\begin{center}

\large{Additional documention for the Gay-Berne ellipsoidal potential \\

\large{Additional documentation for the Gay-Berne ellipsoidal potential \\

  as implemented in LAMMPS}

\end{center}

\mathbf{A}_1, \mathbf{A}_2, \upsilon ) \cdot \chi_{12} ( \mathbf{A}_1,

\mathbf{A}_2, \mathbf{r}_{12}, \mu ) $$

where $\mathbf{A}_1$ and $\mathbf{A}_2$ are the transformation matrices 

from the simulation box frame to the body frame and $\mathbf{r}_{12}$ 

is the center to center vectorb etween the particles.  

$U_r$ controls the shifted distance dependent

interaction based on the distance of closest approach of the two

particles ($h_{12}$) and the user-specified shift parameter gamma:

where $\mathbf{A}_1$ and $\mathbf{A}_2$ are the transformation

matrices from the simulation box frame to the body frame and

$\mathbf{r}_{12}$ is the center to center vector between the

particles.  $U_r$ controls the shifted distance dependent interaction

based on the distance of closest approach of the two particles

($h_{12}$) and the user-specified shift parameter gamma:

$$ U_r = 4 \epsilon ( \varrho^{12} - \varrho^6) $$

\begin{center}

\large{Additional documention for the RE-squared ellipsoidal potential \\

\large{Additional documentation for the RE-squared ellipsoidal potential \\

  as implemented in LAMMPS}

\end{center}