TIME DEPENDENT DENSITY FUNCTIONAL THEORY ... - TDDFT.org

How to describe exchange and correlation
effects in the response properties of valence
electrons Answers from TDDFT and
Many-Boby Perturbation Theory
Lucia Reining
Laboratoire des Solides Irradiés, UMR 7642 CNRS/CEA, École Polytechnique, F-91128
Palaiseau, France
Today, one of the big challenges of theoretical condensed matter physics is to find ways for
describing accurately and efficiently the response of electrons to an external perturbation. In
fact, the knowledge of response functions allows one to directly derive spectra (such as absorption
or electron energy loss); moreover, response functions enter the description of correlation effects,
for example through the screened Coulomb interaction W in Hedin’s GW approximation to the
electron self-energy. Two main developments for the ab initio calculation of response functions of
both finite and infinite systems are, on one side, the solution of the Bethe-Salpeter equation (BSE),
and, on the other hand, Time-Dependent Density Functional Theory (TDDFT). Both approaches
are promising, but suffer from different shortcomings: the solution of the Bethe-Salpeter equation is
numerically very demanding, whereas for TDDFT, despite recent progress a generally reliable but
at the same time very efficient description of exchange-correlation effects has still to be developed.
Therefore, one would ideally like to combine the advantages of both pictures.
In this lesson, we will show that both approaches can be interpreted as containing the same
physics, but in a different world. We focus on their comparison by putting them on the same
footing. The meaning and importance of different contributions to the induced potentials will be
analyzed. The similarities will allow us to propose combinations of TDDFT and the BSE approach
that are leading to a class of exchange-correlation kernels which yield excellent spectra and are
potentially very efficient in numerical calculations.
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