Parallel implementation of γ‐point pseudopotential plane‐wave DFT with exact exchange

Abstract

Semi-local functionals commonly used in density functional theory (DFT) studies of solids usually fail to reproduce localized states such as trapped holes, polarons, excitons, and solitons. This failure is ascribed to self-interaction which creates a Coulomb barrier to localization. Pragmatic approaches in which the exchange correlation functionals are augmented with small amount of exact exchange (hybrid-DFT, e.g. B3LYP and PBE0) have shown promise in rectifying this type of failure, as well as producing more accurate band gaps and reaction barriers. The evaluation of exact exchange is challenging for large, solid state systems with periodic boundary conditions, especially when plane-wave basis sets are used. We have developed parallel algorithms for implementing exact exchange into pseudopotential plane-wave DFT program and we have implemented them in the NWChem program package. The technique developed can readily be employed in Γ-point plane-wave DFT programs. Furthermore, atomic forces and stresses are straightforward to implement, making it applicable to both confined and extended systems, as well as to Car-Parrinello ab initio molecular dynamic simulations. This method has been applied to several systems for which conventional DFT methods do not work well, including calculations for band gaps in oxides and the electronic structure of a charge trapped state in the Fe(II) containing mica, annite.2

Adaptation of the projector-augmented-wave formalism to the treatment of orbital-dependent exchange-correlation functionals

“…Both Hartree-Fock and KLI methods have been previously implemented in all-electron and in norm-conserving pseudopotential codes by many authors, some of which we list here. 59,60,[73][74][75][76][77][78] However, the present work, as well as several other recent studies 56,[79][80][81][82] show that there continue to be non-trivial numerical challenges in the careful evaluation of the Fock exchange interaction. For the PAW method, the evaluation relies on the use of compensation pair charges (Eq.…”

Simulating Interface Growth and Defect Generation in CZT – Simulation State of the Art and Known Gaps

“…In general, these algorithms use an inverse iteration (or Green's function) strategy to define a subspace over an energy range that is then subsequently diagonalized. Even though a couple of groups [310][311][312][313][314] have implemented plane-wave methods that scale from 1000-10,000's of cpus (and even larger cpus for hybrid DFT) by using 2D parallel data decompositions over the number of electrons and plane-wave expansion alongside non-trivial efforts to mask latency. Ultimately, however, the scalability of these methods is limited by the scalability of the FFT algorithm, which is limited to O (N g 1/3 ) processor (or processor groups),where N g is the number of FFT grid points.…”

“…Experience has shown that many of the failures associated with the erroneous self-interaction term can be corrected by approaches in which the DFT exchange-correlation functionals are augmented with some fraction of exact exchange (hybrid DFT, e.g. B3LYP and PBE0) [313]. These methods have been fairly successful in many problems in molecular chemistry and solid-state physics.…”

Analysis of numerical methods for evaluating the Fock exchange integral in a plane-wave basis

“…5,9 The present model falls into the same category as these systems, since we have assumed non-overlapping orbitals. Even for our case where the overlap is less than 10 −7 , we see that Γ-point sampling can introduce an error due to unphysical interactions between unit cells.…”