Magnetic coupling constants J for the complete structures of rare earth\|transition metal compounds:LGdCu(NO\-3)\-3·Me\-2CO(1,Gd(Ⅲ)Cu(Ⅱ)) and [Ce(C\-4H\-7ON)\-4(H\-2O)\-3][Cr(CN)\-6]·2H\-2O(2, Ce(Ⅲ)Cr(Ⅲ)) have been calculated by the combination of the broken\|symmetry approach with the spin project method under the DFT framework.The J value for 1 is a small number in absolute value -2 4cm -1 for calculation,3 5cm -1 for experimental measurement.The spin density distributions are in detail discussed on the basis of Mulliken population analysis,taking into account the coexistence of spin delocalization and spin polarization mechanisms.For 1,the spin distribution in the ground state may be understood as a result of the competition between two mechanisms:a spin delocalization from Cu(Ⅱ) and a spin polarization of Gd(Ⅲ),and the former is dominant.In the case of 2,both transition metal Cr(Ⅲ) and rare earth Ce(Ⅲ) display a spin polarization effect on the surrounding atoms,where a counteraction of the opposite polarization effects leads a low spin density on the bridging ligand C1N1.In the ground state of 2,the stronger polarization effect of Cr(Ⅲ) even causes the positive spin density on the adjacent bridging atom N1.
