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\begin{eqnarray*}
E_{LJ} & = & 4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} - 
                       \left(\frac{\sigma}{r}\right)^6 \right] + S_{LJ}(r)
                       \qquad r < r_c \\
E_C & = & \frac{C q_i q_j}{\epsilon  r} + S_C(r) \qquad r < r_c \\
S(r) & = & C \qquad r < r_1 \\
S(r) & = & \frac{A}{3} (r - r_1)^3 + \frac{B}{4} (r - r_1)^4 + C \qquad  r_1 < r < r_c \\
A & = & (-3 E'(r_c) + (r_c - r_1) E''(r_c))/(r_c - r_1)^2 \\
B & = & (2 E'(r_c) - (r_c - r_1) E''(r_c))/(r_c - r_1)^3 \\
C & = & -E(r_c) + \frac{1}{2} (r_c - r_1) E'(r_c) - \frac{1}{12} (r_c - r_1)^2 E''(r_c)) \\
\end{eqnarray*}                           

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