Efficient Low-Scaling Calculation of THC-SOS-LR-CC2 and THC-SOS-ADC(2) Excitation Energies Through Density-Based...

In recent years, rapid improvements in computer hardware, as well as theoretical and algorithmic advances have enabled the calculation of ever larger systems in computational chemistry. In this avenue, we present efficient implementations of the scaled opposite-spin (SOS) second-order approximate coupled cluster (CC2) method and the closely related second-order algebraic diagrammatic construction (ADC(2)) method. Our implementations applies the least-squares tensor hypercontraction (THC) approximation, for which a new density-based integral-direct reformulation of the grid-projection of the electron integral tensor is presented. Together with screening based on local Cholesky orbitals stemming from the decomposition of the one-particle densities (CDD) in the Laplace integration and optimized block-sparse linear algebra, effectively $O\left(N^2\right)$ scaling variants of linear-response (LR) SOS-CC2 and SOS-ADC(2) are obtained. The derived CDD-THC-SOS-LR-CC2/ADC(2) methods are shown to be capable of targeting excitation energies for systems with up to ∼1000 atoms and ∼10,000 basis functions on a single compute node.