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 <i>O</i>(<i>N</i>³) formal scaling that can accelerate self-consistent field calculations. Using THC, we implement an empirically <i>O</i>(<i>N</i>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.