Weeks-Chandler-Andersen perturbation theory

The Weeks-Chandler-Anderson perturbation theory is based on the following decomposition of the intermolecular pair potential (in particular, the Lennard-Jones potential ):

The reference system pair potential is given by (Eq, 4 Ref. 1):

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 repulsive} (r) = \left\{ \begin{array}{ll} u_{\rm LJ}(r) + \epsilon & {\rm if} \; r < 2^{1/6}\sigma \\ 0 & {\rm if} \; r \ge 2^{1/6}\sigma \end{array} \right. }

and the perturbation potential is given by (Eq, 5 Ref. 1):

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 attractive} (r) = \left\{ \begin{array}{ll} -\epsilon & {\rm if} \; r < 2^{1/6}\sigma \\ u_{\rm LJ}(r) & {\rm if} \; r \ge 2^{1/6}\sigma \end{array} \right. }

References

1. John D. Weeks, David Chandler and Hans C. Andersen "Role of Repulsive Forces in Determining the Equilibrium Structure of Simple Liquids", Journal of Chemical Physics 54 pp. 5237-5247 (1971)