As a proof-of-principle, we have applied the AFM-CG method to coarse grain pure liquid systems of benzene and perylene, with both molecules modeled as uniaxial anisotropic particles with a single non-equivalent principal axis. In both cases, the principal moments of inertia of the CG particles were defined in terms of the average principal moments of inertia of the molecules in the FG simulation used for parametrization. The fluctuations in the principal moments of inertia in the FG simulations were verified to be small compared with their mean values in both cases (SM Figures and, respectively), so approximating the CG principal moments by the corresponding average FG values should accurately satisfy the momentum-space consistency condition described in section II C. While benzene is approximately uniaxial, perylene is more accurately described as biaxial, although the two in-plane axes are relatively similar in length compared with the out-of-plane axis. Thus, we have used a uniaxial CG perylene model here for simplicity as it significantly reduces the number of basis functions needed to represent the anisotropic CG potential. For both molecules, the moments of inertia about the two in-plane principal axes in the CG model were set to be equal to the average of the FG principal moments of inertia about the two inplane axes. Extension of the method to biaxial CG models is possible. Simulation speedups of 40-150 times-due to both the reduction in the computational time per simulation time step and the larger time step that was feasible-were achieved using the CG models compared with the FG models for simulations carried out on eight Intel Core i7 6700K CPUs.