In:
The Journal of Chemical Physics, AIP Publishing, Vol. 142, No. 9 ( 2015-03-07)
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−2 instead of r−1. The perturbation is asymptotically local, and the computation of the Hessian matrix can, in principle, be performed with ON 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.
Type of Medium:
Online Resource
ISSN:
0021-9606
,
1089-7690
Language:
English
Publisher:
AIP Publishing
Publication Date:
2015
detail.hit.zdb_id:
3113-6
detail.hit.zdb_id:
1473050-9
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