Local explicitly correlated second- and third-order Møller-Plesset perturbation theory with pair natural orbitals

Christof Hättig1,a), David P. Tew2,b), Benjamin Helmich1,c),
1 Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780 Bochum, Germany
2 School of Chemistry, University of Bristol, Bristol BS8 1TS, United Kingdom

J. Chem. Phys. 136, 204105 (2012).
(Received 5 April 2012; accepted 7 May 2012; published online 24 May 2012)

We present an algorithm for computing explicitly correlated second- and third-order Møller-Plesset energies near the basis set limit for large molecules with a cost that scales formally as N4 with system size N. This is achieved through a hybrid approach where locality is exploited first through orbital specific virtuals (OSVs) and subsequently through pair natural orbitals (PNOs) and integrals are approximated using density fitting. Our method combines the low orbital transformation costs of the OSVs with the compactness of the PNO representation of the doubles amplitude vector. The N4 scaling does not rely upon the a priori definition of domains, enforced truncation of pair lists, or even screening and the energies converge smoothly to the canonical values with decreasing occupation number threshold, used in the selection of the PNO basis. For MP2.5 intermolecular interaction energies, we find that 99% of benchmark basis set limit correlation energy contributions are recovered using an aug-cc-pVTZ basis and that on average only 50 PNOs are required to correlate the significant orbital pairs.

(C) 2011 American Institute of Physics. [doi:10.1063/1.4719981]

a) Electronic mail: christof.haettig@rub.de
b) Electronic mail: david.tew@bristol.ac.uk
c) Electronic mail: benjamin.helmich@rub.de

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