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Microporous metal organic frameworks (MOFs) show promising application in several fields, but they often suffer from the weak robustness and stability after the removal of guest molecules. Here, three isostructural cationic metal-organic frameworks {[(Cu4Cl)(cpt)4(H2O)4]·3X·4DMAc·CH3OH·5H2O} (FJU-14, X = NO3, ClO4, BF4; DMAc = N,N'-dimethylacetamide) containing two types of polyhedral nanocages, one octahedron, and another tetrahedron have been synthesized from bifunctional organic ligands 4-(4H-1,2,4-triazol-4-yl) benzoic acid (Hcpt) and various copper salts. The series of MOFs FJU-14 are demonstrated as the first examples of the isostructural MOFs whose robustness, thermal stability, and CO2 capacity can be greatly improved via rational modulation of counteranions in the tetrahedral cages. The activated FJU-14-BF4-a containing BF4(-) anion can take CO2 of 95.8 cm(3) cm(-3) at ambient conditions with an adsorption enthalpy only of 18.8 kJ mol(-1). The trapped CO2 density of 0.955 g cm(-3) is the highest value among the reported MOFs. Dynamic fixed bed breakthrough experiments indicate that the separation of CO2/N2 mixture gases through a column packed with FJU-14-BF4-a solid can be efficiently achieved. The improved robustness and thermal stability for FJU-14-BF4-a can be attributed to the balanced multiple hydrogen-bonding interactions (MHBIs) between the BF4(-) counteranion and the cationic skeleton, while the high-density and low-enthalpy CO2 capture on FJU-14-BF4-a can be assigned to the multiple-point interactions between the adsorbate molecules and the framework as well as with its counteranions, as proved by single-crystal structures of the guest-free and CO2-loaded FJU-14-BF4-a samples.