In this manuscript the ability of CO and several CFCs to establish noncovalent carboncarbon interactions (termed as noncovalent carboncarbon bonding) with atmospheric gases CO, ethene and ethyne has been studied at the RI-MP2/def2-TZVPD level of theory. We have used several CFCs (CFCl, CFCl, CFCl and CHF) and the CO molecule as σ- and π-hole carbon bond donors (electron poor carbon atoms). As electron rich moieties we have used CO, ethene and ethyne (electron rich carbon atom bearing molecules). We have also used Bader's theory of "atoms in molecules" to further analyse and characterize the noncovalent interactions described herein. Finally, we have analyzed possible cooperativity effects between the noncovalent carboncarbon bonding and hydrogen bonding interactions in the case of ethyne.