Hard core Yukawa potential

Hard core attractive Yukawa potential:

$\mathrm{\Phi }(r)=\{\begin{array}{ccc}\mathrm{\infty }& ;& r<\sigma \\ -(\frac{ϵ\sigma }{r})\exp [-\kappa (\frac{r}{\sigma }-1)]& ;& r\ge \sigma \end{array}$

where $\mathrm{\Phi }(r)$ is the intermolecular pair potential, $r$ is the distance, $\sigma$ is the hard diameter, $ϵ$ is the energy well depth ($ϵ>0$), and $\kappa$ is a parameter that controls the interaction range ($\kappa >0$).

Phase diagram

Main article: Phase diagram of the Yukawa potential