Direct inversion of the iterative subspace (DIIS) convergence accelerator for crystalline solids employing Gaussian basis sets

When dealing with crystalline solids, convergence of iterative procedures such as self-consistent field (SCF) or coupled–perturbed equations is often more difficult than in the case of molecular systems, specially when a local basis set of atom-centered Gaussians is adopted. Reasons are usually to be found in the close packing of atoms and peculiar chemical characters, such as metallic bond. In this work, a periodic implementation of the direct inversion of the iterative subspace (DIIS) method for crystalline solids is presented for SCF and electric field response up to second order. The error vectors are computed in reciprocal space and implemented for the energy, polarizability and up to second hyperpolarizability. The performance of different DIIS flavors is benchmarked on a representative set of 42 systems including metallic, ionic, molecular and covalent crystals, bulk crystals, surfaces and nanotubes, adopting all-electron basis sets as well as pseudopotentials. Interestingly, it is seen that the error vectors evaluated in the central (gamma) point of the Brillouin zone are sufficient in all cases for an optimal DIIS performance.