("αββα", MS = 0). Each BS determinant is described by an MS value, rather than S, as this is not a spin eigenfunction. The relative energy of each BS determinant from the HS state was used to calculate a set of Jij values for the Sz-only (Ising) Hamiltonian. The calculated exchange coupling constants are used to diagonalize the full HDvV Hamiltonian. The outcome of this step provides the resultant spin ladder and spin projection coefficients. The full details of the procedure have been described extensively in the literature and has been used successfully for many exchange-coupled Mn systems.