\documentclass[12pt]{article}

\begin{document}

\begin{eqnarray*}
\left\{\begin{array}{l}
\eta_{ij}=\delta_{ij},\xi_{IJ}=1 \\
U_{IJ}\left(r\right)=\left\{\begin{array}{lr}
A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right), & r\leq r_{s,1,IJ} \\
A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right)\cdot f_{c,1,IJ}\left(r\right), & r_{s,1,IJ}<r<r_{c,1,IJ} \\
0, & r\ge r_{c,1,IJ}
\end{array}\right. \\
V_{IJ}\left(r\right)=\left\{\begin{array}{lr}
B_{IJ} \cdot exp\left(-\lambda_{2,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right), & r\le r_{s,1,IJ} \\
B_{IJ} \cdot exp\left(-\lambda_{2,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right)+A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot & \\ ~~~~~~ f_{c,IJ}\left(r\right)\cdot \left[1-f_{c,1,IJ}\left(r\right)\right], & r_{s,1,IJ}<r<r_{c,1,IJ} \\
B_{IJ} \cdot exp\left(-\lambda_{2,IJ}\cdot r\right)\cdot f_{c,IJ}\left(r\right)+A_{IJ}\cdot exp\left(-\lambda_{1,IJ}\cdot r\right)\cdot & \\ ~~~~~~ f_{c,IJ}\left(r\right) & r \ge r_{c,1,IJ}
\end{array}\right. \\
F_{IJ}\left(X\right)=\left[1+\left(\beta_{IJ}\cdot X\right)^{n_{IJ}}\right]^{-\frac{1}{2n_{IJ}}} \\
P_{IJ}\left(\Delta r\right)=exp\left(\lambda_{3,IK}\cdot \Delta r^3\right) \\ 
W_{IJ}\left(r\right)=f_{c,IK}\left(r\right) \\
G_{JIK}\left(\theta\right)=1+\frac{c_{IK}^2}{d_{IK}^2}-\frac{c_{IK}^2}{d_{IK}^2+\left(h_{IK}+cos\theta\right)^2}
\end{array}\right.
\end{eqnarray*} 

\end{document}