Comparison of Three Efficient Approximate Exact-Exchange Algorithms: The Chain-of-Spheres Algorithm, Pair-Atomic Resolution-of-the-Identity Method, and Auxiliary Density Matrix Method

Elisa Rebolini; Róbert Izsák; Simen Sommerfelt Reine; Trygve Helgaker; Thomas Bondo Pedersen

doi:10.1021/acs.jctc.6b00074

Comparison of Three Efficient Approximate Exact-Exchange Algorithms: The Chain-of-Spheres Algorithm, Pair-Atomic Resolution-of-the-Identity Method, and Auxiliary Density Matrix Method

J Chem Theory Comput. 2016 Aug 9;12(8):3514-22. doi: 10.1021/acs.jctc.6b00074. Epub 2016 Jul 6.

Authors

Elisa Rebolini¹, Róbert Izsák², Simen Sommerfelt Reine¹, Trygve Helgaker¹, Thomas Bondo Pedersen¹

Affiliations

¹ Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo , P.O. Box 1033, Blindern, N-0315 Oslo, Norway.
² Max-Planck Institute for Chemical Energy Conversion , Stiftstrasse 34-36, D-45470 Mülheim an der Ruhr, Germany.

PMID: 27224306
DOI: 10.1021/acs.jctc.6b00074

Abstract

We compare the performance of three approximate methods for speeding up evaluation of the exchange contribution in Hartree-Fock and hybrid Kohn-Sham calculations: the chain-of-spheres algorithm (COSX; Neese , F. Chem. Phys. 2008 , 356 , 98 - 109 ), the pair-atomic resolution-of-identity method (PARI-K; Merlot , P. J. Comput. Chem. 2013 , 34 , 1486 - 1496 ), and the auxiliary density matrix method (ADMM; Guidon , M. J. Chem. Theory Comput. 2010 , 6 , 2348 - 2364 ). Both the efficiency relative to that of a conventional linear-scaling algorithm and the accuracy of total, atomization, and orbital energies are compared for a subset containing 25 of the 200 molecules in the Rx200 set using double-, triple-, and quadruple-ζ basis sets. The accuracy of relative energies is further compared for small alkane conformers (ACONF test set) and Diels-Alder reactions (DARC test set). Overall, we find that the COSX method provides good accuracy for orbital energies as well as total and relative energies, and the method delivers a satisfactory speedup. The PARI-K and in particular ADMM algorithms require further development and optimization to fully exploit their indisputable potential.