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

Abstract

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.

Submitted to the Journal of Chemical Physics

References in corpus (6)

• First principles calculation of vibrational Raman spectra in large systems: signature of small rings in crystalline SiO2
• Expansion algorithm for the density matrix
• Density Matrix Perturbation Theory
• Linear scaling computation of the Fock matrix. VIII. Periodic boundaries for exact exchange at the $\Gamma$-point
• Non-Orthogonal Density Matrix Perturbation Theory
• Linear scaling computation of the Fock matrix VII. Periodic Density Functional Theory at the $\Gamma$-point

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