  Dynamical Mean-Field Theory (DMFT) has established itself as a reliable and
well-controlled approximation to study correlation effects in bulk solids and
also two-dimensional systems. In combination with standard density-functional
theory (DFT) it has been successfully applied to study materials in which
localized electronic states play an important role. There are several evidences
that for extended systems this DMFT+DFT approach is more accurate than the
traditional DFT+U approximation, particularly because of its ability to take
into account dynamical effects, such as the time-resolved double occupancy of
the electronic orbitals. It was recently shown that this approach can also be
successfully applied to study correlation effects in nanostructures. Here, we
present a brief review of the recently proposed generalizations of the DFT+DMFT
method. In particular, we discuss in details our recently proposed DFT+DMFT
approach to study the magnetic properties of nanosystems [V. Turkowski, A.
Kabir, N. Nayyar and T. S Rahman, J. Phys.: Condens. Matter (Fast Track) 22,
462202 (2010)] and present its application to small (up to five atoms) Fe and
FePt clusters. We demonstrate that being a mean-field approach, DMFT produces
meaningful results even for such small systems. We compare our results with
those obtained using DFT+U and find that, as in the case of bulk systems, the
latter approach tends to overestimate correlation effects in nanostructures.
Finally, we discuss possible ways to farther improve the nano-DFT+DMFT
approximation and to extend its application to molecules and nanoparticles on
substrates and to nonequilibrium phenomena.
