We study the electronic coupling between two silver nanoparticles using ab initio density functional theory for real atoms. We show that the electronic coupling depends on both the gap size of the dimer system and the relative orientation of the particles. As the two particles are separated from touching contact, the dimer undergoes a bond-breaking step, which also establishes the striking existence of an optimal gap size defined by a maximal static polarizability of the dimer. For some dimers, the electronic coupling before the bond breaking can be strong enough to give rise to a net magnetic moment of the dimer, even though the isolated particles are nonmagnetic. These findings may be instrumental in understanding and controlling the physical and chemical properties of closely packed nanoparticle aggregates.