Kohn-Sham density functional theory (KSDFT) is the most powerful tool for performing ab initio electronic structure calculations in quantum chemistry and materials science. However, as the key ingredient in the KSDFT calculations, the exchange and correlation functional to determine the accuracy must be approximated. The widely used LDA and GGA functionals always fail to give accurate electronic structures due to lack of long-range nonlocal Hartree-Fock exchange interaction in the KSDFT calculations. Fortunately, hybrid density functionals, such as B3LYP, PBE0 and HSE, have already proven to improve the accuracy of electronic structure calculations by introducing a fraction of the Hartree-Fock exchange functional. However, hybrid density functional calculations are expensive and challenging even for the systems consisting of hundreds of atoms. Here, we introduce the interpolative separable density fitting (ISDF) decomposition to accelerate large scale hybrid functional calculations. The computational cost of hybrid functional plane-wave calculations is often dominated by the cost of applying the exchange operator to N orbitals, which requires solving N2 Poisson-like equations. We demonstrate that the ISDF decomposition can reduce these N2 equations into Or(N) equations with systematically controlled accuracy, and the validity of the method does not depend on the energy gap. Combined with the recently developed adaptively compressed exchange operator formulation (ACE) [J. Chem. Theory Comput. 13, 1188 (2017)] to reduce the frequency of which the exchange operator needs to be applied, the resulting ACE-ISDF method significantly reduces the computational cost of large scale hybrid functional calculations by nearly two orders of magnitude. We demonstrate that the ACE-ISDF method can obtain accurate energies and forces for insulating and metallic systems, and the converged hybrid functional calculations can be performed for a 1000-atom bulk silicon within 10 minutes using 2000 computational cores. Our method can also scale to 8192 computational cores for a 4096-atom bulk silicon system.

Interpolative separable density fitting decomposition for accelerating large-scale hybrid functional calculations

254th National Meeting (2017)

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