Despite the aforementioned advantages, the use of anisotropic CG models to accurately simulate behavior of condensed-phased systems is limited by a lack of systematic parametrization methods with a rigorous theoretical basis. Some parametrizations of anisotropic CG models have taken a "top-down" approach, in which interactions are tuned to match relevant macroscopic thermodynamic and mechanical properties such as melting temperatures and elastic moduli. For those anisotropic CG models derived from a fine-grained (FG) model such as an all-atom model using a "bottom-up" approach, most have been parametrized by matching the interaction potential between CG particles to the FG potential energy for specific configurations of pairs of molecules or molecular fragments, which neglects finite-temperature and many-body effects that can significantly influence the effective interactions between particles in the condensed phase under thermodynamically relevant conditions. CG interactions have also been fit to the orientation-dependent potential-of-mean-force (PMF) between molecule pairs in condensed-phase FG simulations, which is equivalent to the iterative Boltzmann inversion (IBI) approach, in which CG interactions are iteratively tuned to match structural distribution functions in a FG simulation, in this case applied to pair correlation functions. Although this approach has a basis in statistical mechanics theory, it uses reduced information about the condensed-phase system rather than the full many-body CG PMF, 2 and so is not readily systematically improved to account for higher order correlations.