Higher Order Response in ${\cal O}(N)$ by Perturbed Projection

Details Higher Order Response in ${\cal O}(N)$ by Perturbed Projection Higher Order Response in ${\cal O}(N)$ by Perturbed Projection

2004-12-21

arxiv.org/abs/cond-mat/0412568v1

Physics

Condensed Matter

Materials Science

Submitted to the Journal of Chemical Physics

Scientific paper

10.1063/1.1944724

Perturbed projection for linear scaling solution of the coupled-perturbed self-consistent-field equations [Weber, Niklasson and Challacombe, Phys. Rev.\ Lett. {\bf 92}, 193002 (2004)] is extended to the computation of higher order static response properties. Although generally applicable, perturbed projection is developed here in the context of the self-consistent first and second electric hyperpolarizabilities of three dimensional water clusters at the Hartree-Fock level of theory. Non-orthogonal, density matrix analogues of Wigner's $2n+1$ rule are given up to fourth order. Linear scaling and locality of the higher order response densities under perturbation by a global electric field are demonstrated.

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