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

Giovanni Onida*, Lucia Reining†, and Angel Rubio‡

Giovanni Onida*

  • Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica dell’ Università di Roma “Tor Vergata,” Via della Ricerca Scientifica 1, I-00133 Roma, Italy

Lucia Reining†

  • Laboratoire des Solides Irradiés, UMR 7642 CNRS-CEA, École Polytechnique, F-91128 Palaiseau, France

Angel Rubio‡

  • Departamento de Física de Materiales, Facultad de Químicas, Universidad del País Vasco/Euskal Herriko Unibertsitatea, Centro Mixto CSIC-UPV/EHU and Donostia International Physics Center (DIPC) 20018 San Sebastián/Donostia, Spain
  • Laboratoire des Solides Irradiés, UMR 7642 CNRS-CEA, École Polytechnique, F-91128 Palaiseau, France

  • *Present address: Istituto Nazionale per la Fisica della Materia, Dipartimento di Fisica dell’ Universitá di Milano, via Celoria 16, I-20133 Milano, Italy. Electronic address: Giovanni.Onida@mi.infn.it
  • †Electronic address: Lucia.Reining@polytechnique.fr
  • ‡Electronic address: arubio@sc.ehu.es
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Rev. Mod. Phys. 74, 601 – Published 7 June, 2002

DOI: https://doi.org/10.1103/RevModPhys.74.601

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 Σ and the electron-hole interaction. A good approximation for Σ is obtained with Hedin's GW approach, using density-functional theory as a zero-order solution. First-principles 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 Σ. 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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