Direct inversion of the iterative subspace with contracted planewave basis functions

Pseudodiagonalization-based wavefunction optimization with contracted planewave basis functions

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.