Even Faster Exact Exchange for Solids via Tensor Hypercontraction

Hybrid
density functional theory (DFT) remains intractable for
large periodic systems due to the demanding computational cost of
exact exchange. We apply the tensor hypercontraction (THC) (or interpolative
separable density fitting) approximation to periodic hybrid DFT calculations
with Gaussian-type orbitals using the Gaussian plane wave approach.
This is done to lower the computational scaling with respect to the
number of basis functions (N) and k-points
(Nk) at a fixed system
size. Additionally, we propose an algorithm to fit only occupied orbital
products via THC (i.e., a set of points, NISDF) to further reduce computation time and memory usage. This algorithm
has linear scaling cost with k-points, no explicit dependence
of NISDF on basis set size, and overall
cubic scaling with unit cell size. Significant speedups and reduced
memory usage may be obtained for moderately sized k-point
meshes, with additional gains for large k-point meshes.
Adequate accuracy can be obtained using THC-oo-K for self-consistent
calculations. We perform illustrative hybrid density function theory
calculations on the benzene crystal in the basis set and thermodynamic
limits to highlight the utility of this algorithm.