\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}^m (r_{ij} - r_{ik})^m \right] \\
  g(\theta) & = & \gamma_{ijk} \left( 1 + \frac{c^2}{d^2} - 
                  \frac{c^2}{\left[ d^2 + 
		  (\cos \theta - \cos \theta_0)^2\right]} \right)
\end{eqnarray*}

\end{document}