Efficient distance-including integral screening in linear-scaling Møller-Plesset perturbation theory

Efficient estimates for the preselection of two-electron integrals in atomic-orbital based Møller-Plesset perturbation theory (AO-MP2) theory are presented, which allow for evaluating the AO-MP2 energy with computational effort that scales linear with molecular size for systems with a significant HOMO-LUMO gap. The estimates are based on our recently introduced QQR approach [S. A. Maurer, D. S. Lambrecht, D. Flaig, and C. Ochsenfeld, J. Chem. Phys. 136, 144107 (2012)], which exploits the asympotic decay of the integral values with increasing bra-ket separation as deduced from the multipole expansion and combines this decay behavior with the common Schwarz bound to a tight and simple estimate. We demonstrate on a diverse selection of benchmark systems that our AO-MP2 method in combination with the QQR-type estimates produces reliable results for systems with both localized and delocalized electronic structure, while in the latter case the screening essentially reverts to the common Schwarz screening. For systems with localized electronic structure, our AO-MP2 method shows an early onset of linear scaling as demonstrated on DNA systems. The favorable scaling behavior allows to compute systems with more than 1000 atoms and 10,000 basis functions on a single core that are clearly not accessible with conventional MP2 methods. Furthermore, our AO-MP2 method is particularly suited for parallelization and we present benchmark calculations on a protein-DNA repair complex comprising 2025 atoms and 20,371 basis functions.