In this work, we present an efficient way to accelerate HFX calculations with numerical atomic basis sets. The high cost associated with the evaluation of Hartree-Fock exchange (HFX) makes hybrid functionals computationally challenging for large systems. As proof of principle, we apply the algorithm to large and complex iron garnet materials (YIG, GdIG, TmIG) that are used in several spintronic applications. By porting this algorithm to GPU accelerators, we can leverage future exascale supercomputers which we demonstrate by reporting scaling results for up to 64 GPUs and up to 12,000 CPU cores for a single k-point. This implementation enables the use of hybrid functionals for systems with several hundred atoms.
#Ranking the screening efficacy of atomic orbitals code#
Here, we present a new highly-scalable implementation of the nonlocal Hartree-Fock-type potential into FLEUR-an all-electron electronic structure code that implements the full-potential linearized augmented plane-wave (FLAPW) method.
While hybrid functionals allow many properties such as lattice constants, bond lengths, magnetic moments and band gaps, to be calculated with improved accuracy, they require the calculation of a nonlocal potential, resulting in high computational costs, that scale rapidly with the system size. These can be provided by density functional theory (DFT) using not only simple local approximations to the unknown exchange and correlation functional, but also more complex approaches such as hybrid functionals, which include some part of Hartree–Fock exact exchange. Virtual materials design requires not only the simulation of a huge number of systems, but also of systems with ever larger sizes and through increasingly accurate models of the electronic structure. Our work not only enables DFT+DMFT calculations using popular and rapidly developing NAO-based DFT code packages, but also facilitates the combination of more advanced beyond-DFT methodologies available in this codes with the DMFT machinery. We present a formulation and implementation of the DFT+\textit transition metal compounds, lanthanides, and actinides. The performance and scalability of our implementation with respect to the system size and the number of CPU cores are demonstrated for selected benchmark systems up to 4096 atoms. In this work, we describe the key algorithms and implementation details for the HFX build as implemented in the ABACUS code package. All these factors add together to enable highly efficient hybrid functional calculations for large-scale periodic systems. Our implementation is massively parallel, thanks to a MPI/OpenMP hybrid parallelization strategy for distributing the computational load and memory storage.
By exploiting the locality of basis functions and efficient prescreening of the intermediate three- and two-index tensors, one can achieve a linear scaling of the computational cost for building the HFX matrix with respect to the system size. Our implementation is based on the localized resolution of the identity approximation by which two-electron Coulomb repulsion integrals can be obtained by only computing two-center quantities-a feature that is highly beneficial to NAOs.
We present an efficient, linear-scaling implementation for building the (screened) Hartree-Fock exchange (HFX) matrix for periodic systems within the framework of numerical atomic orbital (NAO) basis functions.
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