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Cited by 13Matrix Theory and AlgorithmsAdvanced Chemical Physics StudiesParallel Computing and Optimization Techniques

Sparse projected-gradient method as a linear-scaling low-memory alternative to diagonalization in self-consistent field electronic structure calculations.

Birgin, Ernesto G., Martı́nez, J. M., Martı́nez, Leandro, Rocha, Gerd B.·2013·Journal of Chemical Theory and Computation
DOI 10.1021/ct3009683
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Abstract

Large-scale electronic structure calculations usually involve huge nonlinear eigenvalue problems. A method for solving these problems without employing expensive eigenvalue decompositions of the Fock matrix is presented in this work. The sparsity of the input and output matrices is preserved at every iteration, and the memory required by the algorithm scales linearly with the number of atoms of the system. The algorithm is based on a projected gradient iteration applied to the constraint fulfillment problem. The computer time required by the algorithm also scales approximately linearly with the number of atoms (or non-null elements of the matrices), and the algorithm is faster than standard implementations of modern eigenvalue decomposition methods for sparse matrices containing more than 50 000 non-null elements. The new method reproduces the sequence of semiempirical SCF iterations obtained by standard eigenvalue decomposition algorithms to good precision.

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  • In the last 10 years, important advances were made in computing hardware, quantum algorithms to compute molecular wave functions, more reliable semi-empirical quantum methods, and new hybrid QM/MM methods.

    “In the last 10 years, important advances were made in computing hardware (e.g., Graphics Processing Units – GPUs), in the development of quantum algorithms to compute molecular wave functions (Dixon and Merz, 1997; Birgin et al., 2013), the development of more reliable semi-empirical quantum methods (Christensen et al., 2016; Yilmazer and Korth, 2016), and development of new hybrid QM/MM methods (”

    From Empirical scoring functions for structure-based virtual screening: applications, critical aspects, and challenges (2018) · cites this paper as Birgin et al., 2013

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Authors
Birgin, E. G., Martı́nez, J. M., Martı́nez, L., & Rocha, G. B.
Affiliations
  • Universidade de São Paulo (BR)
  • Department of Applied Mathematics, Institute of Mathematics, Statistics and Scientfic Computing, State University of Campinas, Campinas, SP, Brazil
  • Universidade Estadual de Campinas (UNICAMP) (BR)
  • Universidade Federal da Paraíba (BR)
Corresponding author
Martı́nez, Leandro
ORCID
Venue
Journal of Chemical Theory and Computation
Publisher
American Chemical Society (ACS)
Published
2013-01-17
Volume
9
Issue
2
Pages
1043-1051
ISSN
  • 1549-9618 (ISSN-L)
  • 1549-9626
DOI
10.1021/ct3009683
OpenAlex
W2039023455
Cited by
13
References
55
Citations by year
2020: 2 · 2018: 1 · 2017: 2 · 2015: 3 · 2014: 4 · 2013: 1
FWCI
2.92
Type
journal article
Language
en
Open access
closed
Locations
  • Journal of Chemical Theory and Computation (publishedVersion)
  • PubMed (publishedVersion)
Topics
  • Physical Sciences › Computer Science › Computational Theory and Mathematics › Matrix Theory and Algorithms
  • Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
  • Physical Sciences › Computer Science › Hardware and Architecture › Parallel Computing and Optimization Techniques
Keywords
self-consistent field, nonlinear eigenvalue problems, Fock matrix, memory-efficient algorithms, linear scaling, sparse matrices, electronic structure calculations

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