Noncovalent interactions in 18 weakly bound binary complexes formed between either of the two end-on orientations of the CO molecule and the methylated carbon positive σ-hole associated with the hydrophobic part of the CH3-X molecules are exploited using the density functional theory to examine the physical chemistry of the recently introduced 'carbon bonds' (Phys. Chem. Chem. Phys., 2013, 15, 14377), where X = -NO2, -CN, -F, -Cl, -Br, -OH, -CF3, -CCl3, and -NH2. The two important types of interactions are identified as C···O and C···C, the latter has probably never studied before, and are found to be stabilized by charge-transfer delocalizations between the electron-acceptor and -donor natural bond orbitals of the interacting partners involved, unveiled using natural bond orbital analysis. Application of atoms in molecular theory revealed preferable quantum mechanical exchange-correlation energy channels and (3, -1) bond critical points (bcps) between the atoms of noncovalently bonded pairs in these complexes, in excellent agreement with the results of the noncovalent-interaction reduced-density-gradient (NCI-RDG) theory that revealed expected isosurfaces and troughs in the low density region of the RDG vs. sign(λ2)ρ plots. The dependencies of the C···O and C···C bcp charge densities on their corresponding local energy densities, as well as on their corresponding bond electron delocalization indices are found to exhibit nontrivial roles of these topological descriptors to explain the stabilities of the investigated binary complexes. Moreover, the vibrational red- and blue-shifts in the CO bond stretching frequencies, and concomitant elongations and contractions of the corresponding bond lengths, both with respect to the monomer values, are observed upon the formation of the C···O- and C···C-bonded complexes, respectively. The increase and decrease in the complex dipole moments, relative to the sum of their respective monomer values, are found to be a characteristic that separates the aforementioned red- and blue-shifted interactions. In analogy with dihydrogen bonding, as well as that with the charge and electrostatic surface potential model descriptions, we suggest the C···C interactions to be referred to as dicarbon bonds.