  We present a theoretical study for the scanning tunneling microscopy (STM)
spectra of surface-supported magnetic nanostructures, incorporating strong
correlation effects. As concrete examples, we study Co and Mn adatoms on the
Cu(111) surface, which are expected to represent the opposite limits of the
Kondo physics and local moment behavior, using a combination of density
functional theory and both quantum Monte Carlo and exact diagonalization
impurity solvers. We examine in detail the effects of temperature $T$,
correlation strength $U$, and the impurity $d$ electron occupancy $N_d$ on the
local density of states. We also study the effective coherence energy scale,
i.e., the Kondo temperature $T_K$, which can be extracted from the STM spectra.
Theoretical STM spectra are computed as a function of the STM tip position
relative to each adatom. Because of the multi-orbital nature of the adatoms,
the STM spectra are shown to consist of a complicated superposition of orbital
contributions, with different orbital symmetries, self-energies and Kondo
temperatures. For the Mn adatom, which is close to half-filling, the STM
spectra are featureless near the Fermi level. On the other hand, the
quasiparticle peak for Co adatom gives rise to strongly position-dependent Fano
line-shapes.

Strongly Correlated Electrons