ms2: A Molecular Simulation Tool for Thermodynamic Properties

−0.5 < x, y, z < 0.5. The advantage of this scaling scheme lies mainly in the efficient application of the
periodic boundary condition [36] and the minimum image convention [37].
The molecular orientations are stored using normalized quaternions [29]. Quaternions are a biunique representa-
tion that avoid divergence problems at low angles. Their use allows for an efficient calculation of site positions,
while being less demanding concerning execution time and memory than updating and storing all site positions.
4.4. Initial configuration
It is important to define a stable and physically reasonable starting configuration for a simulation in a reliable
way. Inms2, the molecules are initially placed on a face-centered cubic lattice in order to avoid overlaps between
molecules. For mixtures, the positions of the different molecule species are distributed randomly on the lattice,
ensuring a homogeneous distribution of all components in the simulation volume.
After the initial molecule placement, the configuration can be relaxed by translational and rotational MC moves.
This step is part of the initialization process and can therefore be performed regardless of the simulation technique
used. The number of relaxation moves is user defined and should be chosen large enough to achieve a physically
reasonable starting configuration. For MD, the molecules are subsequently assigned with initial velocities such
that the temperature is specified and no net translational and rotational moment is present. It is recommended
to continue with a MD equilibration until a physically reasonable configuration and distribution of velocities
is achieved. The MC loops relax possible overlaps in the initial configuration, whereas the MD equilibration
drives the system into a physically reasonable dynamic microstate. Note that the equilibration process does not
contribute to the calculation of the thermodynamic properties.
4.5. Intermolecular interactions
4.5.1. Dispersive and repulsive interactions
In ms2, the dispersive and repulsive interactions between molecules are reduced to pairwise interactionsu LJ
ij of
the different molecule sitesiandj, which are modeled by the 12-6-LJ potential [49]
u LJ
ij = 4ε σ 12 σ 6 − . (13)
rij rij
Here, the site-site distance between two interacting LJ sitesiandj is denoted byrij, whileσ andεare the LJ size
and energy parameters, respectively. The LJ potential is widely used and allows for a fast computation of these
basic interactions. It has only two parameters, which facilitates the parameterization of molecular models.
For pure components, the interactions between two different LJ sites are described by the Lorentz-Berthelot
combination rules [50, 51]. For mixtures, the combination rules are extended to the modified Lorentz-Berthelot
rules, which include two additional parameters η and ξ to describe the interactions between LJ sites of unlike
molecules [52]
σij = η σi +σj
2
, (14)
εij = ξ √ εiεj . (15)
13