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.
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