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\begin{document}

\begin{eqnarray*}
\left\{\begin{array}{l}
\eta_{ij}=1-\delta_{ij},\xi_{IJ}=0 \\
U_{IJ}\left(r\right)=\phi_{IJ}\left(r\right) \\
V_{IJ}\left(r\right)=1 \\
F_{II}\left(X\right)=-2F_I\left(X\right) \\
P_{IJ}\left(\Delta r\right)=1 \\ 
W_{IJ}\left(r\right)=f_{K}\left(r\right) \\
G_{JIK}\left(\theta\right)=1
\end{array}\right.
\end{eqnarray*} 

\end{document}