  We describe and analyze a tight-binding model of single molecule magnets
(SMMs) that captures both the spin and spatial aspects of the SMM electronic
structure. The model generalizes extended Huckel theory to include the effects
of spin polarization and spin-orbit coupling. For neutral and negatively
charged Mn12 SMMs with acetate or benzoate ligands the model yields the total
SMM spin, the spins of the individual Mn ions, the magnetic easy axis
orientation, the size of the magnetic anisotropy barrier and the size of the
HOMO-LUMO gap consistent with experiment. For neutral molecules the predicted
spins and spatial locations of the HOMO are consistent with the results of
density functional calculations. For the total spin and location of the LUMO
density functional theory-based calculations yield varied results while the
present model yield results consistent with experiments on negatively charged
molecules. For Mn12 SMMs with thiolate- and methylsulphide-terminated benzoate
ligands (Mn12-Ph-Th) we find the HOMO to be located on the magnetic core of the
molecule, but (unlike for the Mn12 SMMs that have previously been studied
theoretically), we predict the LUMO and near LUMO orbitals of Mn12-Ph-Th to be
located on ligands. Therefore we predict that for these Mn12 SMMs resonant and
off-resonant coherent transport via near-LUMO orbitals, not subject to Coulomb
blockade, should occur. We propose that this effect can be used to identify
specific experimentally realized SMM transistors in which the easy axis and
magnetic moment are approximately parallel to the direction of the current
flow. We also predict effective spin filtering by these SMMs to occur at low
bias whether the transport is mediated by the HOMO that is on the magnetic core
of the SMM or by near LUMO orbitals located on the nominally non-magnetic
ligands.
