Hard core Yukawa potential

Hard core attractive Yukawa potential:

$\Phi \left(r\right)=\left\{{\begin{array}{lll}\infty &;&r<\sigma \\-\left({\frac {\epsilon \sigma }{r}}\right)\exp \left[-\kappa \left({\frac {r}{\sigma }}-1\right)\right]&;&r\geq \sigma \end{array}}\right.$

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

Phase diagram

Main article: Phase diagram of the Yukawa potential