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Local approximations facilitate the application of post-Hartree–Fock methods in the condensed phase, but simultaneously introduce errors leading to discontinuous potential-energy surfaces. In this work, we explore how these discontinuities arise in periodic systems, their implications, and possible ways of controlling them. In addition, we present a fully periodic Divide-Expand-Consolidate second-order Møller–Plesset approach using an attenuated resolution-of-the-identity approximation for the electron repulsion integrals and a convenient class to handle translation-symmetric tensors in block-Toeplitz format. [ABSTRACT FROM AUTHOR]

We present an investigation of the convergence behaviour of the local second-order Møller-Plesset perturbation theory (MP2) correlation energy toward the canonical result for three insulating crystals with either projected atomic orbitals (PAOs) or various orthonormal representations of the virtual orbital space. Echoing recent results for finite molecular systems, we find that significantly fewer PAOs than localised orthonormal virtual orbitals are required to reproduce the canonical correlation energy. We find no clear-cut correlation between conventional measures of orbital locality and the ability of the representation to span the excitation space of local domains. We show that the PAOs of the reference unit cell span parts of the excitation space that can only be reached with distant local orthonormal virtual orbitals. [ABSTRACT FROM AUTHOR]