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##### Time-Dependent Density Functional Theory

**Authors**: M.A.L. Marques, C. Ullrich, F. Nogueira, A. Rubio, K. Burke, and E.K.U. Gross (Eds.)

**Ref.**: Lecture Notes in Physics (Springer, Berlin) **706** (2006)

**Abstract**: The year 2004 was a remarkable one for the growing field of time-dependent density
functional theory (TDDFT). Not only did we celebrate the 40th anniversary of the
Hohenberg-Kohn paper, which had laid the foundation for ground-state
density functional theory (DFT), but it was also the 20th anniversary of the work by
Runge and Gross, establishing a firm footing for the time-dependent theory.
Because the field had grown to such prominence, and had spread to so many areas
of science (from materials to biochemistry), we felt that a volume dedicated
to TDDFT was most timely.

TDDFT is based on a set of ideas and
theorems quite distinct from those governing ground-state DFT, but employing similar techniques.
It is far more than just applying ground-state
DFT to time-dependent problems, as it involves its own exact theorems and new and
different density functionals.
Presently, the most popular application is the extraction of electronic excited-state properties,
especially transition frequencies. By applying TDDFT after the ground state of
a molecule has been found, we can explore and understand the complexity of its
spectrum, thus providing much more information about the species.
TDDFT is having especially strong impact in the photochemistry of biological
molecules, where the molecules are too large to be handled by traditional
quantum chemical methods, but are too complex to be understood with simple
empirical frontier orbital theory.

Today, the use of TDDFT is continuously growing, in
all areas where interactions are important but direct
solution of the Schrodinger equation is too demanding.
New and exciting applications are beginning to emerge,
from ground-state energies extracted from TDDFT to transport through single molecules,
to high-intensity laser and non-equilibrium phenomena, to
non-adiabatic excited-state
dynamics, to low-energy electron scattering.
In each case, the present approximations were
applied, and found to work well for some properties, but occasionally fail for others.
Thus the search for more accurate, reliable approximations will continue, and
over time, should attain the same maturity as present ground-state DFT.

So, whether you are a physicist calculating optical absorption of a metal cluster,
or a chemist trying to determine the HOMO and LUMO for a chromophore,
we hope you will try TDDFT, and be pleasantly surprised at the usefulness
of the results.
And may the force (or at least, a good functional) be with you.

**URL**: www.springer.com