We systematically studied the solvothermal reactions of transition-metal ions and H(4)abtc ligand and successfully isolated five metalorganic frameworks with various characterized tools, which are formulated as {[Mn-2(abtc)(DMA)(2.75)].1.25(DMA)}(n) (1), {[NH2(CH3)(2)][Co-3(COOH)(2.5)(abtc)(H2O)(2)](2).H2O}(n) (2), {[Zn-3(abtc)(1.5)(DMF)(3)].(1.75)(DMF)}(n) (3), {[Zn-2(abtc)(H2O)(0.75)(DMA)(0.5)].3(DMA).(H2O)}(n) (4), and {[Cd-2(abtc)(DMA)(2)].2(DMA)}(n) (5), (H4abtc = 3,3',5,5'-azobenzenetetracarboxylic acid, DMF = N,N-dimethylformamide, and DMA = N,N-dimethylacetamide). 1-5 all consist of {Mn(CO2)4}-type clusters and H(4)abtc ligands; however, they exhibit four distinct architectures resulting from different coordinated modes of H(4)abtc ligand. A pair of Mn(2+)ions in 1 forms a {Mn-2(CO2)(4)} cluster, which further results in the PtS-type three-dimensional (3D) framework. In 2, three independent Co2+ ions are bridged by COOH groups to afford a {Co-3} core, and {Co-3} cores are connected by abtc(2) to generate a ZSW1-type topology. Two types of {Zn-2(CO2)(4)} secondary building units in 3 linked by abtc(2) give the 3D NbO-type cage. When DMF is replaced by DMA and CH3OH, the scarce nou-type topology of 4 is obtained. And 5 is isomorphous to 1. Photoluminescence properties of 1-5 were characterized. Magnetic measurements demonstrate that dominant antiferromagnetic interactions exist in 1 and 2. In addition, 3 exhibits significant adsorption capability of CO2 and highly selective sorption of CO2 over N-2.