Three new zinc(II) complexes [Zn(H2L3)2(H2O)3] (Zn2), [Zn(H3L2a)(H2O)3]n (Zn3) (H3L2a = 2,4-diiodo-5-(2-(2,4,6-trioxotetrahydropyrimidin-5(2H)-ylidene)hydrazineyl)isophthalate) and [Zn(HL4)(DMF)(H2O)]n (Zn4) were synthesized by the reaction of Zn(II) salts with 5-(2-(2,4-dioxopentan-3-ylidene)hydrazineyl) isophthalic acid (H3L3), 2,4,6-triiodo-5-(2-(2,4,6-trioxotetrahydropyrimidin-5(2H)-ylidene)hydrazineyl) isophthalic acid (H5L2) (in the presence of NH2OH·HCl) and 5-(2-(2,4-dioxopentan-3-ylidene)hydrazineyl)-2,4,6-triiodoisophthalic acid (H3L4), respectively. According to the X-ray structural analysis, the intramolecular resonance-assisted hydrogen bond ring remains intact, with N···O distances of 2.562(5) and 2.573(5) Å in Zn2, 2.603(6) Å in Zn3, and 2.563(8) Å in Zn4. In the crystal packing of Zn3, the cooperation of I···O and I···I types of halogen bonds between tectons leads to a one-dimensional supramolecular polymer, while I···O interactions aggregate 1D chains of coordination polymer Zn4. These new complexes (Zn2, Zn3, and Zn4) and known [Zn(H3L1)(H2O)2]n (Zn1) (H3L1 = 5-(2-(2,4,6-trioxotetrahydropyrimidin-5(2H)-ylidene) hydrazineyl)isophthalate), {[Zn(H3L1)(H2O)3]·3H2O}n (Zn5), [Cd(H3L1)(H2O)2]n (Cd1), {[Cd(HL3)(H2O)2(DMF)]·H2O}n (Cd2), [Cd(H3L3)]n (Cd-3), {[Cd2(μ-H2O)2(μ-H2L4)2(H2L4)2]·2H2O}n (Cd4), and {[Cd(H3L1)(H2O)3]·4H2O}n (Cd5) were tested as catalysts in the cycloaddition reaction of CO2 with epoxides in the presence of tetrabutylammonium halides as the cocatalyst. The halogen-bonded catalyst Zn4 is the most efficient one in the presence of tetrabutylammonium bromide by affording a high yield (85-99%) of cyclic carbonates under solvent-free conditions after 48 h at 40 bar and 80 °C.