In general, the CG potential is a sum of intramolecular and intermolecular interactions, including non-bonded electrostatic and van der Waals dispersion interactions, and bondstretching, angle-bending, and dihedral-torsion interactions. While the AFM-CG method can be applied to construct all of these CG interaction types, in this work we focus on anisotropic non-bonded interactions, as the other interactions are readily approximated using existing coarse-graining methods, such as the MS-CG method for isotropic CG particles or the iterative Boltzmann inversion method. In the general case, a hybrid approach using the AFM-CG method for non-bonded interactions and another method for bonded interactions could be used. Several previous studies of isotropic CG models have obtained the CG potential using hybrid approaches employing more than one coarse-graining method and have demonstrated good structural and thermodynamic accuracy. Similarly to the implementation of the MS-CG method, we have used a linear combination of scalar basis functions to approximate the non-bonded CG potential. In general, this potential is a many-body interaction that depends on the positions and orientations of all CG particles in the system. In the implementation presented here, we have assumed that this potential is the sum of pair-wise interactions between CG particles, which significantly simplifies the CG potential into a function only of the relative positions and orientations of pairs of CG particles. Extension of the method beyond two-body interactions is possible. With this approximation, in general each basis function in the CG potential can be written as a function of a set of 6 scalar variables, ξ ≡ (ξ 1 , ξ 2 , . . . , ξ 6 ), that are functions of the relative position R IJ and orientation Ω IJ of a pair of CG particles I and J. For the simplest case in which the pair interaction is the same for all CG particles (generalization to different interaction types is straightforward), the CG potential can be written as a sum over N b scalar basis functions B b per pair of particles as