Description of molecular nanomagnets by the multi-orbital Hubbard model with correlated hopping

We present a microscopic description of molecular magnets by the multi-orbital Hubbard model, which includes the correlated hopping term, i.e. the dependence of electron hopping amplitude between orbitals on the degree of their occupancy. In the limit of large Coulomb on-site interaction, we derived the spin Hamiltonian using the perturbation theory. The magnetic coupling constant between two ions we determined in two different ways: a)from the expression obtained in the perturbation calculus and b)from the analysis of distances between the lowest levels of the energy spectrum obtained by the diagonalization of the multi-orbital Hubbard model. The procedure we use can be applied to various nanomagnets, but the final calculations we performed for the molecular ring $Cr_8$. We showed that the correlated hopping can reduce the antiferromagnetic exchange between ions, what is essential for a proper description of $Cr_8$.