Localized-orbital computation of linear and nonlinear susceptibilities

TL;DR

This paper introduces a novel method within density functional theory for calculating high-order energy derivatives, simplifying the computation of static linear and nonlinear susceptibilities using a Wannier-like orbital representation.

Contribution

It proves the $2n+1$ theorem for a broad class of energy functionals and derives simplified expressions for susceptibilities with a new orbital representation.

Findings

Validated approach with a 1D model Hamiltonian

Simplified formulas for susceptibilities

Extended $2n+1$ theorem to non-orthonormal orbitals

Abstract

We present a method to compute high-order derivatives of the total energy which can be used in the framework of density functional theory. We provide a proof of the $2n+1$ theorem for a general class of energy functionals in which the orbitals are not constrained to be orthonormal. Furthermore, by combining this result with a recently introduced Wannier-like representation of the electronic orbitals, we find expressions for the static linear and nonlinear susceptibilities which are much simpler than those obtained by standard perturbative expansions. We test numerically the validity of our approach with a 1D model Hamiltonian.