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

TL;DR

This paper extends the perturbed projection method to efficiently compute higher order static response properties, such as electric hyperpolarizabilities, demonstrating linear scaling and locality in water clusters at the Hartree-Fock level.

Contribution

The paper develops a method to compute higher order response properties using perturbed projection, including non-orthogonal density matrix analogues of Wigner's rule up to fourth order.

Findings

Linear scaling of higher order response densities demonstrated.

Method applied to compute electric hyperpolarizabilities of water clusters.

Locality of response densities confirmed under global electric field perturbation.

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.