Direct air capture (DAC) technologies that extract carbon dioxide directly from the atmosphere using chemical processes have the potential to achieve zero or negative emissions and restore the atmospheric composition to an optimal level with respect to the CO2 concentration. However, before such technologies can be developed and applied energy-efficiently, we need to gain fundamental understanding of DAC chemistry. Here we report a structure-properties relationship study of DAC by crystallization of bis-iminoguanidine (BIG) carbonate salts. The study focuses on a series of basic BIG structures including the glyoxal-bis(iminoguanidine) prototype (GBIG) and its simple analogs methylglyoxal-bis(iminoguanidine) (MGBIG) and diacetyl-bis(iminoguanidine) (DABIG). The crystal structures of the BIGs and their carbonate salts have been analyzed by single-crystal X-ray and neutron diffraction to accurately measure key structural parameters including molecular conformations, hydrogen bonding, and p-stacking. Experimental measurements of key BIG properties, such as aqueous solubilities, and regeneration energies and temperatures, are complemented by first-principles calculations of lattice and hydration free energies, as well as free energies of reactions with CO2, and BIG regenerations. We find that minor structural modifications in the molecular structure of GBIG, such as substituting one or two hydrogen atoms with methyl groups, result in major changes in the crystal structures, induced by the increased conformational flexibility and steric hindrance. As a result, the corresponding aqueous solubilities within the series increase significantly, leading in turn to enhanced DAC performances.