Dual-Grid and Mixed-Precision Methods for Accelerating Plane-Wave Hybrid Functional Electronic Structure Calculations

Hybrid functionals that incorporate exact Hartree-Fock exchange (HFX) into density functional theory (DFT) are crucial for accurately predicting the electronic structures of extended systems in condensed-matter physics and materials science. Although the exact exchange contributes only a small fraction of the total energy, HFX calculations in hybrid functionals demand significant computational resources. Here, we introduce dual-grid and mixed-precision techniques, based on two low-rank approximations, adaptively compressed exchange (ACE) and interpolative separable density fitting (ISDF) methods, to significantly improve the computational efficiency of plane-wave hybrid functional calculations in the software package PWDFT (plane wave density functional theory). The dual-grid method introduces a smaller cutoff energy, thereby reducing the number of Fourier and real-space grids involved in the HFX calculations. The mixed-precision method reduces the computational cost by shifting from double precision to single precision during the HFX construction while maintaining double precision for other DFT processes. Numerical results demonstrate that both the dual-grid and mixed-precision techniques can accelerate plane-wave hybrid functional calculations several times, with an acceptable trade-off in accuracy compared to the original low-rank approximations. Furthermore, by utilizing a hybrid MPI and OpenMP parallel implementation, we successfully perform large-scale plane-wave hybrid functional calculations with up to 8,000 silicon atoms using 16,000 CPU cores.