The form of these basis functions plays an important role in defining the shape of the CG potential and the accuracy of the method. Here we have assumed that each multivariate basis function is a product of a cubic spline function of the inter-particle distance R, which ensures smoothness and continuity of the forces and torques, and cosine functions of each the other orientational variables in the case where the CG non-bonded potentials are even periodic functions of angular variables. Hence, we have represented the linear combination of basis functions in Eq. ( ) as