convert pair styles dpd to exp6

\documentclass[12pt]{article}

\usepackage{amsmath}

\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}

\documentstyle[12pt]{article}

\begin{document}

$$

E_{Pauli(ECP_s)}=p_1\exp\left(-\frac{p_2r^2}{p_3+s^2} \right)

$$

\end{document}  

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