Heterospin dinuclear systems

There are 21 combinations of heterospin dinuclear systems between SA = 1/2 and SB = 7/2 local spins. The zero-field energy levels of the coupled systems can be generated in the same way as in the previous case of homospin systems. The result is 

The exchange Hamiltonian in the presence of the magnetic field is enriched by the (spin) Zeeman term, hence 

In order to obtain the magnetic energy levels this Hamiltonian matrix must be diagonalised. Its order is N = (2SA + 1)(2SB + 1). 

Another possibility is to pass into the basis set of coupled spin functions / = 15, Ms) in which the Hamiltonian 

The Zeeman term is added as a perturbation and the magnetic energy levels are given by the diagonalisation of such a matrix. What we need is a transformation of the Zeeman term from the local spin functions into the basis set of molecular spin functions 

---

Isotropic exchange in heterospin dinuclear complexes differs from the homospin case in that the second-order van Vleck coefficients are also non-zero. The final formula for the magnetic susceptibility resembles the case of the narrow multiplets for mononuclear systems spin-orbit coupling can be formally substituted by spin-spin (exchange) coupling. However, the local atomic g-tensors should be properly combined into the molecular-state g-tensor. 

---