Cited by 4,155Advanced Chemical Physics StudiesSpectroscopy and Quantum Chemical StudiesPhysics of Superconductivity and Magnetism

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Electronic excitations: density-functional versus many-body Green’s-function approaches

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Onida, Giovanni, Reining, Lucia, Rubio, Angel·2002·Reviews of Modern Physics

DOI 10.1103/revmodphys.74.601

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Abstract

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green's-function equations, starting with a one-electron propagator and considering the electron-hole Green's function for the response. Key ingredients are the electron's self-energy \ensuremath{\Sigma} and the electron-hole interaction. A good approximation for \ensuremath{\Sigma} is obtained with Hedin's $\mathrm{GW}$ approach, using density-functional theory as a zero-order solution. First-principles $\mathrm{GW}$ calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of \ensuremath{\Sigma}. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green's functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green's functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

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Authors: Onida, G., Reining, L., & Rubio, A.
Affiliations: University of Rome Tor Vergata (IT)
ORCID: Onida, Giovanni
Reining, Lucia
Venue: Reviews of Modern Physics
Publisher: American Physical Society (APS)
Published: 2002-06-07
Volume: 74
Issue: 2
Pages: 601-659
ISSN: 0034-6861 (ISSN-L)
1539-0756
DOI: 10.1103/revmodphys.74.601
OpenAlex: W2053499780
Cited by: 4,155
References: 323
Citations by year: 2026: 238 · 2025: 221 · 2024: 233 · 2023: 232 · 2022: 202 · 2021: 245 · 2020: 270 · 2019: 199 · 2018: 223 · 2017: 210 · 2016: 224 · 2015: 203 · 2014: 217 · 2013: 168 · 2012: 180
FWCI: 48.69
Type: journal article
Language: en
Open access: bronze
doi.org
Licence: link.aps.org/licenses/aps-default-license (vor)
Locations: Reviews of Modern Physics (publishedVersion)
DIGITAL.CSIC (Spanish National Research Council (CSIC)) (submittedVersion, other-oa)
Funders: European Commission
Centre National de la Recherche Scientifique
Topics: Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Advanced Chemical Physics Studies
Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Spectroscopy and Quantum Chemical Studies
Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Physics of Superconductivity and Magnetism
Keywords: electronic excitation, excited states, GW approximation, Bethe-Salpeter equation, time-dependent density functional theory, many-body perturbation theory, Green's function, electron self-energy, electron-hole interaction, adiabatic local density approximation, absorption spectra, spectral line shape, excitonic states

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Electronic excitations: density-functional versus many-body Green’s-function approaches

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