Exchange and Correlation Kernels at the Resonance Frequency -- Implications for Excitation Energies in Density-Functional Theory

TL;DR

This paper computes specific matrix elements of exchange and correlation kernels in time-dependent density-functional theory, linking different approaches to excited states and constraining approximate functionals.

Contribution

It provides new calculations of matrix elements that connect DFT and many-body perturbation theory approaches for excited states.

Findings

Matrix elements constrain approximate functionals.

Links between DFT and many-body methods established.

Implications for excitation energy calculations.

Abstract

Specific matrix elements of exchange and correlation kernels in time-dependent density-functional theory are computed. The knowledge of these matrix elements not only constraints approximate time-dependent functionals, but also allows to link different practical approaches to excited states, either based on density-functional theory, or on many-body perturbation theory, despite the approximations that have been performed to derive them.