Increased concentrations Of CO2 in the atmosphere contribute to global climate change. Improved methods are needed for removing CO2 from the flue gas of power plants and/or directly from the atmosphere. A macrocyclic amiclourea recently synthesized by Brooks et al., when dissolved in DMSO along with tetrabutyl ammonium fluoride, removes CO2 from the atmosphere to form a complex in which a CO3 group is held by a number of O-H-N bonds within the bowl-shaped cavity of the macrocycle. We have calculated the structure, stability, and vibrational spectra of this complex, using density functional techniques and polarized double-zeta basis sets. Both basis set superposition errors and polarizable continuum effects on the complex geometry and stability have been evaluated. The calculated structure is in good agreement with experiment. We predict that this CO3-2 complex (and its HCO3- analogue) have larger formation constants by several orders of magnitude than the analogue complex of the amiclourea macrocycle with Cl- (particularly in DMSO solution compared to aqueous solution). Our calculations also indicate that the CO3-2 and HCO3- complexes can be distinguished by C-13 NMR. The CO3-2 complex also has a distinctive H-N stretch, perturbed by the H-bonding to the CO3 group. We also calculate the CO3-2 complex to absorb within the visible region, unlike the free macrocycle or typical metal carbonates. Macrocycles of this type may provide a useful route to the absorption of atmospheric CO2. Our calculations also indicate that changing the solvent from DMSO to water and/or heating the complex will be an efficient way to decompose it to release CO2.