. 2016] 6 L.J. Centers & 6 Quadrupoles
C6H6_II.pm 71-43-2 Benzene [Huang et al. 2011] 6 L.J. Centers & 6 Quadrupoles
C7H8_I.pm 108-88-3 Toluene [Guevara-Carrion et al. 2016] 7 L.J. Centers & 6 Quadrupoles
C7H8_II.pm 108-88-3 Toluene [Huang et al. 2011] 7 L.J. Centers & 1 Dipole & 5 Quadrupoles
Ca2+.pm 17787-72-3 Calcium ion (2+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
CBr2F2.pm 75-61-6 Dibromodifluoromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CBrCl3.pm 75-62-7 Bromotrichloromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CBrClF2.pm 353-59-3 Bromochlorodifluoromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CC2HBrClF3.pm 151-67-7 Halothane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CCl2O.pm 75-44-5 Phosgene [Huang et al. 2011] 4 L.J. Centers & 1 Dipole & 1 Quadrupole
CCl4_I.pm 56-23-5 Carbon tetrachloride [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
CCl4_II.pm 56-23-5 Carbon tetrachloride [Guevara-Carrion et al. 2016] 5 L.J. Centers & 5 Charges
CClN.pm 506-77-4 Cyanogen chloride [Miroshnichenko et al. 2013] 3 L.J. Centers & 1 Quadrupole & 1 Dipole
CF2CFBr.pm 598-73-2 Bromotrifluoroethylene [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CF4_II.pm 75-73-0 Tetrafluoromethane [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
CH2Br2_D.pm 74-95-3 Dibromomethane [Stoll et al. 2003] 1 L.J. Center & 1 Dipole
CH2Br2_Q.pm 74-95-3 Dibromomethane [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
CH2BrCl.pm 74-97-5 Bromochloromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CH2Cl2.pm 75-09-2 Methylene chloride [Stoll et al. 2003] 1 L.J. Center & 1 Dipole
Continued on next page
3
1 Potential Models in the ms2-distribution
Filename CAS number Name Publication Model Type
CH2I2.pm 75-11-6 Methylene iodide [Stoll et al. 2003] 1 L.J. Center & 1 Dipole
CH2O.pm 50-00-0 Formaldehyde [Eckl et al. 2008c] 2 L.J. Centers & 1 Dipole
CH2O2.pm 64-18-6 Formic acid [Schnabel et al. 2007b] 3 L.J. Centers & 4 Charges
CH3Br.pm 74-83-9 Methyl bromide [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CH3Cl.pm 74-87-3 Methyl chloride [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CH3I.pm 74-88-4 Methyl iodide [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CH3NO2.pm 75-52-5 Nitromethane [Eckl et al. 2008c] 4 L.J. Centers & 1 Dipole & 1 Quadrupole
CH3OCH3.pm 115-10-6 Dimethyl ether [Eckl et al. 2008c] 3 L.J. Centers & 1 Dipole
CH4.pm 74-82-8 Methane [Vrabec et al. 2001] 1 L.J. Center
CH4O_I.pm 67-56-1 Methyl alcohol [Schnabel et al. 2007a] 2 L.J. Centers & 3 Charges
CH5N.pm 74-89-5 Methylamine [Schnabel et al. 2008] 2 L.J. Centers & 2 Charges
CH6N2.pm 60-34-4 Methylhydrazine [Elts et al. 2012] 3 L.J. Centers & 3 Charges
CHBr3.pm 75-25-2 Bromoform [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CHCCH3_I.pm 74-99-7 1-Propyne [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
CHCCH3_II.pm 74-99-7 1-Propyne [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
CHCl2F.pm 75-43-4 Dichlorofluoromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CHCl3.pm 67-66-3 Chloroform [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CHN.pm 74-90-8 Hydrogen cyanide [Eckl et al. 2008c] 2 L.J. Centers & 1 Dipole & 1 Quadrupole
Cl-_I.pm 16887-00-6 Chlorine ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Cl-_II.pm 16887-00-6 Chlorine ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Cl2.pm 7782-50-5 Chlorine [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
CO_D.pm 630-08-0 Carbon monoxide [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
CO_Q.pm 630-08-0 Carbon monoxide [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
CO2_I.pm 124-38-9 Carbon dioxide [Merker et al. 2010] 3 L.J. Centers & 1 Quattropole
CO2_II.pm 124-38-9 Carbon dioxide [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
Cs+.pm 18459-37-5 Cesium ion (1+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
CS2.pm 75-15-0 Carbon disulfide [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
F-_I.pm 16984-48-8 Fluorine ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
F-_II.pm 16984-48-8 Fluorine ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
F2.pm 7782-41-4 Fluorine [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
NH3_II.pm 7664-41-7 Ammonia [Eckl et al. 2008a] 1 L.J. Center & 4 Charges
H4N2.pm 302-01-2 Hydrazine [Elts et al. 2012] 2 L.J. Centers & 6 Charges
HCl.pm 7647-01-0 Hydrochloric acid [Huang et al. 2011] 1 L.J. Center & 2 Charges
I-_I.pm 20461-54-5 Iodide ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
I-_II.pm 20461-54-5 Iodide ion (1-) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
I2.pm 7553-56-2 Iodine [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
K+.pm 24203-36-9 Potassium ion (1+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Continued on next page
4
1 Potential Models in the ms2-distribution
Filename CAS number Name Publication Model Type
Kr.pm 7439-90-9 Krypton [Vrabec et al. 2001] 1 L.J. Center
Li+.pm 17341-24-1 Lithium ion (1+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Mg2+.pm 22537-22-0 Magnesium ion (2+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
N2.pm 7727-37-9 Nitrogen [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
Na+_I.pm 17341-25-2 Sodium ion (1+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Ne.pm 7440-01-9 Neon [Vrabec et al. 2001] 1 L.J. Center
O2.pm 7782-44-7 Oxygen [Stoll 2004] 2 L.J. Centers & 1 Quadrupole
R11_CFCl3.pm 75-69-4 Trichloromonofluoromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R1122_CHCl=CF2.pm 359-10-4 2-Chloro-1,1-difluoroethylene [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R112a_CCl3-CF2Cl.pm 76-11-9 1,1,1,2-Tetrachloro-2,2-difluoroethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R113_CFCl2-CF2Cl.pm 76-13-1 1,1,2-trichloro-1,2,2-trifluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
R114_CF2Cl-CF2Cl.pm 76-14-2 1,2-dichloro-1,1,2,2-tetrafluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
R115_CF3-CF2Cl.pm 76-15-3 Pentafluoroethyl chloride [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
R12_CF2Cl2.pm 75-71-8 Dichlorodifluoromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R123_CHCl2-CF3.pm 306-83-2 2,2-dichloro-1,1,1-trifluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R124_CHFCl-CF3.pm 2837-89-0 2-chloro-1,1,1,2-tetrafluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R125_CHF2-CF3.pm 354-33-6 pentafluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R13_CF3Cl.pm 75-72-9 Chlorotrifluoromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R134_CHF2-CHF2.pm 359-35-3 1,1,2,2-tetrafluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Quadrupole
R134a_CH2F-CF3.pm 811-97-2 Norflurane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R13B1_CBrF3.pm 75-63-8 Bromotrifluoromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R141b_CH3-CFCl2.pm 1717-00-6 1,1-Dichloro-1-fluoroethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R142b_CH3-CF2Cl.pm 75-68-3 1-chloro-1,1-difluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R143a_CH3-CF3.pm 420-46-2 1,1,1-trifluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R152a_CH3-CHF2.pm 75-37-6 1,1-difluoro-Ethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R22_CHF2Cl.pm 75-45-6 Difluorochloromethane [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R227ea_C3HF7.pm 431-89-0 1,1,1,2,3,3,3-heptafluoro-Propane [Eckl et al. 2007] 10 L.J. Centers & 1 Dipole 1 Quadrupole
R23_CHF3.pm 75-46-7 Fluoroform [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
R32_CH2F2.pm 75-10-5 Difluoromethane [Stoll et al. 2003] 1 L.J. Center & 1 Dipole
R41_CH3F.pm 593-53-3 Methyl fluoride [Stoll et al. 2003] 2 L.J. Centers & 1 Dipole
Rb+.pm 22537-38-8 Rubidium ion (1+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
SF6.pm 2551-62-4 Sulfur hexafluoride [Vrabec et al. 2001] 2 L.J. Centers & 1 Quadrupole
SO2.pm 7446-09-5 Sulfur dioxide [Eckl et al. 2008c] 3 L.J. Centers & 1 Dipole & 1 Quadrupole
Sr.pm 22537-39-9 Strontium ion (2+) [Deublein et al. 2012] 1 L.J. Center & 1 Charge
Xe.pm 7440-63-3 Xenon [Vrabec et al. 2001] 1 L.J. Center
5
Bibliography
Deublein, S., J. Vrabec, and H. Hasse (2012). “A set of molecular models for alkali and halide ions in
aqueous solution”. In: The Journal of Chemical Physics (cit. on pp. 2, 4, 5).
Deublein, S., S. Reiser, J. Vrabec, and H. Hasse (2012). “A Set of Molecular Models for Alkaline-
Earth Cations in Aqueous Solution”. In: Journal of Physical Chemistry B 116.18, p. 5448. doi:
10.1021/jp3013514 (cit. on pp. 2–5).
Deublein, S., P. Metzler, J. Vrabec, and H. Hasse (2013). “Automated development of force fields for
the calculation of thermodynamic properties acetonitrile as a case study” . In: Molecular Simulation
39.2, p. 109. doi:10.1080/08927022.2012.705434 (cit. on p. 2).
Eckl, B., Y. Huang, and H. Vrabec J.and Hasse (2007). “Vapor pressure of R227ea + ethanol at 343.13K
by molecular simulation”. In: Fluid Phase Equilibria 260, 177–182. doi:
10.1016/j.fluid.2007.05.011
(cit. on p. 5).
Eckl, B., J. Vrabec, and H. Hasse (2008a). “An optimised molecular model for ammonia”. In: Molecular
Physics: An International Journal at the Interface Between Chemistry and Physics 106.8, p. 1039. doi:
10.1080/00268970802112137 (cit. on p. 4).
Eckl, B., J. Vrabec, and H. Hasse (2008b). “On the application of force fields for predicting a wide
variety of properties: Ethylene oxide as an example”. In: Fluid Phase Equilibria 274.1. doi:
10.1016/j.
fluid.2008.02.002 (cit. on p. 2).
Eckl, B., J. Vrabec, and H. Hasse (2008c). “Set of Molecular Models Based on Quantum Mechanical
Ab Initio Calculations and Thermodynamic Data”. In: The Journal of Physical Chemistry B (cit. on
pp. 2–5).
Elts, E., T. Windmann, D. Staak, and J. Vrabec (2012). “Fluid phase behavior from molecular simulation
Hydrazine, Monomethylhydrazine, Dimethylhydrazine and binary mixtures containing these compounds” .
In: Fluid Phase Equilibria 322. doi:10.1016/j.fluid.2012.03.008 (cit. on pp. 2, 4).
Guevara-Carrion, G., T. Janzen, Y. Munoz-Munoz, and J. Vrabec (2016). “Mutual diffusion of binary
liquid mixtures containing methanol, ethanol, acetone, benzene, cyclohexane, toluene, and carbon
tetrachloride”. In: The Journal of Chemical Physics 144. doi:
10.1063 / 1 .4943395
.url:
http:
//dx.doi.org/10.1063/1.4943395 (cit. on p. 3).
Huang, Y., M. Heilig, J. Vrabec, and H. Hasse (2011). “Vapor-Liquid Equilibria of Hydrogen Chloride,
Phosgene, Benzene, Chlorobenzene, Ortho-Dichlorobenzene and Toluene by Molecular Simulation”. In:
AIChE Journal 57.4, p. 1043. doi:10.1002/aic.12329 (cit. on pp. 3, 4).
Huang Y. aHuang, Y. T., M. Heilig, H. Hasse, and J. Vrabec (2012). “Molecular Modeling and Simulation
of Vapor–Liquid Equilibria of Ethylene Oxide, Ethylene Glycol, and Water as Well as their Binary
Mixtures”. In: Ind. Eng. Chem. Res. 51.21. doi:10.1021/ie300248z (cit. on p. 2).
6
Bibliography
Köster, A., P. Nandi, T. Windmann, D. Ramjugernath, and J. Vrabec (2012). “Vapor–liquid equilibria
of ethylene (C2H4) + decafluorobutane (C4F10) at 268–298 K from experiment, molecular simulation
and the Peng–Robinson equation of state”. In: Fluid Phase Equilibria 336. doi:
10.1016/j.fluid.
2012.08.023 (cit. on p. 3).
Merker, T., J. Vrabec, and H. Hasse (2012). “Molecular simulation study on the solubility of carbon
dioxide in mixtures of cyclohexane + cyclohexanone”. In: Fluid Phase Equilibria 315, p. 77. doi:
10.1016/j.fluid.2011.11.003 (cit. on p. 3).
Merker, T., G. Guevara-Carrion, J. Vrabec, and H. Hasse (2009). HIGH PERFORMANCE COMPUTING
IN SCIENCE AND ENGINEERING ’08. Ed. by W. E. Nagel, D. B. Kroner, and M. M. Resch. Springer.
doi:10.1007/978-3-540-88303-6_37 (cit. on p. 3).
Merker, T., C. Engin, J. Vrabec, and H. Hasse (2010). “ Molecular model for carbon dioxide optimized to
vapor-liquid equilibria”. In: The Journal of Chemical Physics 132, p. 234512. doi:
10.1063/1.3434530
(cit. on p. 4).
Miroshnichenko, S., T. Grützner, D. Staak, and J. Vrabec (2013). “Molecular simulation of the va-
por–liquid phase behavior of cyanides and their binary mixtures”. In: Fluid Phase Equilibria 354. doi:
10.1016/j.fluid.2013.06.039 (cit. on p. 3).
Munoz-Munoz, Y.M., G. Guevara-Carrion, M. Llano-Restrepo, and J. Vrabec (2015). “Lennard-Jones
force field parameters for cyclic alkanes from cyclopropane to cyclohexane”. In: Fluid Phase Equilibria
404, p. 150. doi:10.1016/j.fluid.2015.06.033 (cit. on p. 3).
Schnabel, T., J. Vrabec, and H. Hasse (2005). “Henry’s law constants of methane, nitrogen, oxygen and
carbon dioxide in ethanol from 273 to 498 K: Prediction from molecular simulation”. In: Fluid Phase
Equilibria 233, pp. 134–143. doi:10.1016/j.fluid.2005.04.016 (cit. on p. 2).
Schnabel, T., J. Vrabec, and H. Hasse (2008). “Molecular simulation study of hydrogen bonding mixtures
and new molecular models for mono- and dimethylamine”. In: Fluid Phase Equilibria 263, 144–159.
doi:10.1016/j.fluid.2007.10.003 (cit. on p. 4).
Schnabel, T., A. Srivastava, J. Vrabec, and H. Hasse (2007a). “Hydrogen Bonding of Methanol in
Supercritical CO2: Comparison between 1H NMR Spectroscopic Data and Molecular Simulation Results”.
In: J.Phys.Chem. B 111.33, p. 9871. doi:10.1021/jp0720338 (cit. on p. 4).
Schnabel, T., M. Cortada, J. S. Vrabec JVrabec, and H. Hasse (2007b). “Molecular model for formic
acid adjusted to vapor–liquid equilibria”. In: Chemical Physics Letters 435.4, p. 268. doi:
10.1016/j.
cplett.2006.12.091 (cit. on p. 4).
Stoll, J. (2004). “Molecular Models for the Prediction of Thermophysical Properties of Pure Fluids and
Mixtures”. PhD thesis. Universität Stuttgart (cit. on pp. 2, 4, 5).
Stoll, J., J. Vrabec, and H. Hasse (2003). “A set of molecular models for carbon monoxide and halogenated
hydrocarbons”. In: The Journal of Chemical Physics 119, p. 11396. doi:
10.1063/1.1623475
(cit. on
pp. 2–5).
Vrabec, J., J. Stoll, and H. Hasse (2001). “A Set of Molecular Models for Symmetric Quadrupolar
Fluids”. In: The Journal of Physical Chemistry B 105.48, p. 12126. doi:
10.1021/jp012542o
(cit. on
pp. 2–5).
7
How to compile and run ms2 - Version 3.0
1 Citation information & license 1
2 Support, development & maintenance 2
3 Installation 2
3.1 Downloadingthesourcecode .............................................. 2
3.2 Building ms2 .......................................................... 2
3.2.1 Building ms2onLinuxplatforms ...................................... 2
3.2.2 BuildingonWindows............................................... 5
4 Running ms2 5
4.1 Inputstructure......................................................... 5
4.1.1 Parameter( )le ............................................... 6
4.1.2 Potentialmodel( )le............................................ 7
4.2 Outputstructure........................................................ 9
5 Keywords for input files 10
5.1 Keywords for les................................................... 10
5.2 Keywords for les.................................................... 12
1 Citation information & license
ms2 is a noncommercial software, which was published in Computer Physics Communications. The
most current manuscript as the preceding ones along with their Supplementary Materials can be down-
loaded from the ms2 home page (http://www.ms-2.de). It is free of charge for scientific research and can
be obtained after registration. Users need to acknowledge the use of ms2 by citing the following publica-
tion:
S. Deublein, B. Eckl, J. Stoll, S. Lishchuk, G. Guevara-Carrion, C.W. Glass, T. Merker, M. Bernreuther,
H. Hasse, J. Vrabec
Computer Physics Communication 182 (2011) 2350
doi:10.1016/j.cpc.2011.04.026
The NonCommercial 3.0 (CC by-NC 3.0) licence applies for ms2. The full licence is available under (cre-
ative commons. You may not use the material for commercial purposes. You must give appropriate credit,
provide a link to the license, and indicate if changes were made. You may do so in any reasonable man-
ner, but not in any way that suggests the licensor endorses you or your use. You are free to share a copy
and redistribute the material in any medium or format and adapt, transform, and build upon the mate-
rial.
1
2 Support, development & maintenance
Supply the version and compiling details with a support request.
The newest version of the ms2 molecular simulation package is available at the ms2 homepage:
http://www.ms-2.de
The source code of ms2 can be downloaded there as a tarball.
The following email address is the general contact point:
contact@ms-2.de
ms2 users are encouraged to report bugs to the aforementioned email address.
3 Installation
3.1 Downloading the source code
The ms2 distribution is available on the webpage: http://www.ms-2.de/download. Users must either be a
natural person or an academic institution represented by a natural person. The ms2 distribution consists
of four major parts: the source code, java tools for pre- and postprocessing, force field models from the
Boltzmann-Zuse Society of Computational Molecular Engineering database as input files for ms2 and some
example input files for the calculation of different properties. The installation and use of the ms2 program is
explained in section 4 and 5.
3.2 Building ms 2
ms2 was tested on Linux and Windows platforms, a short explanation how to install ms2 on these two sys-
tems is given in the following.
3.2.1 Building ms 2 on Linux platforms
The compilation can be carried out using the provided “Makefile” found in the “src” directory (e.g. with
GNU make) and the compiler-related -files in the -subdirectory. The “Makefile” and the
”-file should be adopted to the local system requirements as described below. Alternatively (or addi-
tionally) variables can be set through the make command line options as compiler flags. An overview of all
options can be found in Table 1.
When compiling ms2, a variety of settings can be specified according to the users needs and optimize the per-
formance. The following strings are recognizedin the makefile: , , , , , ,
, and . After settings these variable according to the users hardware and computational need,
typing in the command line from the “src” directory compiles ms2 and creates and executable in the
current directory.
Settings in the
First of all a compiler has to be chosen. Through the definition of the variable, the corresponding
file with suffix “.mk” in the “makefiles” subdirectory will be included during the execution of . These
files contain specific settings for compilers and/or systems that ms2 is suitable for.
2
• Version:
or
The version is manly used by developers. Default is .
FORTRAN compiler:
, or
The entry found in the given Makefile corresponds to “makefiles/GNU.mk, which contains
settings for the widely used GNU compiler. There are other predefined settings available, like “INTEL
for the INTEL compiler. The default value is , since that compiler is freeware.
Parallelisation protocol:
or or
or
These parameters have to be set to invoke the implemented parallelisation schemes.
The make command produces one executable file of ms2. To optimise the execution speed of the program
for each application, the user should set the feature compiler flags , , and according
the simulation dependencies – especially if the user wants to run large numbers of simulations with one exe-
cutable. We suggestonly to set a if you want to use this certain feature,otherwise
they will slow down yoursimulation speed.
Transport properties:
or
To produce an executable that samples transport properties (e.g. diffusion and conductivity)
has to be set. A value of means, that the routines for calculation of transport properties are not
compiled. The default value is , since the program execution for the sampling of default properties
is faster in that case.
Hydrogen-bonding evaluation:
or
If you want to have a look atthe hydrogen bonds in your system, turn this on (set variable ). It enables
you to specify a geometric criterion for hydrogen bonds in your input files. ms2 evaluates then the
pursuant hydrogen bonding statistics. A value of means, that the routines for the calculation of
hydrogen bonds are not to be compiled. The default value is , since the program execution for the
sampling of the default properties is faster in that case.
Osmotic pressure:
, or
This flag enables the osmotic pressure method. The value enables the pressure profile calculation
along the density profile and osmotic pressure results. A value of means, that the routines for use of
the osmotic pressure method are not to be compiled. The default value is .
Single precision:
or
To speed up your simulation you can choose single precision (set value ) instead of the default
double precision (set value ). Users are advised to use with care.
Name of the executable file:
The user can set the value to adapt the name of the executable file, that is produced by the make com-
mand. According to the values of , , , , and the executable
will have an addition in its name respectively.
3
Variable Description Values Description
Compiler settings
Compiler presets GNU compiler
INTEL compiler
PGI compiler
see makefiles subdirectory
see above for production simulations
for code developing
Parallelization setting
MPI off
on
OpenMP off
on
Features to be accessible
Single Precision off
on
Transport off
on
Osmotic pressure off
on
H-Bonding statistics off
on
Name of executable String can be set by user
Table 1: Makefile definitions
Compiler related files
For each supported compiler, the subdirectory in contains one file, e g. .
The first three lines define the used FORTRAN90 comilers. In rare system depending cases, the optimi-
sation degree (the integer after the -O for the has to be decreased to 2 or 1). It is
suggested to use the slightly faster -compiler instead of the in case you are using the
.
make command line options
Instead of changing the Makefile, the definitions can also be set directly in the command line, that will
overwrite the settings in the Makefile. For example:
4
Compiler flags
Depending on compiler and preprocessor variables set in the Makefile, the following com-
piler flags are used in the compilation/build process:
OMPFlags: -mp/openmp/fopenmp
CPPFlags: -DARCH=2 –DFORTRAN=90 (replaces compiler flags for ARCH and FORTRAN)
Releaseflags: -O3 -vec/qopt-report=3/5
Debugflags: -O0 -vec/qopt-report=0 -g
GNU: -ffree-line-length-none -mtune=generic
INTEL: -fpp –r8
PGI: -C
If the user is unsure whatcompiler flags to set, itis suggested to leave the Makefile blank.
3.2.2 Building on Windows
ms2 can also be executed on Windows systems. The source code has to be downloaded and compiled in a
similar way as for Linux platforms. It is suggested to use a Linux-like shell, for example cygwin. It provides a
terminal window that runs a handsome Linux shell and comes with the GNU gfortran compiler
1
. This is very
useful, since ms2 is a command line-based program, whose utilization is in our experience best in combina-
tion with the standard Linux commands, such as , , , etc.. Additionally, the preparation of
input files and analysis of the output files of ms2 can be done by shell scripts. The installation of ms2 in cyg-
win follows the installation instructions on Linux platforms discussed above. Of course, ms2 can also be com-
piled using standard Windows tools.
4 Running ms2
ms2 was designed to be an easily applicable simulation program. Therefore, the input files are restricted to
one file for the definition of the simulation scenario and one file for each of the molecular species that are
used in the simulation. The output files contain structured information on the simulation. All calculated
thermodynamic properties are summarized in one output file, which is straightforwardly readable and self-
explaining. For a more detailed evaluation ofthe simulation, the instantaneous and running averages of the
most important thermodynamic properties are written to other files. In total,the current status of the simula-
tion and many more details are written to six files and can be accessed during execution. The structure ofthe
input files as well as the output files is shown in Figure 1.
4.1 Input structure
ms2 expects two input files: the
and the
file. The
file specifies the simulation parameters and
the file the molecular potential model. The
file is the main file steering the actual simulation. It
contains all input variables for the simulation process, such as simulation type, ensemble, number of equili-
bration and production steps, time step length etc. Also the potential models needto be declared here. Each
file specifies exactly one chemical substance. To calculate mixtures, several
files have to be specified
in the
file.
Each line in both input file types sets one parameter, is empty or contains a comment. The comment symbol
# and everything after it up to the end of the line is ignored by ms2 in the same way as empty lines are. It is
1During the installation of cygwin, all the FORTRAN depending packages have to be tagged.
5
Figure 1: File structure needed and generated by ms2.
suggested to use only blanks instead of tabs, since the latter may cause trouble using input files generated on
otherplatforms.
A line setting a parameter in either
or
file always consists of a keyword , the symbol and
the parameter value YYY, e. g.
Leading spaces, trailing spaces and spaces surrounding =symbol are ignored. Parameter values can be
strings in some cases or numeric values. Parameter names and values that ms2 expects for the parameter
file and potential model files are described in sections 5. All parameters must be present in the input files
in the certain order. The program reads the input file sequentially. Unidentified parameters are ignored.
Missing or misplaced parameters lead to the termination of the program with the corresponding error mes-
sage.
4.1.1 Parameter ( ) file
Below is an exemplary
file for a MD simulation of pure oxygen in the
N V T
ensemble.
files are
organised in three sections: the first section sets the general simulation parameters, such as timestep, MD
or MC, unit systems etc. (lines 3 to 20 in the oxygen example), the second section sets the thermodynamic
quantities to define the ensemble, such as temperature, density, number of components etc. (lines 21 to
26). The third section contains the potential models that shall be simulated and indicate their mole fraction
(lines 28 to 31). The value for the keyword needs to be set according to the name of the potential
model file that shall be used, including the tailing
. Each
file ends with the cutoff radius that shall
be applied throughout the simulation.
This example runs a MD simulation of pure oxygen at a constant temperature of 40 K with an equilibration of
100 000 timesteps and a production period of 1000 000 timesteps. The simulation contains 1372 molecules
and uses a cutoff distance of 15 Å.
2
1
2
3
4
5
6
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
Table 2 in section 5 lists all input parameters and options to be specified in the
file. Creating a
file
is facilitated by the ms2 feature program ms2par.
4.1.2 Potential model ( ) file
A
file contains the molecular model, also called force field,for a given substance. It contains the relative
positions and parameters of all interaction sites. The potential model file for methanol is shown below.
Methanol was modeled by two Lennard-Jones sites and three point charges .
All positions and distances in the
file are given in Å, the Lennard-Jones interaction parameters
σ
and
ε/kB
are given in Å and K, respectively, while the mass is given in atomic units (u =1
.
6605
×
10
27
kg). The
magnitudes of the charges are specified in electronic charges (e=1
.
602
×
10
19
C), while dipole moments
and quadrupole moments are given in Debye (
D
=3
.
33564
×
10
30
Cm) and Buckingham (
B
=3
.
33564
×
10
40 Cm2
), respectively. The orientations of the dipole and quadrupole are represented by spherical coordi-
nates, where the azimuthal angle
φ
specifies the angle to the positive
x
axis and the polar angle
θ
defines the
angle to the positive
z
axis. Both angles are specified in degrees. Molecular models can be orientated arbitrar-
ily in the
file. All site positions are automatically transformed into a principal axes coordinate system at
the beginning of each simulation run by ms2. The normalized site positions are written to a
output file
for each component.
7
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
8
All input parameters and options to be specified in the
file are given in Table 3. A
file has a specific
structure, which is described in the following. The parameter gives the number of different po-
tential types (not the number of sites). Different potential types are 12-6 Lennard-Jones sites, point charges,
point dipoles and point quadrupoles. Then the descriptions for each potential type follow sequentially. Each
of them contains the number of sites of the corresponding type ,followed by the definition of each in-
dividual site. Each site requires
x
,
y
and
z
coordinates and the mass in addition to its interaction parameters,
depending on the site type. Lennard-Jones sites require one size and one energy parameter, point charges
only the magnitude of the charge,while point dipoles and point quadrupoles require magnitude andorienta-
tion. At the end of a
file, the parameter is specified. Parameters , and
are read if the moments of inertia are to be specified manually, set according to the
value.
4.2 Output structure
ms2 yields different output files depending on the specifications made in the
file:
file - stores a complete summary of all execution steps taken by ms2.
file - contains the results of the simulation in an aggregated form. The data are written to file
in reduced quantities as well as in SI units, along with the statistical uncertainties of the calculated
properties. The file is created during simulation and updated every specified number of time
steps or loops.
file - contains the calculated properties of the simulation for a specified time step or loop
interval. The file is in tabular form, where the data are given in reduced units. The file is subsequently
updated according to the user specification, which is set in the file.
file - contains the block averages of the calculated properties. The file is in tabular form, where
the data are given in reduced units. The file is updated according to the user specification, which is
set in the file.
file - is the restart file of the simulation. It contains all molecular positions, velocities, orien-
tations, forces, torques and block averages for the thermodynamic properties. It is written once at
the end of a simulation or immediately after having received a termination signal of the operating
system. The
file allows for a stepwise execution of the simulation, necessary e.g. in case of an
early interruption of the simulation, time limits on a queuing system or unexpected halts.
file - is the trajectory visualization file. It contains the positions and orientations of all molecules
in an aggregated ASCII format. The configurations are written to file after a user-specified interval of
time steps or loops. The
file is readable by the visualization tool ms2molecules, which is also
part of the simulation package.
file - stores the normalized coordinates of a potential model after a principal axes transforma-
tion.
file - stores the final value of the correlation functions and theirintegrals. The number of output
lines is equal to divided by . These parameters have to be defined in
the file.
file - contains the averaged radial distribution functions between different sites over the cutoff
radius.
file - stores the potential energy states of the fluctuating test particle for the chemical potential
calculation with thermodynamic integration.
9
5 Keywords for input files
Tables 2 and 3 give an overview over the keywords that can be specified in the
and the
files and the expected values. A short explanation of the keywords
and recommended values are also given.
5.1 Keywords for files
keyword value explanation recommended value
Simulation specific:
limiting wall time for the simulation given in minutes
time limit for sending the termination signal before reaching the wall time given in minutes
physical properties in the *.par file are given in SI units
physical properties in the *.par file are given in
reduced units with respect to the reference values of length σre f ,
energy εre f and mass mre f
reference length σre f in Å
reference energy εre f /kBin K
reference mass mre f in atomic units u =1.6605 ×1027 kg 100.0
molecular dynamics simulation
Monte-Carlo simulation
gear predictor-corrector integrator (MD only)
Leapfrog integrator (MD only)
TimeStep time step of one MD step in fs (MD only) 1
acceptance rate for MC moves (MC only)
canonical ensemble
micro-canonical ensemble
isobaric-isothermal ensemble
GE Grand equilibrium method (pseudo-µV T )
isoenthalpic–isobaric ensemble
MC relaxation loops for pre-equilibration
number of equilibration time steps (MD) or loops (MC) in the N V T ensemble
number of equilibration time steps (MD) or loops (MC) in the N p T ensemble (optional)
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10
keyword value explanation recommended value
number of production time steps (MD) or loops (MC)
size of block averages in time steps or loops
frequency of writing the *.res file in time steps or loops
frequency of saving trajectories in the *.vim file
center of mass cut-off
site-site cut-off
number of ensembles in the simulation 1
number of ensemble groups 1
yes calculation of correlation functions enabled
no calculation of correlation functions disabled
specified temperature
specified pressure
specified density
piston mass for simulations at constant pressure
total number of molecules
number of shells for the calculation of RDF 300
yes enable pressure calculation in the NpT ensemble (MC only)
no disable pressure calculation in the NpT ensemble (MC only)
yes One common equlilibration (for parallelized MC run only)
no Separate equlilibration for each subtask (for parallelized MC run only)
number of components
simulation result density
statistical uncertainty of density
simulation result residual enthalpy
statistical uncertainty of residual enthalpy
simulation result isothermal compressibility
statistical uncertainty of isothermal compressibility
simulation result (d h /d p )T
statistical uncertainty of (d h /d p )T
number of components
length of the correlation functions in time steps
time steps separating subsequent correlation functions
output frequency of the full correlation functions into the *.rtr file
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11
keyword value explanation recommended value
output frequency of transport properties into the *.res file
potential model *.pm file of a component
molar fraction of a component
no calculation of the chemical potential for this component
calculation of the chemical potential for this component using Widoms’s test molecule method
calculation of the chemical potential for this component using thermodynamic integration
number of test molecules for Widoms test molecule method
for gradual insertion: use user defined initial values for the weight Guess
factors with optimization of these factors during simulation
for gradual insertion: values for the weight factors without adjustment during simulation
binary size interaction parameter η– combination rule
binary energy interaction parameter ξ– combination rule
number of hydrogen bonding criteria
cut-off radius for center of mass cut-off
cut-off radius for LJ interactions (site-site cut-off)
cut-off radius for dipole-dipole interactions (site-site cut-off)
cut-off radius for dipole-quadrupole interactions (site-site cut-off)
CutoffQQ cut-off radius for quadrupole-quadrupole interactions (site-site cut-off )
reaction field parameter
Table 2: Parameters and options specified in the file.
5.2 Keywords for files
keyword value explanation recommended value
int number of site types to appear in file
type of interaction site must be specified
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12
keyword value explanation recommended value
int number of sites for the corresponding interaction site type must be specified
double spatial coordinate of a site in Å must be specified for each site
double spatial coordinate of a site in Å must be specified for each site
double spatial coordinate of a site in Å must be specified for each site
double angle θbetween the dipole or quadrupole and the positive zaxis in degree must be specified for dipole or quadrupole site
double angle φbetween the dipole or quadrupole and the positive xaxis in degree must be specified for dipole or quadrupole site
double Lennard-Jones radius σin Å must be specified for Lennard-Jones site
double Lennard-Jones energy "/kBin K must be specified for Lennard-Jones site
double magnitude of point charge site must be specified for charge site
double dipole moment for dipole site must be specified for dipolar site
double quadrupole moment for quadrupole site must be specified for quadrupolar site
double mass in atomic units must be specified for each site
double shielding radius in Å for MC steps can be specified to get better convergence in MC run
number of rotation axes of the molecule
double mass of molecule in atomic units optional
double component of inertia moment in atomic mass unit multiplied by Å2if is 2 or 3
double component of inertia moment in atomic mass unit multiplied by Å2if is 2 or 3
double component of inertia moment in atomic mass unit multiplied by Å2if is 3
Table 3: Parameters and options specified in a file.
13
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