pair_dipole.tex
8b6f939ef9aelammps-icms

pair_dipole.tex
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			\documentclass[12pt]{article}

			\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}