  Within the framework of time-dependent density functional theory combined
with the Korringa-Kohn-Rostoker Green function formalism, we present a real
space methodology to investigate dynamical magnetic excitations from
first-principles. We set forth a scheme which enables one to deduce the correct
effective Coulomb potential needed to preserve the spin-invariance signature in
the dynamical susceptibilities, i.e. the Goldstone mode. We use our approach to
explore the spin dynamics of 3d adatoms and different dimers deposited on a
Cu(001) with emphasis on their decay to particle-hole pairs.
