  We study the behavior of the magnetization and the magnetic susceptibility of
molecular magnets with complex bridging structure. Our computations are based
on a post-Hartree-Fock method accounting for the intricate network of
interatomic bonds and an effective spin-like Hamiltonian that captures the
essential magnetic features of magnetic molecules. The devised method and the
constructed Hamiltonian are further employed to characterize the magnetic
properties of the molecular magnet Ni$_4$Mo$_{12}$. The obtained results
reproduce both quantitatively and qualitatively the main features of the
magnetic spectrum. Furthermore, the computations for the magnetization and the
low-field susceptibility are in very good agreement with their experimental
counterparts. In this respect, they improve upon the results obtained with
conventional Heisenberg models.
