Dynamical Kernels for Optical Excitations

TL;DR

This paper compares three frequency-dependent kernels for optical excitation calculations, highlighting their ability to reveal higher-order excitations and analyzing their accuracy and spurious features using simple models.

Contribution

It introduces and evaluates three dynamical kernels for optical excitations, emphasizing their capacity to capture double excitations and analyzing spurious states.

Findings

Dynamical kernels can reveal higher-order excitations like double excitations.

Spurious excitations can arise from approximate kernels.

Different kernels show varying accuracy in simple models.

Abstract

We discuss the physical properties and accuracy of three distinct dynamical (ie, frequency-dependent) kernels for the computation of optical excitations within linear response theory: i) an a priori built kernel inspired by the dressed time-dependent density-functional theory (TDDFT) kernel proposed by Maitra and coworkers, ii) the dynamical kernel stemming from the Bethe-Salpeter equation (BSE) formalism derived originally by Strinati , and iii) the second-order BSE kernel derived by Yang and coworkers . The principal take-home message of the present paper is that dynamical kernels can provide, thanks to their frequency-dependent nature, additional excitations that can be associated to higher-order excitations (such as the infamous double excitations), an unappreciated feature of dynamical quantities. We also analyze, for each kernel, the appearance of spurious excitations originating from the approximate nature of the kernels, as first evidenced by Romaniello. Using a simple two-level model, prototypical examples of valence, charge-transfer, and Rydberg excited states are considered.