Theoretical studies of the copper gyromagnetic factors for three novel Cu²⁺ coordination polymers with bi-triazole...

The copper electron paramagnetic resonance gyromagnetic factors are theoretically studied for three novel Cu²⁺ coordination polymers [Cu(XL)(NO₃ )₂ ]_n (1), {[Cu(XL)(4,4'-bpy)(NO₃ )₂ ]•CH₃ CN}_n (1a) and {[Cu(XL)₃ ](NO₃ )₂ •3.5H₂ O}_n (2) with bi-triazole ligand (XL) = N,N'-bicyclo[2.2.2]oct-7-ene-2,3,5,6-tetracarboxdiimide bi(1,2,4-triazole) from the high-order perturbation calculations of the g factors for a rhombically elongated octahedral 3d⁹ group. The order (1 ≤ 1a < 2) of g_z can be illustrated by the dominant second-order perturbation term roughly proportional to the square of the covalency factor N. g_x (and g_y ) relies on the combination of the contributions from N, cubic field parameter D_q , and axial elongation of the copper sites and exhibits the sequence (1 ≤ 2 < 1a). As regards the axiality (g_x  ≈ g_y ) of g factors, this is because the perpendicular rhombic contribution from the deviations of the bond lengths and bond angles for the planar ligands with respect to an ideal octahedron and that from the discrepancies between the crystal fields of the planar ligands O^2- and N^3- largely cancel each other. The present theoretical studies on the copper electron paramagnetic resonance g factors would be helpful to understand the structures and properties of some promising coordination polymers containing copper with the novel bi-triazole ligand XL.