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\begin{document}

\begin{align*}
E =& E_2 \sum_{i,j}e^{-k_2 r_{ij}} + E_A \sum_{\substack{i,j,k,\ell \\\in \textrm{type A}}} f(r_{ij})f(r_{k\ell}) + E_B \sum_{\substack{i,j,k,\ell \\\in \textrm{type B}}} f(r_{ij})f(r_{k\ell}) + E_C \sum_{\substack{i,j,k,\ell \\\in \textrm{type C}}} f(r_{ij})f(r_{k\ell}) \\
f(r) =& e^{-k_3 r}s(r) \\
s(r) =& \begin{cases}
  1 & r<R_s \\
  \displaystyle\frac{(R_f-r)^2(R_f-3R_s+2r)}{(R_f-R_s)^3} & R_s\leq r\leq R_f \\
  0 & r>R_f\\
\end{cases}
\end{align*}

\end{document}
