Accelerating Hartree–Fock and Density Functional Theory Calculations Using Tensor Hypercontraction

With the widespread use of self-consistent field methods, including Hartree–Fock and Density Functional Theory, the implications of accelerating these methods are immense. To this end, we develop a tensor hypercontraction (THC) construction with O ( N 3 ) formal scaling that can accelerate self-consistent field calculations. Using THC, we implement an empirically O ( N 2 ) scaling Fock matrix construction that is 2–4× faster than existing integral-direct methods, as it avoids the repeated recalculation of two-electron repulsion integrals. In combination with a density-difference ansatz, our THC self-consistent field implementation tests show errors below 1 kcal/mol for relative energies on protein systems containing up to 3000 basis functions. We also highlight the use of a linear solver instead of pseudoinversion to optimize matrix factors in THC. This is likely to be useful for all variants of THC, including applications to both self-consistent field and correlated wave functions.