DLPNO-MP2 for periodic systems. II. Megacell embedding

We present a domain-based local pair natural orbital Møller-Plesset second-order perturbation theory (DLPNO-MP2) for periodic systems, working within a linear combination of atomic orbitals formalism in the Turbomole program package. This approach, Megacell-DLPNO-MP2, embeds a supercell correlation treatment within a megacell and does not involve periodic image summation for the Coulomb integrals. Working in a basis of well-localized Wannier functions, periodicity is instead imposed through rigorous translational symmetry of Hamiltonian integrals and wavefunction parameters. The accuracy of the method is validated through comparison with a complementary periodic DLPNO-MP2 method that employs Born-von Kármán boundary conditions, described in Paper I of this series [Nejad et al., J. Chem. Phys. 163 (2025)]. The PNO approximations are shown to be equivalent in the two approaches and entirely consistent with molecular DLPNO-MP2 calculations. The Megacell-DLPNO-MP2 method displays sub-linear scaling with respect to supercell size at the asymptotic limit, and example calculations are presented with up to 15 000 basis functions in the correlation treatment.