Continuous shouldered well model

The continuous shouldered well model is given by (^[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 Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle r := |\mathbf{r}_1 - \mathbf{r}_2|} .