Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure

Hoy, Erik P.

doi:10.1063/1.4928064

Title: Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure

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Abstract

Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.

Authors:: Hoy, Erik P.

Publication Date:: Fri Aug 14 00:00:00 EDT 2015

OSTI Identifier:: 22493498

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 143; Journal Issue: 6; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9606

Country of Publication:: United States

Language:: English

Subject:: 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ACCURACY; ALKANES; DENSITY FUNCTIONAL METHOD; DIAGRAMS; ELECTRON CORRELATION; ELECTRONIC STRUCTURE; ELECTRONS; FACTORIZATION; HARTREE-FOCK METHOD; INTEGRALS; MOLECULES; POTENTIAL ENERGY; POTENTIALS; TENSORS

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                    Hoy, Erik P., and Mazziotti, David A., E-mail: damazz@uchicago.edu. Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4928064.

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                    Hoy, Erik P., & Mazziotti, David A., E-mail: damazz@uchicago.edu. Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure.  United States.  https://doi.org/10.1063/1.4928064

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                    Hoy, Erik P., and Mazziotti, David A., E-mail: damazz@uchicago.edu. 2015.  
        "Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure".  United States.  https://doi.org/10.1063/1.4928064.

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@article{osti_22493498,

  title        = {Positive semidefinite tensor factorizations of the two-electron integral matrix for low-scaling ab initio electronic structure},

  author       = {Hoy, Erik P. and Mazziotti, David A., E-mail: damazz@uchicago.edu},

  abstractNote = {Tensor factorization of the 2-electron integral matrix is a well-known technique for reducing the computational scaling of ab initio electronic structure methods toward that of Hartree-Fock and density functional theories. The simplest factorization that maintains the positive semidefinite character of the 2-electron integral matrix is the Cholesky factorization. In this paper, we introduce a family of positive semidefinite factorizations that generalize the Cholesky factorization. Using an implementation of the factorization within the parametric 2-RDM method [D. A. Mazziotti, Phys. Rev. Lett. 101, 253002 (2008)], we study several inorganic molecules, alkane chains, and potential energy curves and find that this generalized factorization retains the accuracy and size extensivity of the Cholesky factorization, even in the presence of multi-reference correlation. The generalized family of positive semidefinite factorizations has potential applications to low-scaling ab initio electronic structure methods that treat electron correlation with a computational cost approaching that of the Hartree-Fock method or density functional theory.},

  doi          = {10.1063/1.4928064},

  url          = {https://www.osti.gov/biblio/22493498},
  journal      = {Journal of Chemical Physics},

  issn         = {0021-9606},

  number       = 6,

  volume       = 143,

  place        = {United States},

  year         = {Fri Aug 14 00:00:00 EDT 2015},

  month        = {Fri Aug 14 00:00:00 EDT 2015}

}

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