title: Higher-order response in O(N) by perturbed projection.
abstract: Perturbed projection for linear scaling solution of the coupled-perturbed self-consistent-field equations [V. Weber, A.M.N. Niklasson, and M. Challacombe, Phys. Rev. Lett. 92, 193002 (2004)] is extended to the computation of higher-order static response properties. Although generally applicable, perturbed projection is further developed here in the context of the self-consistent first and second electric hyperpolarizabilities at the Hartree-Fock level of theory. Nonorthogonal, density-matrix analogs of Wigner's 2n+1 rule valid for linear one-electron perturbations 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 for three-dimensional water clusters.
authors.affiliation: Department of Chemistry, University of Fribourg, 1700 Fribourg, Switzerland. valery.weber@unifr.ch
authors.forename: Valéry
authors.initials: V
authors.lastname: Weber
authors.forename: Anders M N
authors.initials: AM
authors.lastname: Niklasson
authors.forename: Matt
authors.initials: M
authors.lastname: Challacombe