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Through investigate the origin of the relaxation barriers and the magneto-structural correlations in three(DMF)4MReⅣCl4(CN)2(DMF = dimethylformamide; M = MnⅡ(1),NiⅡ(2),CoⅡ(3))single-chain magnets(SCMs)in the intermediate regime between the Ising and the Heisenberg limits using density functional theory(DFT)andab initio methods,we succeeded in obtaining the expressions of the magnetic anisotropy and correlation energybarriers ΔAand Δξin terms of D,J and S.DFT calculations show that the antiferromagnetic ReⅣ-MnⅡcouplinginteractions decrease with the increase of the Mn-N-C angle,while the ferromagnetic ReⅣ-NiⅡcouplinginteractions increase with the increase of the Ni-N-C angle.But,the ReⅣ-CoⅡexchange interactions with thevariation of the Co-N-C angle are almost the same.The total energy barriers Δτof 1 and 2 mainly come from thecontribution of the transverse anisotropy of ReⅡ,while the MnⅡand NiⅡions only transmit the exchange couplingsbetween ReⅣand almost have no contributions.For 3,however,both of the ReⅣand CoⅡ ions have contributionsto the total energy barrier.Further calculations show that the influence of the ReⅣ-MnⅡexchange interactions onthe Δτof the models for 1 with the Mn-N-C angle ranging from 140° to 180 ° is very small,while the ReⅣ-M(M= NiⅡand CoⅡ)interactions have important influences on the Δτfor the models of 2 and 3 with the M-N-C angleranging from 140° to 180°.