Three p-tert-butylthiacalix[4]arene (H(4)TC4A)-supported Co-II compounds, [Co-4(TC4A)(N-3)(4)(N6H2)(CH3OH)](CH3OH)(2) (1), [Co-8(TC4A)(2)(N-3)(2)(N6H2)(2)(CH3COO)(4)(CH3OH)(4)](OH)(2)(CH3OH)(4) (2), and [Co-10(TC(4)A)(4)(N-3)(4)](CH3OH)(4) (3), have been solvothermally obtained in one pot and structurally characterized by single-crystal X-ray diffraction analyses, powder XRD, and IR spectroscopy. This work presents the first one-dimensional (1) cobalt cluster for the calixarene complexes and another two octanuclear (2) or decanuclear (3) cobalt clusters. In the structures of compounds 1 and 2, a novel N6H2 ligand formed by the in situ (2 + 3) cycloaddition of two azides was observed. Density functional theory (DFT) calculations give the heat of formation (2N(3)(-) + 2H(+) -> N6H2) and decomposition energy (N6N2 -> 3N(2) + H-2) of 677.47 and 124.85 kcaVmol, respectively. Furthermore, an intergradation was determined at the B3LYP/6-311++g(d,p) level for the formation of the N6H2 ligand. In addition, one TC4A ligand of a sandwich unit adopts a cone conformation, while the other adopts a pinched cone conformation in 3. The magnetic properties of these three compounds were influenced mainly by the orbital contributions of the distorted octahedral Co-II ions.