Fomin potential

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

\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.