Modified Lennard-Jones model

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

${\mathrm{\Phi }}_{12}(r)=\{\begin{array}{cc}4ϵ[{(\frac{\sigma }{r})}^{12}-{(\frac{\sigma }{r})}^6]+C_1& r\le 2.3\sigma \\ C_2{(\frac{\sigma }{r})}^{12}+C_3{(\frac{\sigma }{r})}^6+C_4{(\frac{r}{\sigma })}^2+C_5& 2.3\sigma <r<2.5\sigma \\ 0& 2.5\sigma \le r\end{array}$

where $C_1=0.016132ϵ$, $C_2=3136.6ϵ$ $C_3=-68.069ϵ$ $C_4=0.083312ϵ$ and $C_5=0.74689ϵ$. These parametrs are chosen so that the function ${\mathrm{\Phi }}_{12}(r)$, 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 $C_1=0.0163169237ϵ$, $C_2=3136.5686ϵ$ $C_3=-68.069ϵ$ . Failed to parse (syntax error): {\displaystyle C_4 = −0.0833111261\epsilon} and $C_5=0.746882273ϵ$.

Virial coefficients

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