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[en] Highlights: • Hartree-Fock (HF) exchange effect is studied on the CO adsorption on B12N12. • By an increase in the %HF, the LUMO level is nearly constant. • While the HOMO level is strongly stabilized, expanding gap. • By the %HF increment the volume of the all structures decreased. • Sensitivity of the B12N12 is slightly increased toward CO molecule by %HF. We studied the effect of Hartree-Fock (HF) exchange percentage of a density functional on the adsorption properties and electronic sensitivity of the B12N12 nanocluster to CO molecule. It was found that by an increase in the %HF, the LUMO level is nearly constant while the HOMO level is strongly stabilized, expanding the HOMO-LUMO gap (Eg). Also, the volume of the all structures decreased and the sensitivity of the B12N12 is slightly increased to CO molecule. For the pristine B12N12 cluster, the B66 and B64 bonds are about 1.43 and 1.49 Å at 10% HF, and 1.23 and 1.26 Å at 100% HF, respectively. The HF exchange between 10–20% may predict an accurate Eg for the B12N12 system. We concluded that functionals with a large %HF such as M06-HF, and M06-2X may significantly overestimate the Eg, and bond strength. We obtained a parabolic relationship between the %HF and the adsorption energy of CO molecule on the B12N12 cluster. Also, an increase in the %HF predicts a larger charge transfer from the CO molecule to the cage.