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

作者：Kussmann Joerg^*; Luenser Arne; Beer Matthias; Ochsenfeld Christian

来源：Journal of Chemical Physics, 2015, 142(9): 094101.

DOI：10.1063/1.4908131

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.

• 出版日期2015-3-7