Ab initio quantum mechanics methods were applied to investigate the hydrogen bonds between CO and HNF2, H2NF, and HNO. We use the Hartree-Fock, MP2, and MP4( SDQ) theories with three basis sets 6-311++ G(d,p), 6-311++G(2df, 2p), and AUG-cc-pVDZ, and both the standard gradient and counterpoise-corrected gradient techniques to optimize the geometries in order to explore the effects of the theories, basis sets, and different optimization methods on this type of H bond. Eight complexes are obtained, including the two types of (CH)-H-center dot center dot center dot-N and (OH)-H-center dot center dot center dot-N hydrogen bonds: (OCHNF2)-H-center dot center dot center dot(C-s), (OCH2NF)-H-center dot center dot center dot(C-s and C-1), and (OCHNO)-H-center dot center dot center dot(C-s), and (COHNF2)-H-center dot center dot center dot(C-s), (COH2NF)-H-center dot center dot center dot(C-s and C-1), and (COHNO)-H-center dot center dot center dot(C-s). The vibrational analysis shows that they have no imaginary frequencies and are minima in potential energy surfaces. The N-H bonds exhibit a small decrease with a concomitant blue shift of the N-H stretch frequency on complexation, except for (OCHNF2)-H-center dot center dot center dot and (OCH2NF)-H-center dot center dot center dot(C-1), which are red-shifting at high levels of theory and with large basis sets. The (OH)-H-center dot center dot center dot-N hydrogen bonds are very weak, with 0 K dissociation energies of only 0.2-2.5 kJ/mol, but the (CH)-H-center dot center dot center dot-N hydrogen bonds are stronger with dissociation energies of 2.7-7.0 kJ/mol at the MP2/AUG-ccpVDZ level. It is notable that the IR intensity of the N-H stretch vibration decreases on complexation for the proton donor HNO but increases for HNF2 and H2NF. A calculation investigation of the dipole moment derivative leads to the conclusion that a negative permanent dipole moment derivative of the proton donor is not a necessary condition for the formation of the blue-shifting hydrogen bond. Natural bond orbital analysis shows that for the (CH)-H-center dot center dot center dot-N hydrogen bonds a large electron density is transferred from CO to the donors, but for the (OH)-H-center dot center dot center dot-N hydrogen bonds a small electron density transfer exists from the proton donor to the acceptor CO, which is unusual except for (COH2NF)-H-center dot center dot center dot(C-s). From the fact that the bent hydrogen bonds in OC(CO)(H2NF)-H-center dot center dot center dot(C-s) are quite different from those in the others, we conclude that a greatly bent H-bond configuration shall inhibit both hyperconjugation and rehybridization.