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\begin{document}

\begin{eqnarray*}
E_{LJ} & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
                        \left(\frac{\sigma}{r}\right)^6 \right] \\
E_{qq} & = & \frac{q_i q_j}{r} \\
E_{qp} & = & \frac{q}{r^3} (p \bullet \vec{r}) \\
E_{pp} & = & \frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) - 
             \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r}) 
\end{eqnarray*}                           

\begin{eqnarray*}
F_{qq} & = & \frac{q_i q_j}{r^3} \vec{r} \\
F_{qp} & = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5} 
             (\vec{p} \bullet \vec{r}) \vec{r} \\
F_{pp} & = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} -
             \frac{15}{r^7} (\vec{p_i} \bullet \vec{r}) 
	     (\vec{p_j} \bullet \vec{r}) \vec{r} + 
             \frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} + 
             (\vec{p_i} \bullet \vec{r}) \vec{p_j} \right]
\end{eqnarray*}                           

\begin{eqnarray*}
T_{pq} = T_{ij} & = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\
T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\
T_{pp} = T_{ij} & = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) + 
                      \frac{3}{r^5} (\vec{p_j} \bullet \vec{r})
		      (\vec{p_i} \times \vec{r}) \\
T_{pp} = T_{ji} & = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) + 
                      \frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) 
		      (\vec{p_j} \times \vec{r}) \\
\end{eqnarray*}                           

\end{document}


