We present a corresponding states correlation based on the description of fluid phase properties by means of an Mie intermolecular potential applied to tangentially bonded spheres. The macroscopic properties of this model fluid are very accurately represented by a recently proposed version of the Statistical Associating Fluid Theory (the SAFT-γ version). The Mie potential can be expressed in a conformal manner in terms of three parameters that relate to a length scale, σ, an energy scale, ε, and the range or functional form of the potential, λ, while the nonsphericity or elongation of a molecule can be appropriately described by the chain length, m. For a given chain length, correlations are given to scale the SAFT equation of state in terms of three experimental parameters: the acentric factor, the critical temperature, and the saturated liquid density at a reduced temperature of 0.7. The molecular nature of the equation of state is exploited to make a direct link between the macroscopic thermodynamic parameters used to characterize the equation of state and the parameters of the underlying Mie potential. This direct link between macroscopic properties and molecular parameters is the basis to propose a top-down method to parametrize force fields that can be used in the coarse grained molecular modeling (Monte Carlo or molecular dynamics) of fluids. The resulting correlation is of quantitative accuracy and examples of the prediction of simulations of vapor-liquid equilibria and interfacial tensions are given. In essence, we present a recipe that allows one to obtain intermolecular potentials for use in the molecular simulation of simple and chain fluids from macroscopic experimentally determined constants, namely the acentric factor, the critical temperature, and a value of the liquid density at a reduced temperature of 0.7.