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
