Comparative computational analysis of binding energies between several divalent first-row transition metals (Cr²⁺, Mn²⁺, Fe ²⁺, Co²⁺, Ni²⁺, and Cu²⁺) and ligands (porphine, corrin, and TMC)

B3LYP density functional theory calculations were performed to quantify the binding affinities of six divalent first-row transition metals (Cr ²⁺, Mn²⁺, Fe²⁺, Co²⁺, Ni ²⁺, and Cu²⁺) for three well-known macrocyclic ligands (porphine, corrin, and 1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecane [TMC]). Our calculations show that, as expected from the neutral, monoanionic, and dianionic characters of the TMC, corrin, and porphine ligands, respectively, the binding energy increases in the order TMC <corrin <porphine. This is because a more anionic ligand gives rise to greater electrostatic stabilization upon interaction with the metal cations. For all ligands, the binding energy increases in the order Mn²⁺ <Cr²⁺ ∼ Fe²⁺ <Co²⁺ <Ni²⁺ <Cu²⁺. Single occupation of all five d orbitals in the high-spin Mn²⁺ complexes does not afford large stabilization due to either ligand-to-metal or metal-to-ligand charge transfer, thereby resulting in the minimum binding energies observed for Mn²⁺ among the six different metal ions considered.