  The electronic structure of a monolayer of single-molecule magnets Mn$_{12}$
on a Au(111) surface is studied using spin-polarized density-functional theory.
The Mn$_{12}$ molecules are oriented such that the magnetic easy axis is normal
to the surface, and the terminating ligands in the Mn$_{12}$ are replaced by
thiol groups (-SH) where the H atoms are lost upon adsorption onto the surface.
This sulfur-terminated Mn$_{12}$ molecule has a total magnetic moment of 18
$\mu_B$ in the ground state, in contrast to 20$\mu_B$ for the standard
Mn$_{12}$. The Mn$_{12}$ molecular orbitals broaden due to the interaction of
the molecule with the gold surface and the broadening is of the order of 0.1
eV. It is an order of magnitude less than the single-electron charging energy
of the molecule so the molecule is weakly bonded to the surface. Only electrons
with majority spin can be transferred from the surface to the sulfur-terminated
Mn$_{12}$ since the gold Fermi level is well above the majority lowest
unoccupied molecular orbital (LUMO) but below the minority LUMO. The amount of
the charge transfer is calculated to be 1.23 electrons, dominated by the tail
in the electronic distribution of the gold surface. A calculation of level
shift upon charging provides 0.28 electrons being transferred. The majority of
the charge transfer occurs at the S, C, and O atoms close to the surface. The
total magnetic moment also changes from 18 $\mu_B$ to 20 $\mu_B$, due to
rearrangements of the magnetic moments on the S and Mn atoms upon adsorption
onto the surface. The magnetic anisotropy barrier is computed including
spin-orbit interaction self-consistently in density-functional theory. The
barrier for the Mn$_{12}$ on the gold surface decreases by 6 K in comparison to
that for an isolated Mn$_{12}$ molecule.
