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.
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