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

J. Chem. Phys., 142, 094101, http://dx.doi.org/10.1063/1.4908131
J. Chem. Phys., online article

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.
 

Campus Movie 2020

CIPSM Movie

Campus Movie 2012

CIPSM Movie
LMUexcellent
TU München
MPG
Helmholtz München
MPI of Neurobiology
MPI of Biochemistry