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.

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Electronic structure calculations representing the molecular orbitals (MOs) with contracted planewave basis functions (CPWBFs) have been reported recently. CPWBFs are Fourier‐series representations of atom‐centered basis functions. The mathematical features of CPWBFs permit the construction of matrix–vector products, FC o, involving the application of the Fock matrix, F, to the set of occupied MOs, C o, without the explicit evaluation of F. This approach offers a theoretical speed‐up of M/n over F‐based methods, where M and n are the number of basis functions and occupied MOs, respectively. The present study reports methodological advances that permit FC o‐based optimization of wavefunction formed from CPWBFs. In particular, a technique is reported for optimizing wavefunctions by combining pseudodiagonalization techniques based on an exact representation of FC o, approximate information regarding the virtual orbital energies, and direct inversion of the iterative subspace optimization schemes to guide the wavefunction to a converged solution. This method is found to speed‐up wavefunction optimizations by factors of up to ~6 − 8 over F‐based optimization methods while providing identical results. Further, the computational cost of this technique is relatively insensitive to basis set size, thus providing further benefits in calculations using large CPWBF basis sets. The results of density functional theory calculations show that this method permits the use of hybrid exchange‐correlation (XC) functionals with a small increase in effort over analogous calculations using generalized gradient approximation XC functionals. © 2019 Wiley Periodicals, Inc.