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(-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.
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany.
Jörg
J
Kussmann
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany.
Arne
A
Luenser
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany.
Matthias
M
Beer
Chair of Theoretical Chemistry, Department of Chemistry, University of Munich (LMU), Butenandtstr. 7, D-81377 München, Germany.
Christian
C
Ochsenfeld
D000688:Amylose / Q000737:chemistry; D002627:Chemistry, Physical / Q000379:methods*; D003198:Computer Simulation; D004247:DNA / Q000737:chemistry; D008956:Models, Chemical; D015394:Molecular Structure; D011789:Quantum Theory
D000688:Amylose; D004247:DNA