Many-Body Perturbation Theory (MBPT) and Time-Dependent Density-Functional Theory (TD-DFT): MBPT Insights About What Is Missing In, and Corrections To, the TD-DFT Adiabatic Approximation

  • Mark E. CasidaEmail author
  • Miquel Huix-Rotllant
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 368)


In their famous paper, Kohn and Sham formulated a formally exact density-functional theory (DFT) for the ground-state energy and density of a system of N interacting electrons, albeit limited at the time by certain troubling representability questions. As no practical exact form of the exchange-correlation (xc) energy functional was known, the xc-functional had to be approximated, ideally by a local or semilocal functional. Nowadays, however, the realization that Nature is not always so nearsighted has driven us up Perdew’s Jacob’s ladder to find increasingly nonlocal density/wavefunction hybrid functionals. Time-dependent (TD-) DFT is a younger development which allows DFT concepts to be used to describe the temporal evolution of the density in the presence of a perturbing field. Linear response (LR) theory then allows spectra and other information about excited states to be extracted from TD-DFT. Once again the exact TD-DFT xc-functional must be approximated in practical calculations and this has historically been done using the TD-DFT adiabatic approximation (AA) which is to TD-DFT very similar to what the local density approximation (LDA) is to conventional ground-state DFT. Although some of the recent advances in TD-DFT focus on what can be done within the AA, others explore ways around the AA. After giving an overview of DFT, TD-DFT, and LR-TD-DFT, this chapter focuses on many-body corrections to LR-TD-DFT as one way to build hybrid density-functional/wavefunction methodology for incorporating aspects of nonlocality in time not present in the AA.


Electronic excited states Many-body perturbation theory Photochemistry Time-dependent density-functional theory 



We thank Andrei Ipatov, Mathias Ljungberg, Hemanadhan Myneni, Valerio Olevano, Giovanni Onica, Lucia Reining, Pina Romaniello, Angel Rubio, Davide Sangalli, Jochen Schirmer, and Eric Shirley for useful discussions. M. H. R. would like to acknowledge an Allocation de Recherche from the French Ministry of Education. Over the years, this work has been carried out in the context of several programs: the French Rhône-Alpes Réseau thématique de recherche avancée (RTRA): Nanosciences aux limites de la nanoélectronique, the Rhône-Alpes Associated Node of the European Theoretical Spectroscopy Facility (ETSF), and, most recently, the grant ANR-12-MONU-0014-02 from the French Agence Nationale de la Recherche for the ORGAVOLT project (ORGAnic solar cell VOLTage by numerical computation).


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Authors and Affiliations

  1. 1.Département de Chimie Moléculaire, Institut de Chimie Moléculaire de GrenobleUniversité Joseph Fourier (Grenoble I)Grenoble Cedex 9France
  2. 2.Institut für Physikalische und Theoretische ChimieUniversität Frankfurt am MainFrankfurtGermany

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