Higher-order response in O(N) by perturbed projection -: art. no. 044106

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. (C) 2005 American Institute of Physics.