  We consider tunneling transport through a Mn$_{12}$ molecular magnet using
spin density functional theory. A tractable methodology for constructing
many-body wavefunctions from Kohn-Sham orbitals allows for the determination of
spin-dependent matrix elements for use in transport calculations. The tunneling
conductance at finite bias is characterized by peaks representing transitions
between spin multiplets, separated by an energy on the order of the magnetic
anisotropy. The energy splitting of the spin multiplets and the spatial part of
their many-body wave functions, describing the orbital degrees of freedom of
the excess charge, strongly affect the electronic transport, and can lead to
negative differential conductance.
