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pair_vashishta.tex
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Fri, Feb 21, 17:18
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rLAMMPS lammps
pair_vashishta.tex
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\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
U & = & \sum_i^N \sum_{j > i}^N U_{ij}^{(2)} (r_{ij}) +
\sum_i^N \sum_{j \neq i}^N \sum_{k > j, k \neq i}^N
U_{ijk}^{(3)} (r_{ij}, r_{ik}, \theta_{ijk})
\\
U_{ij}^{(2)} (r) & = & \frac{H_{ij}}{r^{\eta_{ij}}}
+ \frac{Z_i Z_j}{r}\exp(-r/\lambda_{1,ij})
- \frac{D_{ij}}{r^4}\exp(-r/\lambda_{4,ij})
- \frac{W_{ij}}{r^6}, r < r_{c,{ij}}
\\
U_{ijk}^{(3)}(r_{ij},r_{ik},\theta_{ijk}) & = & B_{ijk}
\frac{\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2}
{1+C_{ijk}\left[ \cos \theta_{ijk} - \cos \theta_{0ijk} \right]^2} \times \\
& & \exp \left( \frac{\gamma_{ij}}{r_{ij} - r_{0,ij}} \right)
\exp \left( \frac{\gamma_{ik}}{r_{ik} - r_{0,ik}} \right), r_{ij} < r_{0,ij}, r_{ik} < r_{0,ik}
\end{eqnarray*}
\end{document}
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