Time-dependent density-functional theory and density-functional theory are applied to study the cis influence of the equatorial macrocycle in vitamin B(12) derivatives. A series of dicyanocobalt corrinoids, CN-[Co(III)-corrin]-CN, where the C(10)H of the corrin ring is replaced by different substituents, X, is considered. The calculated UV-visible absorption spectra, the charge distribution obtained from a Bader QTAIM analysis of the electron density, the CN stretch frequencies of the axial cyano ligands and the electron densities at some bond critical points are compared. The main absorption bands in the UV-visible spectra depend on the electron donating or withdrawing power of X, as assessed from its Hammett σ(p) constants. For X with a stronger electron donating power than H, the other properties do not change appreciably. However, when σ(p)(X) > σ(p)(H), these properties vary linearly with the electron withdrawing power of the substituent. This helps explain the experimental observation that substitution of the axial ligand is more difficult and proceeds more slowly with the increase of the electron withdrawing power of the C(10) substituent.