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

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:
; ; ;  [1]
  1. Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 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; SELF-CONSISTENT FIELD