We propose a nonadiabatic time-dependent spin-density functional theory
(TDSDFT) approach for studying the single-electron excited states and the
ultrafast response of systems with strong electron correlations. The
correlations are described by the correlation part of the nonadiabatic
exchange-correlation (XC) kernel, which is constructed by using some exact
results for the Hubbard model of strongly correlated electrons. We demonstrate
that the corresponding nonadiabatic XC kernel reproduces main features of the
spectrum of the Hubbard dimer and infinite-dimensional Hubbard model, some of
which are impossible to obtain within the adiabatic approach. The theory may be
applied for DFT study of strongly correlated electron systems in- and
out-of-equilibrium, including the important case of nanostructures, for which
it leads to a dramatic reduction of necessary computational power
