Electronically Excited States of Vitamin B12: Benchmark Calculations Including Time-Dependent Density Functional Theory and Correlated Ab Initio Methods

Abstract: Time-dependent density functional theory (TD-DFT) and correlated ab initio methods have been applied to the electronically excited states of vitamin B12 (cyanocobalamin or CNCbl). Different experimental techniques have been used to probe the excited states of CNCbl, revealing many issues that remain poorly understood from an electronic structure point of view. Due to its efficient scaling with size, TD-DFT emerges as one of the most practical tools that can be used to predict the electronic properties of these fairly complex molecules. However, the description of excited states is strongly dependent on the type of functional used in the calculations. In the present contribution, the choice of a proper functional for vitamin B12 was evaluated in terms of its agreement with both experimental results and correlated ab initio calculations. Three different functionals, i.e. B3LYP, BP86, and LC-BLYP, were tested. In addition, the effect of relative contributions of DFT and HF to the exchange-correlation functional was investigated as a function of the range-separation parameter, {\mu}. The issues related to the underestimation of charge transfer (CT) excitation energies by TD-DFT was validated by Tozer's L diagnostic, which measures the spatial overlap between occupied and virtual orbitals involved in the particular excitation. The nature of low-lying excited states was also analyzed based on a comparison of TD-DFT and ab initio results. Based on an extensive comparision against experimental results and ab initio benchmark calculations, the BP86 functional was found to be the most appropriate in describing the electronic properties of CNCbl. Finally, an analysis of electronic transitions and a new re-assignment of some excitations are discussed.