with respect to the contribution of an additional virtual orbital n (≤ N vir ). In theory, the effective Hilbert space defined by the numerical basis has the size N G = N occ + N vir and the virtual space is the algebraic consequence of the basis set being larger than the number of electrons in the system. As an illustration, the MP2 calculation with the largest basis set considered in this work has N G = 408 126 and N occ = 37, which makes the entire Fock matrix diagonalization and the direct evaluation of Eq.2 simply intractable (N vir = 408 089, ∼ 10 13 summands, ∼ 6 • 10 12 ρ ia (G) points to be stored with double precision in 45 TB of RAM). For comparison, the same calculation with the GTO aug-cc-pV5Z basis set requires only 2945 basis functions. Therefore, the enormous size of the basis set coupled with the steep scaling of the methods constitute the main challenges when carrying out correlated calculations with PWs. Fortunately, as it was established by numerical and analytical considerations, the PW correlation energy can be extrapolated to the CBS limit with respect to the virtual orbitals. Relying on the model of the homogeneous electron gas (HEG) in a finite cell, Shepherd et al. showed that the MP2 correlation energy in the large basis set limit (E