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  Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals

Pinski, P., Riplinger, C., Vallev, E. F., & Neese, F. (2015). Sparse maps—A systematic infrastructure for reduced-scaling electronic structure methods. I. An efficient and simple linear scaling local MP2 method that uses an intermediate basis of pair natural orbitals. The Journal of Physical Chemistry, 143(3): 034108. doi:10.1063/1.4926879.

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 Creators:
Pinski, Peter1, Author              
Riplinger, Christoph1, Author              
Vallev, Edward F.2, Author
Neese, Frank1, Author              
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1Research Department Neese, Max Planck Institute for Chemical Energy Conversion, Max Planck Society, ou_3023886              
2Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, USA, ou_persistent22              

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 Abstract: In this work, a systematic infrastructure is described that formalizes concepts implicit in previous work and greatly simplifies computer implementation of reduced-scaling electronic structure methods. The key concept is sparse representation of tensors using chains of sparse maps between two index sets. Sparse map representation can be viewed as a generalization of compressed sparse row, a common representation of a sparse matrix, to tensor data. By combining few elementary operations on sparse maps (inversion, chaining, intersection, etc.), complex algorithms can be developed, illustrated here by a linear-scaling transformation of three-center Coulomb integrals based on our compact code library that implements sparse maps and operations on them. The sparsity of the three-center integrals arises from spatial locality of the basis functions and domain density fitting approximation. A novel feature of our approach is the use of differential overlap integrals computed in linear-scaling fashion for screening products of basis functions. Finally, a robust linear scaling domain based local pair natural orbital second-order Möller-Plesset (DLPNO-MP2) method is described based on the sparse map infrastructure that only depends on a minimal number of cutoff parameters that can be systematically tightened to approach 100% of the canonical MP2 correlation energy. With default truncation thresholds, DLPNO-MP2 recovers more than 99.9% of the canonical resolution of the identity MP2 (RI-MP2) energy while still showing a very early crossover with respect to the computational effort. Based on extensive benchmark calculations, relative energies are reproduced with an error of typically <0.2 kcal/mol. The efficiency of the local MP2 (LMP2) method can be drastically improved by carrying out the LMP2 iterations in a basis of pair natural orbitals. While the present work focuses on local electron correlation, it is of much broader applicability to computation with sparse tensors in quantum chemistry and beyond.

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Language(s): eng - English
 Dates: 2015-03-182015-07-212015-07-21
 Publication Status: Published in print
 Pages: 17
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: DOI: 10.1063/1.4926879
 Degree: -

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Title: The Journal of Physical Chemistry
  Abbreviation : J. Phys. Chem.
Source Genre: Journal
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Publ. Info: Washington, D.C. : American Chemical Society
Pages: - Volume / Issue: 143 (3) Sequence Number: 034108 Start / End Page: - Identifier: ISSN: 1932-7447
CoNE: https://pure.mpg.de/cone/journals/resource/954926947766_3