Beyond time-dependent exact-exchange: the need for long-range correlation

Abstract

In the description of the interaction between electrons beyond the classical Hartree picture, bare exchange often yields a leading contribution. Here we discuss its effect on optical spectra of solids, comparing three different frameworks: time-dependent Hartree-Fock, a recently introduced combined density-functional and Green's functions approach applied to the bare exchange self-energy, and time-dependent exact-exchange within time-dependent density-functional theory (TD-EXX). We show that these three approximations give rise to identical excitonic effects in solids; these effects are drastically overestimated for semiconductors. They are partially compensated by the usual overestimation of the quasiparticle band gap within Hartree-Fock. The physics that lacks in these approaches can be formulated as screening. We show that the introduction of screening in TD-EXX indeed leads to a formulation that is equivalent to previously proposed functionals derived from Many-Body Perturbation Theory. It can be simulated by reducing the long-range part of the Coulomb interaction: this produces absorption spectra of semiconductors in good agreement with experiment.

12 pages, 3 figures, 1 table

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• Accurate optical spectra through time-dependent density functional theory based on screening-dependent hybrid functionals
• Direct calculation of exciton binding energies with time-dependent density-functional theory
• Time-dependent density-functional approach for exciton binding energies
• Koopmans Meets Bethe-Salpeter: Excitonic Optical Spectra without GW
• Time-dependent density-functional theory for ultrafast interband excitations
• Molecular bonding with the RPAx: from weak dispersion forces to strong correlation
• A Snapshot of Time-Dependent Density-Functional Theory
• Design of effective kernels for spectroscopy and molecular transport: time-dependent current-density-functional theory
• Progress towards understanding ultranonlocality through the wavevector and frequency dependence of approximate exchange-correlation kernels