Theoretical Prediction of the Co−C Bond Strength in Cobalamins

The homolytic Co−C bond dissociation energy (BDE) is central to the understanding of the function of vitamin B 12, an important coenzyme of many proteins. We investigate why earlier density functional (B3LYP) estimations of the BDE in methylcobalamin have given so poor results (91−117 kJ/mol) compared to the experimental estimate (155 ± 13 kJ/mol). Improving the basis set increases the discrepancy, as does a proper treatment of basis set superposition error (∼3 kJ/mol) and inclusion of zero-point energy corrections (−21 kJ/mol). On the other hand, relativistic (+6 kJ/mol), solvation (+7 kJ/mol in water), and thermal corrections (+6 kJ/mol) increase the BDE. However, neither of these corrections can explain the discrepancy. Instead, the problem seems to be the B3LYP density functional, which gives a corrected BDE of 78 kJ/mol, whereas the density functional Becke−Perdew-86 method and second-order perturbation theory (MP2) give BDEs of 134−139 kJ/mol. A comparison with other methods indicates that the error comes from the Hartree−Fock exchange (∼40 kJ/mol) and the LYP functional (∼15 kJ/mol). The problem is not restricted to methylcobalamin but seems to be general for homolytic metal−carbon BDEs of transition metals in tetra-pyrrole-like systems.