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  Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange

Neese, F., Wennmohs, F., Hansen, A., & Becker, U. (2009). Efficient, approximate and parallel Hartree–Fock and hybrid DFT calculations. A ‘chain-of-spheres’ algorithm for the Hartree–Fock exchange. Chemical Physics, 356(1-3), 98-109. doi:10.1016/j.chemphys.2008.10.036.

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 Creators:
Neese, Frank1, 2, Author           
Wennmohs, Frank1, Author           
Hansen, Andreas1, Author
Becker, Ute3, Author           
Affiliations:
1Lehrstuhl für Theoretische Chemie, Institut für Physikalische und Theoretische Chemie, Universität Bonn, Wegelerstrasse 12, D-53115 Bonn, Germany, ou_persistent22              
2Research Department Neese, Max Planck Institute for Bioinorganic Chemistry, Max Planck Society, ou_3023879              
3Research Department Wieghardt, Max Planck Institute for Bioinorganic Chemistry, Max Planck Society, ou_3023881              

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 Abstract: In this paper, the possibility is explored to speed up Hartree–Fock and hybrid density functional calculations by forming the Coulomb and exchange parts of the Fock matrix by different approximations. For the Coulomb part the previously introduced Split-RI-J variant (F. Neese, J. Comput. Chem. 24 (2003) 1740) of the well-known ‘density fitting’ approximation is used. The exchange part is formed by semi-numerical integration techniques that are closely related to Friesner’s pioneering pseudo-spectral approach. Our potentially linear scaling realization of this algorithm is called the ‘chain-of-spheres exchange’ (COSX). A combination of semi-numerical integration and density fitting is also proposed. Both Split-RI-J and COSX scale very well with the highest angular momentum in the basis sets. It is shown that for extended basis sets speed-ups of up to two orders of magnitude compared to traditional implementations can be obtained in this way. Total energies are reproduced with an average error of <0.3 kcal/mol as determined from extended test calculations with various basis sets on a set of 26 molecules with 20–200 atoms and up to 2000 basis functions. Reaction energies agree to within 0.2 kcal/mol (Hartree–Fock) or 0.05 kcal/mol (hybrid DFT) with the canonical values. The COSX algorithm parallelizes with a speedup of 8.6 observed for 10 processes. Minimum energy geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angels from their canonical values. These developments enable highly efficient and accurate self-consistent field calculations including nonlocal Hartree–Fock exchange for large molecules. In combination with the RI-MP2 method and large basis sets, second-order many body perturbation energies can be obtained for medium sized molecules with unprecedented efficiency. The algorithms are implemented into the ORCA electronic structure system.

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Language(s): eng - English
 Dates: 2009-02-17
 Publication Status: Published in print
 Pages: 12
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1016/j.chemphys.2008.10.036
 Degree: -

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Title: Chemical Physics
  Abbreviation : Chem. Phys.
Source Genre: Journal
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Publ. Info: Amsterdam : Elsevier B.V.
Pages: - Volume / Issue: 356 (1-3) Sequence Number: - Start / End Page: 98 - 109 Identifier: ISSN: 0301-0104
CoNE: https://pure.mpg.de/cone/journals/resource/954925509371