A Linear-Scaling MP2 Method for Large Molecules by Rigorous Integral-Screening Criteria

Abstract

Abstract A brief review of our linear-scaling method for atomic-orbital (AO) second-order Møller-Plesset perturbation theory (MP2) is given. The key feature of our method is the rigorous preselection of numerically significant four-center two-electron integrals based on multipole-based integral estimates (MBIE) that do not only account for the exponential coupling between the Gaussian-type basis functions forming charge distributions, but also for the 1/R coupling between the charge distributions. This coupling turns for the required integral products in AO-MP2 into at least a 1/R4 or even a 1/R6 decay behavior. Using MBIE we attain linear scaling, which is illustrated for DNA fragments with up to 1052 atoms and 10 674 basis functions as computed on a single processor. The largest molecule calculated in our present work at the scaled-opposite spin (SOS-) AO-MP2 level is an RNA system comprising 1664 atoms and 19 182 basis functions. Furthermore, we present results for the use of Cholesky-decomposed pseudo-density matrices in Laplace-based MP2, that offers the advantage of exploiting occupied/virtual blocking both with and without auxiliary basis sets.