Pseudo hard sphere potential

The pseudo hard sphere potential (PHS) is a piecewise continuous variant of the Mie potential, which is "cut-and-shifted" according to the Weeks-Chandler-Andersen recipe. The potential is given by (Eq. 9):

$\Phi _{\rm {50,49}}(r)=\left\{{\begin{array}{ll}50\left({\frac {50}{49}}\right)^{49}\epsilon \left[\left({\frac {\sigma }{r}}\right)^{50}-\left({\frac {\sigma }{r}}\right)^{49}\right]+\epsilon &{\rm {if}}\;r<{\frac {50}{49}}\sigma \\0&{\rm {if}}\;r\geq {\frac {50}{49}}\sigma \end{array}}\right.$

Molecular dynamics simulations of this idealised model, when performed at a reduced temperature of $T^{*}=1.5$ reproduces results for the hard sphere model (for example, the Carnahan-Starling equation of state), which is generally only amenable to Monte Carlo simulations, or advanced techniques such as Event-driven molecular dynamics.