Assessing Electronically Excited States of Cobalamins …
231
mated (Fig. 5). The underestimation correlates with the percentage of Hartree–Fock
(HF) exchange that is included in calculations. It has been suggested that the neglect
of dispersion interactions at shorter Co–C Me bond lengths is a contributing factor to
the poor performance of the hybrids. Alternatively, pure functionals give much better agreement with experiment, and addition of dispersion corrections tends to bring
the predicted BDEs to even closer agreement with experiment. The best-performing
DFT functionals, with the 6-311++G** basis set, were B97-D and BP86 corrected for
dispersion as these predicted Co–C Me BDE to be 35 and 40 kcal/mol, respectively. A
further conclusion of this study is that high-level calculations such as CASSCF and
CASPT2 seem to be far too expensive for any realistic study of cobalamins because
appropriate active space would be prohibitively large.
Previously, the Co–C bond strength was studied in the context of determining why
B3LYP, the density functional of choice for an enormous majority of computational
studies, performed so poorly in determining BDE in MeCbl [34]. It was suggested
that this error comes from the HF exchange and the LYP functional. This study also
indicated that BP86 is an appropriate functional to use for the analysis of cobalamins,
especially over MP2 and B3LYP, citing several reasons. BP86 is much less expensive
than MP2. There is a smaller basis set dependence for DFT methods than for ab initio
methods and finally BP86 gives better agreement with experimentally determined
structural details than B3LYP and MP2. It was further suggested that the B3LYP
functional is a problematic choice in general for determining homolytic metal-carbon
BDEs in tetrapyrroles and other highly conjugated systems.
Co–C BDE was also studied in AdoCbl [36, 45]. These benchmark studies yielded
similar conclusions to those where MeCbl was the cofactor under study. Namely,
it was found that BP86 is an appropriate functional to predict BDE in AdoCbl.
B3LYP significantly underestimates the strength of the Co–C Ado bond. Beyond the
poor performance of B3LYP in predicting Co–C Ado BDE, this functional does not
properly reproduce axial bond distances from crystal structures in cobalamins in
the base-on form. It was also shown that B3LYP underestimates the energies of the
bonding orbitals and overestimates the energies of the antibonding orbitals.
8 Benchmarks for Electronically Excited States
In order to use calculations to aid in the interpretation of experimental spectroscopic
data, benchmarks for electronically excited states within the TD-DFT framework
are critical. Results from benchmarks can be relied upon to choose the proper functional that will ensure meaningful conclusions. These have been performed for both
CNCbl [38] and MeCbl [28, 39, 41]. In particular for CNCbl, which has been referred
to as the paradigm system for the evaluation of excited states of cobalamins, a benchmark analysis targeting the manifold of low-lying excited states was performed [38].
TD-DFT calculations were compared with high-level ab initio calculations and experimental results in order to analyze the nature of the low-lying excited states. The
performance of three density functionals, B3LYP, BP86, and LC-BLYP, represent-
231
mated (Fig. 5). The underestimation correlates with the percentage of Hartree–Fock
(HF) exchange that is included in calculations. It has been suggested that the neglect
of dispersion interactions at shorter Co–C Me bond lengths is a contributing factor to
the poor performance of the hybrids. Alternatively, pure functionals give much better agreement with experiment, and addition of dispersion corrections tends to bring
the predicted BDEs to even closer agreement with experiment. The best-performing
DFT functionals, with the 6-311++G** basis set, were B97-D and BP86 corrected for
dispersion as these predicted Co–C Me BDE to be 35 and 40 kcal/mol, respectively. A
further conclusion of this study is that high-level calculations such as CASSCF and
CASPT2 seem to be far too expensive for any realistic study of cobalamins because
appropriate active space would be prohibitively large.
Previously, the Co–C bond strength was studied in the context of determining why
B3LYP, the density functional of choice for an enormous majority of computational
studies, performed so poorly in determining BDE in MeCbl [34]. It was suggested
that this error comes from the HF exchange and the LYP functional. This study also
indicated that BP86 is an appropriate functional to use for the analysis of cobalamins,
especially over MP2 and B3LYP, citing several reasons. BP86 is much less expensive
than MP2. There is a smaller basis set dependence for DFT methods than for ab initio
methods and finally BP86 gives better agreement with experimentally determined
structural details than B3LYP and MP2. It was further suggested that the B3LYP
functional is a problematic choice in general for determining homolytic metal-carbon
BDEs in tetrapyrroles and other highly conjugated systems.
Co–C BDE was also studied in AdoCbl [36, 45]. These benchmark studies yielded
similar conclusions to those where MeCbl was the cofactor under study. Namely,
it was found that BP86 is an appropriate functional to predict BDE in AdoCbl.
B3LYP significantly underestimates the strength of the Co–C Ado bond. Beyond the
poor performance of B3LYP in predicting Co–C Ado BDE, this functional does not
properly reproduce axial bond distances from crystal structures in cobalamins in
the base-on form. It was also shown that B3LYP underestimates the energies of the
bonding orbitals and overestimates the energies of the antibonding orbitals.
8 Benchmarks for Electronically Excited States
In order to use calculations to aid in the interpretation of experimental spectroscopic
data, benchmarks for electronically excited states within the TD-DFT framework
are critical. Results from benchmarks can be relied upon to choose the proper functional that will ensure meaningful conclusions. These have been performed for both
CNCbl [38] and MeCbl [28, 39, 41]. In particular for CNCbl, which has been referred
to as the paradigm system for the evaluation of excited states of cobalamins, a benchmark analysis targeting the manifold of low-lying excited states was performed [38].
TD-DFT calculations were compared with high-level ab initio calculations and experimental results in order to analyze the nature of the low-lying excited states. The
performance of three density functionals, B3LYP, BP86, and LC-BLYP, represent-