Efficient Explicitly Correlated Many-Electron Perturbation Theory for Solids: Application to the Schottky Defect in MgO

We introduce a novel and efficient explicitly correlated implementation of second-order perturbation theory for solids. The required three-electron integrals are computed directly using a plane wave basis set. We parametrize the employed correlation factors using results previously obtained for a finite uniform electron gas simulation cell. We demonstrate for a range of solids that basis set converged correlation energies, equilibrium volumes, and bulk moduli can be obtained efficiently in this theory using a few ten orbitals per atom. To stretch the capabilities of this novel method we compute the Schottky defect formation energy in MgO, studying systems with 54 atoms in the supercell. We verify the accuracy of the calculated formation energies using the more accurate coupled cluster singles and doubles theory. Furthermore, we discuss other potential applications for the derived and implemented expressions such as an occupied orbital only correlation energy functional.