## IMD |
## Gay-Berne Potential (option uniax)The Gay-Berne potential models the pair interaction of uniaxial molecules. It depends not only on the scalar distance of their centres of mass but also on their mutual orientation. Due to this complicated dependence the Gay-Berne interaction cannot be tabulated. In IMD it is calculated from its analytical expression. Forces and torques are also evaluated analytically as derivatives of the potential. ## Gay-Berne model
The Gay-Berne potential for uniaxial molecules (UNIAX) was implemented
by Joachim Stelzer. It is a model for the pair interaction of two
axially symmetric ellipsoidal molecules. The original model was
invented by J. G. Gay and B. J. Berne ## Molecular PropertiesIn conventional IMD an atom is completely described by its mass m and the vectors [rx ry rz] and [vx vy vz] which denote its position and orientation, respectively. For uniaxial molecules the data structure is enlarged. Each translational quantity is supplemented by a rotational one. - The molecule possesses both mass m and moment of inertia I.
- Its centre of mass is located at [rx ry rz] and the orientation of its main axis is given by a unit vector [ux, uy, uz], with ux^2 + uy^2+ uz^2 = 1.
- Its velocity is [vx vy vz] and its angular velocity is [wx wy wz].
- The total force exerted on the molecule under consideration is [fx fy fz]. In addition the rotational state of the molecule is changed due to the torque [tx ty tz].
- The shape of the uniaxial molecule is given by the lengths of its principal axes [sx sy sz]. Thereby, sx must be equal to sy. The original version of the Gay-Berne model deals with ellipsoids that possess a shape of sx : sy : sz = 1 : 1 : 3. However, the current implementation in IMD allows for arbitrary values of sx and sz.
- The anisotropy of the interaction energy is given by the well depths of the potential [ex ey ez]. They measure the interaction of a pair of molecules whose main axes are mutually parallel along the z direction. The three values then correspond to the intermolecular separation vector pointing along the x y z direction, respectively. For uniaxial molecules ex must be equal to ey. The original version of the Gay-Berne model deals with an energy anisotropy of ex : ey : ez = 1 : 1 : 1/5. However, the current implementation in IMD allows for arbitrary values of ex and ez.
The moment of inertia, particle shape, and potential depths, which are common to all particles, are specified in the parameter file, and the other properties in the configuration file.
## Gay-Berne Potential
For fixed shape and energy anisotropy of the unaxial ellipsoidal
molecules the Gay-Berne pair potential is depending on four quantities:
the scalar separation r Due to this complicated dependence the Gay-Berne potential cannot be tabulated. Instead it is calculated from its analytical expressions. Likewise, the forces and torques are evaluated analytically as derivatives of the potential. ## Integrators for Uniaxial MoleculesNewton's equations of motion govern the time development of the translational degrees of freedom of the molecules. Uniaxial molecules in addition possess rotational degrees of freedom (main axis, angular velocity). These quantities change according to a simplified version of Euler's gyroid equations. Therefore the integration algorithms implemented in IMD must be supplemented. This has been performed for the ensembles with the option NVE, NVT, and NPT_ISO. Due to the constraint of the main axis [ux uy uz] being a unit vector, the integration of the gyroid equations is more complicated than only a one-to-one mapping of the corresponding way for solving Newton's equations. In particular, the angular velocity has always to be perpendicular to the main axis, because a uniaxial molecule cannot rotate around its main axis. The number of its rotational degree of freedoms is only two. The Nosé-Hoover thermostat has been supplemented by an analogous method that keeps the total rotational energy on average at the value of 2/2 * kT, according to the equipartition theorem. ## ParametersNo potential table is necessary for the Gay-Berne interaction, because the potential, forces and torques are calculated analytically. However, the potential and other parameters must be specified in the parameter file.
## Compiling IMD for UNIAX
When compiling IMD for UNIAX, the option gmake imd_nve_uniax gmake imd_mpi_nvt_uniax ## Generating Initial Configurations
A separate code (in c) is provided in the IMD user directory:
A sample both for a configuration file |