Description of molecular nanomagnets by the multiorbital Hubbard model with correlated hopping

We present a microscopic description of molecular magnets by the multiorbital Hubbard model, which includes the correlated hopping term, i.e., the dependence of the electron hopping amplitude between orbitals on the degree of their occupancy. In the limit of large Coulomb on-site interaction, we derive the spin Hamiltonian using the perturbation theory. We determine the magnetic coupling constant between two ions 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 diagonalization of the multiorbital Hubbard model. The procedure we use can be applied to various nanomagnets, but we perform the final calculations for the molecular ring ${\text{Cr}}₈$. We show that the correlated hopping can reduce the antiferromagnetic exchange between ions, which is essential for a proper description of ${\mathrm{Cr}}₈$.