Modified Lennard-Jones model

The modified Lennard-Jones model is given by (Eq. 2 ):

$\Phi _{12}(r)=\left\{{\begin{array}{ll}4\epsilon \left[\left({\frac {\sigma }{r}}\right)^{12}-\left({\frac {\sigma }{r}}\right)^{6}\right]+C_{1}&r\leq 2.3\sigma \\C_{2}\left({\frac {\sigma }{r}}\right)^{12}+C_{3}\left({\frac {\sigma }{r}}\right)^{6}+C_{4}\left({\frac {r}{\sigma }}\right)^{2}+C_{5}&2.3\sigma <r<2.5\sigma \\0&2.5\sigma \leq r\end{array}}\right.$

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 , leading to $C_{1}=0.0163169237\epsilon$, $C_{2}=3136.5686\epsilon$ $C_{3}=-68.069\epsilon$ . Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle C_4 = −0.0833111261\epsilon} and $C_{5}=0.746882273\epsilon$.

Virial coefficients

The virial coefficients up to the seventh order have been calculated for the range of temperatures $k_{B}T/\epsilon =0.3-70$ . See also .