Fomin potential

The Fomin potential was firstly introduced as (Eq. 2):

${\mathrm{\Phi }}_{12}(r)={(\frac{d}{r})}^n+\frac{ϵ}{2}(1-\tanh (k_0(r-{\sigma }_s)))$

where ${\mathrm{\Phi }}_{12}(r)$ is the intermolecular pair potential, $r:=|{\mathbf{r}}_1-{\mathbf{r}}_2|$ is the distance between site 1 and site 2, $n=14$ and $k_0=10$. $d$ is the diameter of the hard core, ${\sigma }_s$ is the width of the repulsive shoulder, $ϵ$ is the height of the shoulder. As such, this model can be viewed as a softened square shoulder model.

Later it was generalized to the form  :

${\mathrm{\Phi }}_{12}(r)={(\frac{d}{r})}^n+{\lambda }_0+\sum _{i=1}^{i=i_{\mathrm{m}\mathrm{a}\mathrm{x}}}{\lambda }_i\tanh (k_i(r-{\sigma }_i))$

By varying coefficients ${\lambda }_i$ one can add repulsive shoulders or attractive wells to the potential.