Direct inversion of the iterative subspace with contracted planewave basis functions

Ways to reduce the computational cost of periodic electronic structure calculations by using basis functions corresponding to linear combinations of planewaves have been examined recently. These contracted planewave (CPW) basis functions correspond to Fourier series representations of atom-centered basis functions, and thus provide access to some beneficial properties of planewave (PW) and localized basis functions. This study reports the development and assessment of a direct inversion of the iterative subspace (DIIS) method that employs unique properties of CPW basis functions to efficiently converge electronic wavefunctions. This method relies on access to a PW-based representation of the electronic structure to provide a means of efficiently evaluating matrix-vector products involving the application of the Fock matrix to the occupied molecular orbitals. These matrix-vector products are transformed into a form permitting the use of direct diagonalization techniques and DIIS methods typically employed with atom-centered basis sets. The abilities of this method are assessed through periodic Hartree-Fock calculations of a range of molecules and solid-state systems. The results show that the method reported in this study is approximately five times faster than CPW-based calculations in which the entire Fock matrix is calculated. This method is also found to be weakly dependent upon the size of the basis set, thus permitting the use of larger CPW basis sets to increase variational flexibility with a minor impact on computational performance. © 2018 Wiley Periodicals, Inc.