where σ ij determines the distance at which the potential becomes repulsive, and the depth of the minimum. Each atom type (element) are assigned their own σ and parameters, and are combined via simple geometric combination rules, σ ij = (σ i + σ j )/2 and ij = √ i j , also called the Lorentz-Berthelot combination rules . By employing the LJ potential, we prioritize computational conveniences such as differentiability over a completely well-defined hard-sphere excluded volume, meaning that pressure and density will affect the resulting excluded volume.