A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level

Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian

doi:10.1063/1.4908131

Title: A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level

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Abstract

An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r{sup −2} instead of r{sup −1}. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.

Authors:

Kussmann, Jörg; Luenser, Arne; Beer, Matthias; Ochsenfeld, Christian ^[1]

Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München (Germany)

Publication Date:: Sat Mar 07 00:00:00 EST 2015

OSTI Identifier:: 22416199

Resource Type:: Journal Article

Journal Name:: Journal of Chemical Physics

Additional Journal Information:: Journal Volume: 142; Journal Issue: 9; 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:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; CALCULATION METHODS; COULOMB FIELD; DENSITY; DENSITY MATRIX; DISTURBANCES; ELECTRONIC STRUCTURE; ELECTRONS; EXPANSION; IMPLEMENTATION; INTEGRALS; SELF-CONSISTENT FIELD

Citation Formats


                    Kussmann, Jörg, Luenser, Arne, Beer, Matthias, and Ochsenfeld, Christian. A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level.  United States: N. p., 2015. 
        Web.  doi:10.1063/1.4908131.

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                    Kussmann, Jörg, Luenser, Arne, Beer, Matthias, & Ochsenfeld, Christian. A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level.  United States.  https://doi.org/10.1063/1.4908131

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                    Kussmann, Jörg, Luenser, Arne, Beer, Matthias, and Ochsenfeld, Christian. 2015.  
        "A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level".  United States.  https://doi.org/10.1063/1.4908131.

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@article{osti_22416199,

  title        = {A reduced-scaling density matrix-based method for the computation of the vibrational Hessian matrix at the self-consistent field level},

  author       = {Kussmann, Jörg and Luenser, Arne and Beer, Matthias and Ochsenfeld, Christian},

  abstractNote = {An analytical method to calculate the molecular vibrational Hessian matrix at the self-consistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulomb-type two-electron integral contractions, we show that the effect of the perturbation on the electronic structure due to the displacement of nuclei decays at least as r{sup −2} instead of r{sup −1}. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with O(N) complexity. Our implementation exhibits linear scaling in all time-determining steps, with some rapid but quadratic-complexity steps remaining. Sample calculations illustrate linear or near-linear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably sub-quadratic to quadratic, depending on the density of the underlying electronic structure.},

  doi          = {10.1063/1.4908131},

  url          = {https://www.osti.gov/biblio/22416199},
  journal      = {Journal of Chemical Physics},

  issn         = {0021-9606},

  number       = 9,

  volume       = 142,

  place        = {United States},

  year         = {Sat Mar 07 00:00:00 EST 2015},

  month        = {Sat Mar 07 00:00:00 EST 2015}

}

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