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

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 Gaussiantype 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.R 4 or even a 1.R 6 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.

Perspectives for hybrid ab initio/molecular mechanical simulations of solutions: from complex chemistry to proton-transfer reactions and interfaces

“…Since at the same time the benefit/cost ratio of computational resources is continuously increasing as well, theoretical methods are already considered as an indispensible tool providing an alternative route to study chemical phenomena, complementing experimental approaches. Since the acceleration of theoretical methods via linear scaling techniques [127][128][129][130][131][132][133][134] and the implementation of algorithms in the context of graphical processing unit (GPU) [135][136][137][138][139][140][141][142] enable a further dramatic increase in the capabilities of computational methods, these trends can be expected to persist and even accelerate within the next decades.…”

The divide-expand-consolidate family of coupled cluster methods: Numerical illustrations using second order Møller-Plesset perturbation theory

“…[29][30][31] For second order Møller-Plesset (MP2) theory linear scaling has been obtained using a Laplace transformation 32, 33 of the energy denominators and using effective integral screening techniques. [34][35][36][37] In the local CC methods, ad hoc approximations are introduced in the cluster amplitude equations and in the correlation energy, for example by assigning fixed virtual correlating orbital spaces to local occupied HF orbitals (e.g., using a) Electronic mail: idamh@chem.au.dk. the completeness criterion of Boughton and Pulay,38 ) or by carrying out a physical fragmentation of the molecule (e.g., using dangling bonds).…”

Theoretische Chemie 2010

“…Viele neuere Publikationen belegen die Fortschritte dieser Techniken und stellen zahlreiche methodische Entwicklungen,1_13—1_17 neue Algorithmen1_18—1_21 oder Anwendungen zur Berechnung molekularer Eigenschaften von großen Systemen 1_22—1_25 vor.…”