  Impressive advances in the field of molecular spintronics allow one to study
electron transport through individual magnetic molecules embedded between
metallic leads in the purely quantum regime of single electron tunneling.
Besides fundamental interest, this experimental setup, in which a single
molecule is manipulated by electronic means, provides the elementary units of
possible forthcoming technological applications, ranging from spin valves to
transistors and qubits for quantum information processing. Theoretically, while
for weakly correlated molecular junctions established first-principles
techniques do enable the system-specific description of transport phenomena,
methods of similar power and flexibility are still lacking for junctions
involving strongly correlated molecular nanomagnets. Here we propose an
efficient scheme based on the ab initio construction of material-specific
Hubbard models and on the master-equation formalism. We apply this approach to
a representative case, the Ni$_2$ molecular spin dimer, in the regime of weak
molecule-electrode coupling, the one relevant for quantum-information
applications. Our approach allows us to study in a realistic setting many-body
effects such as current suppression and negative differential conductance. We
think that this method has the potential for becoming a very useful tool for
describing transport phenomena in strongly correlated molecules.
