forked from lijiext/lammps
39 lines
1.5 KiB
TeX
39 lines
1.5 KiB
TeX
\documentclass[12pt]{article}
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\begin{document}
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\begin{eqnarray*}
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E_{LJ} & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
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\left(\frac{\sigma}{r}\right)^6 \right] \\
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E_{qq} & = & \frac{q_i q_j}{r} \\
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E_{qp} & = & \frac{q}{r^3} (p \bullet \vec{r}) \\
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E_{pp} & = & \frac{1}{r^3} (\vec{p_i} \bullet \vec{p_j}) -
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\frac{3}{r^5} (\vec{p_i} \bullet \vec{r}) (\vec{p_j} \bullet \vec{r})
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\end{eqnarray*}
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\begin{eqnarray*}
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F_{qq} & = & \frac{q_i q_j}{r^3} \vec{r} \\
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F_{qp} & = & -\frac{q}{r^3} \vec{p} + \frac{3q}{r^5}
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(\vec{p} \bullet \vec{r}) \vec{r} \\
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F_{pp} & = & \frac{3}{r^5} (\vec{p_i} \bullet \vec{p_j}) \vec{r} -
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\frac{15}{r^7} (\vec{p_i} \bullet \vec{r})
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(\vec{p_j} \bullet \vec{r}) \vec{r} +
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\frac{3}{r^5} \left[ (\vec{p_j} \bullet \vec{r}) \vec{p_i} +
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(\vec{p_i} \bullet \vec{r}) \vec{p_j} \right]
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\end{eqnarray*}
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\begin{eqnarray*}
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T_{pq} = T_{ij} & = & \frac{q_j}{r^3} (\vec{p_i} \times \vec{r}) \\
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T_{qp} = T_{ji} & = & - \frac{q_i}{r^3} (\vec{p_j} \times \vec{r}) \\
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T_{pp} = T_{ij} & = & -\frac{1}{r^3} (\vec{p_i} \times \vec{p_j}) +
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\frac{3}{r^5} (\vec{p_j} \bullet \vec{r})
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(\vec{p_i} \times \vec{r}) \\
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T_{pp} = T_{ji} & = & -\frac{1}{r^3} (\vec{p_j} \times \vec{p_i}) +
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\frac{3}{r^5} (\vec{p_i} \bullet \vec{r})
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(\vec{p_j} \times \vec{r}) \\
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\end{eqnarray*}
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\end{document}
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