The parameterisation of the force field of a molecular system is essential for accurately describing and predicting macroscopic thermophysical properties. Here, we discuss three approaches to obtain the molecular parameters (σ, ε, and λr) of the Mie force field from experimental data for quasi-spherical molecules. The first approach is based on a classical strategy that considers fitting only to vapour-liquid equilibria data. The second approach entails a simultaneous fit to equilibrium properties and liquid shear viscosity. Finally, a third approach incorporates solid-fluid equilibrium data. The fitting procedure is facilitated by the use of recently published machine-learned equations of state for the Mie particle, which allows the prediction of thermophysical properties given a set of molecular parameters. The goodness-of-fit is assessed based on the deviations between calculated and experimental data. We also assess the behaviour of the thermal conductivity and speed of sound of the saturated liquid phase to evaluate the transferability of the molecular parameters to properties not used in the parametrisation. Apart from the singular case of monoatomic molecules, no single set
of parameters can simultaneously describe the fluid phase equilibria, transport, and solid transition properties of quasi-spherical molecules. This result highlights the limitations of the Mie potential for modelling the thermophysical properties of small molecules. Therefore, a compromise must be made, either to achieve a good description of a specific set of properties or to attain modest accuracy across all phase space.