Pseudo hard sphere potential
The pseudo hard sphere potential (PHS) [1] 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):
- 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 \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 \ge \frac{50}{49} \sigma \end{array} \right. }
Molecular dynamics simulations of this idealised model, when performed at a reduced temperature of 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 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.