A reducedscaling density matrixbased method for the computation of the vibrational Hessian matrix at the selfconsistent field level
Abstract
An analytical method to calculate the molecular vibrational Hessian matrix at the selfconsistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulombtype twoelectron 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 timedetermining steps, with some rapid but quadraticcomplexity steps remaining. Sample calculations illustrate linear or nearlinear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably subquadratic to quadratic, depending on the density of the underlying electronic structure.
 Authors:
 Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D81377 München (Germany)
 Publication Date:
 OSTI Identifier:
 22416199
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 9; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 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; SELFCONSISTENT FIELD
Citation Formats
Kussmann, Jörg, Luenser, Arne, Beer, Matthias, and Ochsenfeld, Christian, Email: christian.ochsenfeld@unimuenchen.de. A reducedscaling density matrixbased method for the computation of the vibrational Hessian matrix at the selfconsistent field level. United States: N. p., 2015.
Web. doi:10.1063/1.4908131.
Kussmann, Jörg, Luenser, Arne, Beer, Matthias, & Ochsenfeld, Christian, Email: christian.ochsenfeld@unimuenchen.de. A reducedscaling density matrixbased method for the computation of the vibrational Hessian matrix at the selfconsistent field level. United States. doi:10.1063/1.4908131.
Kussmann, Jörg, Luenser, Arne, Beer, Matthias, and Ochsenfeld, Christian, Email: christian.ochsenfeld@unimuenchen.de. 2015.
"A reducedscaling density matrixbased method for the computation of the vibrational Hessian matrix at the selfconsistent field level". United States.
doi:10.1063/1.4908131.
@article{osti_22416199,
title = {A reducedscaling density matrixbased method for the computation of the vibrational Hessian matrix at the selfconsistent field level},
author = {Kussmann, Jörg and Luenser, Arne and Beer, Matthias and Ochsenfeld, Christian, Email: christian.ochsenfeld@unimuenchen.de},
abstractNote = {An analytical method to calculate the molecular vibrational Hessian matrix at the selfconsistent field level is presented. By analysis of the multipole expansions of the relevant derivatives of Coulombtype twoelectron 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 timedetermining steps, with some rapid but quadraticcomplexity steps remaining. Sample calculations illustrate linear or nearlinear scaling in the construction of the complete nuclear Hessian matrix for sparse systems. For more demanding systems, scaling is still considerably subquadratic to quadratic, depending on the density of the underlying electronic structure.},
doi = {10.1063/1.4908131},
journal = {Journal of Chemical Physics},
number = 9,
volume = 142,
place = {United States},
year = 2015,
month = 3
}

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