Representation of the virtual space in extended systems - a correlation energy convergence study

We present an investigation of the convergence behaviour of the local second-order Moller-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.