Journal
JOURNAL OF CHEMICAL PHYSICS
Volume 142, Issue 9, Pages -Publisher
AMER INST PHYSICS
DOI: 10.1063/1.4908131
Keywords
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Funding
- Deutsche Forschungsgemeinschaft (DFG) [Oc35/4-1]
- DFG [SFB 749]
- DFG cluster of excellence Center for Integrated Protein Science Munich (CIPSM) [EXC 114]
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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 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. (c) 2015 AIP Publishing LLC.
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