pair_tersoff_mod.tex
3759b7e2ddc5efficient_neuronet

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

			\begin{document}

			\begin{eqnarray*}
			E & = & \frac{1}{2} \sum_i \sum_{j \neq i} V_{ij} \\
			V_{ij} & = & f_C(r_{ij}) \left[ f_R(r_{ij}) + b_{ij} f_A(r_{ij}) \right] \\
			f_C(r) & = & \left\{ \begin{array} {r@{\quad:\quad}l}
			1 & r < R - D \\
			\frac{1}{2} - \frac{9}{16} \sin \left( \frac{\pi}{2} \frac{r-R}{D} \right) - \frac{1}{16} \sin \left( \frac{3\pi}{2} \frac{r-R}{D} \right) &
			R-D < r < R + D \\
			0 & r > R + D
			\end{array} \right. \\
			f_R(r) & = & A \exp (-\lambda_1 r) \\
			f_A(r) & = & -B \exp (-\lambda_2 r) \\
			b_{ij} & = & \left( 1 + {\zeta_{ij}}^\eta \right)^{-\frac{1}{2n}} \\
			\zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk})
			\exp \left[ \alpha (r_{ij} - r_{ik})^\beta \right] \\
			g(\theta) & = & c_1 + g_o(\theta) g_a(\theta) \\
			g_o(\theta) & = & \frac{c_2 (h - \cos \theta)^2}{c_3 + (h - \cos \theta)^2} \\
			g_a(\theta) & = & 1 + c_4 \exp \left[ -c_5 (h - \cos \theta)^2 \right] \\
			\end{eqnarray*}

			\end{document}