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):

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

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

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle \Phi _{\rm {attractive}}(r)=\left\{{\begin{array}{ll}-\epsilon &{\rm {if}}\;r<2^{1/6}\sigma \\\Phi _{\rm {LJ}}(r)&{\rm {if}}\;r\geq 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)