# Modified Lennard-Jones model

$\Phi_{12}(r) = \left\{ \begin{array}{ll} 4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}- \left( \frac{\sigma}{r}\right)^6 \right] + C_1 & r \leq 2.3 \sigma \\ C_2 \left(\frac{\sigma}{r} \right)^{12} + C_3 \left(\frac{\sigma}{r} \right)^{6} + C_4 \left(\frac{r}{\sigma} \right)^{2} + C_5 & 2.3 \sigma < r < 2.5 \sigma\\ 0 & 2.5 \sigma \leq r \end{array} \right.$
where $C_1 = 0.016132 \epsilon$, $C_2 = 3136.6 \epsilon$ $C_3 = -68.069 \epsilon$ $C_4 = 0.083312 \epsilon$ and $C_5 = 0.74689\epsilon$. These parametrs are chosen so that the function $\Phi_{12}(r)$, as well as the first derivative, is continuous both at $r = 2.3\sigma$ and $r = 2.5\sigma$. These parameters have recently been recalculated with greater precision by Asano and Fuchizaki [2], leading to $C_1 = 0.0163169237\epsilon$, $C_2 = 3136.5686 \epsilon$ $C_3 = -68.069 \epsilon$ [3], $C_4 = -0.0833111261 \epsilon$ and $C_5 = 0.746882273 \epsilon$.
The virial coefficients up to the seventh order have been calculated for the range of temperatures $k_BT/\epsilon = 0.3-70$ [4]. See also [5].