# Fomin potential

The Fomin potential was firstly introduced as [1] (Eq. 2):

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

where ${\displaystyle \Phi _{12}\left(r\right)}$ is the intermolecular pair potential, ${\displaystyle r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|}$ is the distance between site 1 and site 2, ${\displaystyle n=14}$ and ${\displaystyle k_{0}=10}$. ${\displaystyle d}$ is the diameter of the hard core, ${\displaystyle \sigma _{s}}$ is the width of the repulsive shoulder, ${\displaystyle \epsilon }$ 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 [2] :

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

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