Weeks-Chandler-Andersen perturbation theory: Difference between revisions
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\Phi_{\rm repulsive} (r) = \left\{ | \Phi_{\rm repulsive} (r) = \left\{ | ||
\begin{array}{ll} | \begin{array}{ll} | ||
\Phi_{\rm LJ}(r) + \epsilon & {\rm if} \; r < 2^{1/6}\sigma \\ | |||
0 & {\rm if} \; r \ge 2^{1/6}\sigma | 0 & {\rm if} \; r \ge 2^{1/6}\sigma | ||
\end{array} \right. | \end{array} \right. | ||
| Line 18: | Line 18: | ||
\begin{array}{ll} | \begin{array}{ll} | ||
-\epsilon & {\rm if} \; r < 2^{1/6}\sigma \\ | -\epsilon & {\rm if} \; r < 2^{1/6}\sigma \\ | ||
\Phi_{\rm LJ}(r) & {\rm if} \; r \ge 2^{1/6}\sigma | |||
\end{array} \right. | \end{array} \right. | ||
</math> | </math> | ||
Revision as of 14:25, 21 June 2007
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} \Phi_{\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 \\ \Phi_{\rm LJ}(r) & {\rm if} \; r \ge 2^{1/6}\sigma \end{array} \right. }