Difference between revisions of "Weeks-Chandler-Andersen perturbation theory"

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Line 7: Line 7:
 
\Phi_{\rm repulsive} (r) = \left\{  
 
\Phi_{\rm repulsive} (r) = \left\{  
 
\begin{array}{ll}
 
\begin{array}{ll}
u_{\rm LJ}(r) + \epsilon & {\rm if} \; r < 2^{1/6}\sigma \\
+
\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 \\
u_{\rm LJ}(r) &  {\rm if} \; r \ge 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 15:25, 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):


\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):


\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.

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)