Editing Modified Lennard-Jones model

The '''modified Lennard-Jones model''' is given by (Eq. 2 <ref>[http://dx.doi.org/10.1063/1.445633  Jeremy Q. Broughton and George H. Gilmer "Molecular dynamics investigation of the crystal–fluid interface. I. Bulk properties", Journal of Chemical Physics '''79''' pp. 5095-5104 (1983)]</ref>):

:<math>
\Phi_{12}(r) = \left\{ 
\begin{array}{ll}
4 \epsilon \left[ \left(\frac{\sigma}{r} \right)^{12}-  \left( \frac{\sigma}{r}\right)^6 \right]  + C_1 &  r \leq  2.3 \sigma \\
C_2 \left(\frac{\sigma}{r} \right)^{12}   + C_3 \left(\frac{\sigma}{r} \right)^{6}  + C_4  \left(\frac{\sigma}{r} \right)^{2}  + C_5 &  2.3 \sigma < r < 2.5 \sigma\\
0 &  2.5 \sigma \leq r
\end{array} \right.
</math>

where <math>C_1 = 0.016132 \epsilon</math>, 
<math>C_2 = 3136.6 \epsilon</math> 
<math>C_3 = -68.069 \epsilon</math> 
<math>C_4 = 0.083312 \epsilon</math> 
and <math>C_5 = 0.74689\epsilon</math>. THese parametrs are chosen so that the function <math>\Phi_{12}(r)</math>, as well as the first derivative, is continuous both at <math>r = 2.3\sigma</math> and <math>r = 2.5\sigma</math>.
These parameters have recently been recalculated by Asano and Fuchizaki <ref>[http://dx.doi.org/10.1063/1.4764855  Yuta Asano and Kazuhiro Fuchizaki "Phase diagram of the modified Lennard-Jones system", Journal of Chemical Physics '''137''' 174502 (2012)]</ref>, leading to
<math>C_1 = 0.0163169237\epsilon</math>, 
<math>C_2 = 3136.5686  \epsilon</math> 
<math>C_3 = 68.069 \epsilon</math> 
<math>C_4 =  −0.0833111261\epsilon</math> 
and <math>C_5 = 0.746882273 \epsilon</math>.
==References==
<references/>

[[category: models]]