Low-Rank Approximations Accelerated Plane-Wave Hybrid Functional Calculations with k-Point Sampling

The low-rank approximations of the adaptively compressed exchange (ACE) operator and interpolative separable density fitting (ISDF) algorithms significantly reduce the computational cost and memory usage of hybrid functional calculations in real space, but the lack of k-point sampling hinders their implementation in reciprocal space for periodic systems with the plane-wave basis set. Here, we combine the ACE operator and ISDF decomposition into a new ACE-ISDF algorithm for periodic systems in reciprocal space with k-point sampling. On the basis of the ACE-ISDF algorithm with the improved reciprocal space ACE operator and k-point Fourier convolution, the time complexity of the hybrid functional calculation is reduced from $$ to $$ (N_e and N_k are the number of electrons and k-points, respectively) with a much smaller prefactor and much lower memory consumption compared to the standard method for periodic systems with a plane-wave basis set.