Reduced-Scaling Correlation Methods for the Excited States of Large Molecules: Implementation and Benchmarks for the Second-Order Algebraic-Diagrammatic Construction Approach.

A framework for reduced-scaling implementation of excited-state correlation methods is presented. An algorithm is introduced to construct excitation-specific local domains, which include all important molecular orbitals for the excitation as well as for electron correlation. The orbital space dimensions of the resulting compact domains are further decreased utilizing our reduced-cost techniques developed previously [. 094111 (2018)] based on the natural auxiliary function and local natural orbital approaches. Additional methodological improvements for the evaluation of density matrices are also discussed. Benchmark calculations are presented at the second-order algebraic-diagrammatic construction level. Compared to our reduced-cost algorithm significant, up to 3-9-fold speedups are achieved even for systems of smaller than 100 atoms. At the same time, additional errors introduced by domain approximations are highly acceptable, being about 2-4 meV on the average. The presented reduced-scaling algorithm allows us to carry out correlated excited-state calculations using triple-ζ basis sets with diffuse functions for systems of up to 400 atoms or 13 000 atomic orbitals in a matter of days using an 8-core processor.