Exp-6 potential: Difference between revisions

Latest revision as of 11:04, 14 May 2015

The exp-6 potential (or Exp-Six potential) is a modified form of the Buckingham potential and is given by (Eq. 1 in ^[1]):

\Phi _{12}(r)={\frac {\epsilon }{1-6/\alpha }}\left[\left({\frac {6}{\alpha }}\right)\exp \left[\alpha \left(1-{\frac {r}{r_{min}}}\right)\right]-\left({\frac {r_{min}}{r}}\right)^{6}\right]

where

$r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$
$\Phi _{12}(r)$ is the intermolecular pair potential between two particles or sites
$r_{min}$ is the value of $r$ at which $\Phi _{12}(r)$ is a minimum.
$\epsilon$ is the well depth (energy)
$\alpha$ is the "steepness" of the repulsive energy

An approximate method to locate the melting point is given in ^[2]. See also ^[3].

Related reading

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-The '''exp-6 potential''' is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):
+{{lowercase title}}
+The '''exp-6 potential''' (or '''Exp-Six''' potential) is a modified form of the [[Buckingham potential]] and is given by (Eq. 1 in <ref>[http://dx.doi.org/10.1063/1.1740026 Edward A. Mason "Transport Properties of Gases Obeying a Modified Buckingham (Exp‐Six) Potential", Journal of Chemical Physics '''22''' pp. 169-186 (1954)]</ref>):
 :<math> \Phi_{12}(r) =  \frac{\epsilon}{1-6/\alpha} \left[   \left( \frac{6}{\alpha} \right)
-\exp \left[ \alpha \left( 1-\frac{r}{\sigma} \right) \right]   - \left( \frac{\sigma}{r}\right)^6 \right] </math>
+\exp \left[ \alpha \left( 1-\frac{r}{r_{min}} \right) \right]   - \left( \frac{r_{min}}{r}\right)^6 \right] </math>
 where
 * <math>r := |\mathbf{r}_1 - \mathbf{r}_2|</math>
 * <math> \Phi_{12}(r) </math> is the [[intermolecular pair potential]] between two particles or ''sites''
-* <math> \sigma </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)=0</math>
+* <math> r_{min} </math> is the value of <math>r</math> at which <math> \Phi_{12}(r)</math> is a minimum.
 * <math> \epsilon </math> is the well depth (energy)
 * <math>\alpha</math> is the "steepness" of the repulsive energy