Mie potential

From SklogWiki

The Mie potential was proposed by Gustav Mie in 1903. It is given by

$\Phi_{12}(r) = \left( \frac{n}{n-m}\right) \left( \frac{n}{m}\right)^{m/(n-m)} \epsilon \left[ \left(\frac{\sigma}{r} \right)^{n}- \left( \frac{\sigma}{r}\right)^m \right]$

where:

$r := |\mathbf{r}_1 - \mathbf{r}_2|$
$Φ 12 (r)$ is the intermolecular pair potential between two particles at a distance r;
$σ$ is the diameter (length), i.e. the value of $r$ at $Φ(r) = 0$ ;
$ε$ : well depth (energy)