  We study the role of static and dynamical Coulomb correlation effects on the
electronic and magnetic properties of individual Mn, Fe and Co adatoms
deposited on the CuN surface. For these purposes, we construct a realistic
Anderson model, solve it by using finite-temperature exact diagonalization
method and compare the calculated one-particle spectral functions with the
LDA+$U$ densities of states. In contrast to Mn/CuN and Fe/CuN, the cobalt
system tends to form the electronic excitations at the Fermi level. Based on
the calculated magnetic response functions, the relative relaxation times for
the magnetic moments of impurity orbitals are estimated. To study the effect of
the dynamical correlations on the exchange interaction in nanoclusters, we
solve the two-impurity Anderson model for the Mn dimer on the CuN surface. It
is found that the experimental exchange interaction can be well reproduced by
employing $U$=3 eV, which is two times smaller than the value used in static
mean-field LDA+$U$ calculations. This suggests on important role of dynamical
correlations in the interaction between adatoms on a surface.
