Top Curr Chem (2016) 368: 1–60
DOI: 10.1007/128_2015_632
# Springer International Publishing Switzerland 2015
Published online: 24 May 2015
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. Casida and Miquel Huix-Rotllant
Abstract 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. Timedependent (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/
M.E. Casida (*)
De ´partement de Chimie Mole ´culaire, Institut de Chimie Mole ´culaire de Grenoble, Universite ´
Joseph Fourier (Grenoble I), 301 rue de la Chimie, BP 53, 38041 Grenoble Cedex 9, France
e-mail: mark.casida@ujf-grenoble.fr
M. Huix-Rotllant
Institut fu ¨r Physikalische und Theoretische Chimie, Universita ¨t Frankfurt am Main, Frankfurt,
Germany
e-mail: miquel.huix@gmail.com
DOI: 10.1007/128_2015_632
# Springer International Publishing Switzerland 2015
Published online: 24 May 2015
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. Casida and Miquel Huix-Rotllant
Abstract 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. Timedependent (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/
M.E. Casida (*)
De ´partement de Chimie Mole ´culaire, Institut de Chimie Mole ´culaire de Grenoble, Universite ´
Joseph Fourier (Grenoble I), 301 rue de la Chimie, BP 53, 38041 Grenoble Cedex 9, France
e-mail: mark.casida@ujf-grenoble.fr
M. Huix-Rotllant
Institut fu ¨r Physikalische und Theoretische Chimie, Universita ¨t Frankfurt am Main, Frankfurt,
Germany
e-mail: miquel.huix@gmail.com