Fomin potential

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

$\Phi _{12}\left(r\right)=\left({\frac {d}{r}}\right)^{n}+{\frac {\epsilon }{2}}(1-\tanh(k_{0}(r-\sigma _{s})))$

where $\Phi _{12}\left(r\right)$ 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, $\epsilon$ 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  :

$\Phi _{12}\left(r\right)=\left({\frac {d}{r}}\right)^{n}+\lambda _{0}+\sum _{i=1}^{i=i_{\mathrm {max} }}\lambda _{i}\tanh(k_{i}(r-\sigma _{i}))$

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