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$$ 
E = \epsilon \left[ \frac{2  \sigma_{LJ}^{12} \left(7 r^5+14 r^3 \sigma_{n}^2+3 r \sigma_{n}^4\right) }{945 \left(r^2-\sigma_{n}^2\right)^7} -\frac{ \sigma_{LJ}^6 \left(2 r \sigma_{n}^3+\sigma_{n}^2 \left(r^2-\sigma_{n}^2\right)\log{ \left[\frac{r-\sigma_{n}}{r+\sigma_{n}}\right]}\right) }{12 \sigma_{n}^5 \left(r^2-\sigma_{n}^2\right)} \right]\qquad \sigma_n < r < r_c
$$


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