Spin-Hamiltonian and density functional theory descriptions of spin exchange interactions

For a general spin dimer that has different numbers of unpaired electrons at the two spin sites, we examined the relationship between the spin exchange parameter J and the energy difference between the broken-symmetry and highest-spin states of the spin dimer on the basis of the spin-Hamiltonian Ĥ=−JŜ1⋅Ŝ2. The resulting relationship was shown to be a generalization of Noodleman’s formulas derived from the broken-symmetry method within density functional theory. We proposed a new method of calculating spin exchange parameters J within density functional theory on the basis of Slater’s transition state concept. The intrachain J values of magnetic solids A2MnF5 (A=Rb, Cs, NH4, Na, Li) were calculated by using the “transition-state” and Noodleman’s methods. The J values calculated by the transition-state method are in much better quantitative agreement with experiment.