A new and efficient approach to time-dependent density-functional perturbation theory for optical spectroscopy

TL;DR

This paper introduces an efficient super-operator approach to time-dependent density-functional perturbation theory, enabling rapid calculation of full optical spectra with minimal additional computational cost.

Contribution

It presents a novel matrix continued-fraction representation and a non-symmetric block-Lanczos method for calculating dynamical polarizability efficiently.

Findings

Successfully computed benzene's optical spectrum

Achieved full spectrum calculation with workload close to static polarizability

Discussed potential for large-scale optical spectrum computations

Abstract

Using a super-operator formulation of linearized time-dependent density-functional theory, the dynamical polarizability of a system of interacting electrons is given a matrix continued-fraction representation whose coefficients can be obtained from the non-symmetric block-Lanczos method. The resulting algorithm allows for the calculation of the {\em full spectrum} of a system with a computational workload which is only a few times larger than that needed for {\em static} polarizabilities within time-independent density-functional perturbation theory. The method is demonstrated with the calculation of the spectrum of benzene, and prospects for its application to the large-scale calculation of optical spectra are discussed.