Tensor-based approach to accelerate exact exchange calculations in DFT

We propose a tensor structured approach based on systematically convergent Tucker-tensor decomposition to accelerate the evaluation of exact exchange functional in generalized Kohn-Sham (KS) density functional theory. In particular, the action of the Fock operator on the KS orbitals, which involves a convolution integral that is extended in real space, is reformulated as a tensor contraction involving quantities that are computed using convolution integrals in 1D. By exploiting various HPC strategies and optimal communication patterns, we have developed an efficient and scalable implementation on multi-core architectures. This approach, along with the ACE formulation, has been incorporated into DFT-FE, a finite-element-based DFT code. Benchmark studies involving Pt clusters show systematic convergence with an excellent agreement in the ground-state energies when compared to current state-of-the-art plane-wave DFT implementations. Further, we obtain a 3.5-7.5x speed up in the exact exchange computation in comparison to plane-wave DFT calculations, which translates to a 2-4x speed up in the full ground-state calculation for 38-88 atom Pt clusters. Notably, the speed up in the exact exchange computation increases with increasing system size, with an 11x speed up observed for a TiO2 cluster consisting of 480 atoms.