Density functional theory calculations were performed to study the adsorption behavior of hazardous gases (NH3, CO2, CO, and NO) on twelve adsorbents (cyclo[18]carbon (C18) and its analogues Al9N9, B9N9, C6B6N6, C12B3N3, C14B2N2, d-C14B2N2, C16BN, C17Si; cyclo[12]carbon (C12) and its analogues Al6N6 and B6N6). The molecular electrostatic potential (MESP) maps of C18 revealed its polyynic structure with alternating electron-rich and electron-deficient regions. The most negative-valued MESP point (Vmin) indicates that the replacement of carbon atoms of C18/C12 by BN/AlN/Si units increases the electron-rich environment in the molecules. In general, NH3 and CO2 are found to be physisorbed on C18/C12 and its analogues. An important result is that the Vmin of C18/C12 and its analogues is linearly correlated with the NH3 and CO2 adsorption energies. The quantum theory of atoms in molecules (QTAIM) results indicate that the interactions of NH3 and CO2 with C18/C12 and its analogues are non-covalent in nature. In general, CO and NO are found to be chemisorbed on C18/C12 and its analogues. In contrast to the cases of NH3 and CO2 adsorption, the Vmin of C18/C12 and its analogues is generally inversely related to the CO and NO adsorption energies. The QTAIM results indicate the strong covalent character of the bonding for CO/C18, CO/C6B6N6, CO/d-C14B2N2, CO/C12, NO/C18, NO/C17Si, and NO/C12 systems. The adsorption process significantly influenced the chemical potential and/or hardness, especially for CO– and NO-adsorbed C18/C12 and its analogues.