For two anisotropic CG particles I and J, the basis functions in the pair-wise expansion of the CG potential can be written in general as a function of the set of variables ξ = {R, α, β, γ, ϕ, θ}, where R is the inter-particle distance, α, β, and γ are Euler angles that describe the rotation of particle I into the frame of particle J, and θ and ϕ are angles between the inter-particle vector and a specific principal axis on each particle. Details of the calculations of the relative positions and orientations of pairs of CG particles and the formulas for the scalar variables are given in section SIV of the SM.