pair_tersoff.tex
b704a82dafc5efficient_neuronet

pair_tersoff.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{1}{2} \sin \left( \frac{\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 + \beta^n {\zeta_{ij}}^n \right)^{-\frac{1}{2n}} \\
			\zeta_{ij} & = & \sum_{k \neq i,j} f_C(r_{ik}) g(\theta_{ijk})
			\exp \left[ {\lambda_3}^3 (r_{ij} - r_{ik})^3 \right] \\
			g(\theta) & = & 1 + \frac{c^2}{d^2} -
			\frac{c^2}{\left[ d^2 +
			(\cos \theta - \cos \theta_0)^2\right]}
			\end{eqnarray*}

			\end{document}