Tighter multipole-based integral estimates and parallel implementation of linear-scaling AO–MP2 theory

Abstract

Within an atomic-orbital-based (AO-based) formulation of second-order Møller–Plesset perturbation theory (MP2), we present a novel screening procedure which allows us to preselect numerically significant two-electron integrals more efficiently, especially for large basis sets. The screening is based on our recently introduced multipole-based integral estimates (MBIE) method [J. Chem. Phys., 2005, 123, 184102], that allows to exploit the 1/R⁴ or 1/R⁶ coupling between electronic charge distributions in transformed integral products within AO–MP2. In this way, linear scaling is attained with fully-controlled numerical accuracy. Furthermore, a parallel implementation of our linear-scaling AO–MP2 method is described, which also allows us to perform calculations with larger basis sets. First calculations reveal that for e.g. linear alkanes the scaling of the number of required transformed integral products is almost equal for 6-31G* and cc-pVTZ basis sets. Using the improved MBIE screening, the largest parallel calculation was performed for a ribozyme fragment consisting of 497 atoms and 5697 basis functions, while our largest AO–MP2 calculation was performed for a stacked DNA system (16 base pairs) comprising 1052 atoms and 10 674 basis functions on a single processor.