Lowering the Scaling of Self-Consistent Field Methods by Combining Tensor Hypercontraction and a Density Difference Ansatz

We present the tensor hypercontraction difference self-consistent field (SCF) method, an approach that reduces the formal computational scaling of traditional naive self-consistent field methods from O(N4) to O(N3) with system size N. The scaling reduction is achieved by developing a new technique for constructing the tensor hypercontraction decomposition based on the fundamental approximation made in density fitting. Combining this scheme with the difference self-consistent field methodology, we achieve a method that enables O(N3) scaling SCF calculations with only O(N2) storage requirements. Our proof-of-concept numerical tests demonstrate robust performance with errors in total energies below 8 × 10–4 Eh and with sub 1 kcal/mol errors for relative energies.