Continuous shouldered well model

The continuous shouldered well model is given by (Ref. 1 Eq. 1):

$\Phi _{12}(r)={\frac {U_{R}}{1+\exp[\Delta (r-R_{R})/a]}}-U_{A}\exp \left[-{\frac {(r-R_{A})^{2}}{2\delta _{A}^{2}}}\right]+\left({\frac {a}{r}}\right)^{24}$

where $\Phi _{12}$ is the intermolecular pair potential, $U_{R}$ is the energy of the repulsive shoulder, $U_{A}$ is the energy of the attractive well, $a$ is the diameter of the particles, and $r:=|\mathbf {r} _{1}-\mathbf {r} _{2}|$.

References

1. Giancarlo Franzese "Differences between discontinuous and continuous soft-core attractive potentials: The appearance of density anomaly", Journal of Molecular Liquids 136 pp. 267-273 (2007)
2. Alan Barros de Oliveira, Giancarlo Franzese, Paulo A. Netz, and Marcia C. Barbosa "Waterlike hierarchy of anomalies in a continuous spherical shouldered potential", Journal ofChemical Physics 128 064901 (2008)