In this section, we outline the steps for the implementation of the MRF with Gaussian basis set. We first describe a refined scheme for the spherical average of two Gaussian functions that we need for the spherically averaged density ρ(r, u), an intermediate to the N e ([ρ]; r, u) integral, which is the key building block of MRF (Eq. 1). Then we explain our numerically robust scheme for computing the inverse of N e ([ρ]; r, u), which we also need for the MRF evaluation (Eq. 10). Finally, we introduce the algorithm for the reverse MRF machinery (Sec. 2.3), which for example, enables us to 'translate' the exact exchange energy density to MRF's fluctuation function -a starting point for building MRF's correlation on the top of exact exchange.