TD-DFT insight into photodissociation of the Co-C bond in coenzyme B12

Coenzyme B12 (AdoCbl) is one of the most biologically active forms of vitamin B12, and continues to be a topic of active research interest. The mechanism of Co-C bond cleavage in AdoCbl, and the corresponding enzymatic reactions are however, not well understood at the molecular level. In this work, time-dependent density functional theory (TD-DFT) has been applied to investigate the photodissociation of coenzyme B12. To reduce computational cost, while retaining the major spectroscopic features of AdoCbl, a truncated model based on ribosylcobalamin (RibCbl) was used to simulate Co-C photodissociation. Equilibrium geometries of RibCbl were obtained by optimization at the DFT/BP86/TZVP level of theory, and low-lying excited states were calculated by TD-DFT using the same functional and basis set. The calculated singlet states, and absorption spectra were simulated in both the gas phase, and water, using the polarizable continuum model (PCM). Both spectra were in reasonable agreement with experimental data, and potential energy curves based on vertical excitations were plotted to explore the nature of Co-C bond dissociation. It was found that a repulsive 3(σCo−C → σ*Co−C) triplet state became dissociative at large Co-C bond distance, similar to a previous observation for methylcobalamin (MeCbl). Furthermore, potential energy surfaces (PESs) obtained as a function of both Co-CRib and Co-NIm distances, identify the S1 state as a key intermediate generated during photoexcitation of RibCbl, attributed to a mixture of a metal-to-ligand charge transfer (MLCT) and a σ bonding-ligand charge transfer (SBLCT) states.

when excited at 400 nm as a result of partitioning between Co-C homolysis and heterolytic cleavage. Heterolytic bond cleavage products were identified as a metal-to-ligand charge transfer (MLCT) state upon excitation at 400 nm (Cole et al., 2002), and only metastable cob(III)alamin for 520 nm (Shiang et al., 1999). In contrast, photoexcitation of AdoCbl produces wavelength independent photoproducts at 400 and 520 nm, that correspond to an intermediate state observed as decay over a 14 ps time scale, of two relaxed radical pairs. These radical pairs were characterized as cob(II)alamin and an adenosyl-based radical. This observation corresponds to Co-C homolysis, or a trapped excited state with a weak Co-C bond (Shiang et al., 1999). Furthermore, although the photoproducts of AdoCbl were found to be insensitive to excitation wavelength, environmental effects have been shown to influence its photophysics (Yoder et al., 2001).
The photodissociation of Co-C in cobalamins has also been investigated computationally by means of time-dependent density functional theory (TD-DFT) (Jaworska et al., 2007;Lodowski et al., 2009Lodowski et al., , 2011. In the case of MeCbl, the key metastable photoproduct present during the photolysis process was identified as an S 1 state with MLCT character (Jaworska et al., 2007), in accordance with experiment. Further analysis of the electron density map of S 1 and S 0 states indicated an additional contribution from σ bond, revealing that σ bonding-ligand charge transfer (SBLCT) character was mixed with MLCT . To explain the nature of the Co-C photo-scission in MeCbl, the presence of a repulsive 3 (σ Co−C → σ * Co−C ) triplet state was proposed based on TD-DFT analysis of electronically excited states along the stretched Co-C bond. The same approach has also been applied to EtCbl, and the presence of a repulsive triplet state was used to explain the energetic differences between MeCbl and EtCbl, as well as why the photolysis mechanism is wavelength dependent in the case of MeCbl .
A similar study was performed for vitamin B 12 (CNCbl) to explain its photostability and the nature of its low-lying excited states . Potential energy curves for lowlying excited states along the Co-CN coordinate reveal that CNCbl has a repulsive triplet state, but is not dissociative. It was found that the CNCbl potential energy surface (PES) of the S 1 state, when represented as a function of axial distances, had two energy minima. The first minima was located above the S 0 minimum as an excitation with mixed π → π * /MLCT/SBLCT character, similar to the alkylcobalamin S 1 state. The second minimum was found at longer Co-N Im and Co-CN bond lengths, and was characterized as ligand-to-metal charge-transfer (LMCT) excitation.
Interestingly, the Co-OH bond in hydroxycobalamin (HOCbl) is dissociative upon light exposure above 300 nm (Shell and Lawrence, 2011), although it is among the non-alkylcobalamins. Photolysis of HOCbl has also been studied by TD-DFT, by focusing on the Co-OH cleavage . TD-DFT results suggest that the photoactivity of HOCbl is mediated by the repulsive 1 (n+d Co → σ * Co−OH ) singlet state whose energy drops with Co-OH bond stretching, to yield the cob(II)alamin and hydroxyl radical.
Although spectroscopic techniques have been extensively applied to alkyl-and non-alkylcobalamins, the mechanism of Co-C bond dissociation is still not well understood. The aim of this study is to provide the further insight into the photodissociation mechanism of the Co-C bond in the coenzyme B 12 (AdoCbl, Figure 1) by TD-DFT computations. To accomplish this we employed the simplified structural model of AdoCbl, (RibCbl, Figure 1), in which the Ado group was simplified to a ribosyl (Rib) moiety. The intermediates involved in the photodissociation process were identified by systematically analyzing the nature of low-lying excited states as well as their changes along stretched Co-C Rib coordinate. Finally, in order to provide a more accurate picture of key intermediates, the PESs of ground state and low-lying singlet states were analyzed as a function of both Co-C Rib and Co-N Im axial bond distances.
Vertical excitations were obtained in both the gas phase and water solvent. Low-lying excited states were calculated from their corrdepsonding ground state geometries by TD-DFT, and both singlet and triplet excitations have been calculated to forty states (Tables S1-S4). To simulate the photodissociation process of RibCbl, the Co-C Rib bond was stretched with a step size of 0.05 Å and the DFT/BP86/TZVP optimization was repeated at each point, followed by TD-DFT calculations at the BP86/TZVP level of theory. In addition, PESs of the ground state and key singlet states were plotted by stretching axial bonds in step of 0.05 Å. At each grid point, the geometry was optimized by DFT/BP86/TZVP, and the vertical excitation was obtained for S 1 and S 2 states.

STRUCTURAL MODEL OF RibCbl
The initial molecular structure of RibCbl was obtained from the high-resolution crystal structure of AdoCbl (Ouyang et al., 2004). The full structure of AdoCbl (Figure 1) consists of Co III equatorially cooridinated via four nitrogen atoms to the corrin ring. The lower axial ligand, dimethylbenzimidazole (DBI) coordinates to the central Co atom via N ax , with the other N atom bound to the side of the corrin plane by a nucleotide loop. In the actual AdoCbl structure, the upper Ado ligand is 5 -deoxy-5 -adenosine.
To reduce computational cost, calculations were performed using the simplified structural model of RibCbl, denoted Im-[Co III (corrin)]-Rib + for consistency with previous studies (Jaworska et al., 2007;Lodowski et al., 2009Lodowski et al., , 2011. In the RibCbl model (see Figure 1), the Ado group was simplified to ribosyl (Rib) by omitting the purine ring, leaving only ribose in the upper corrin plane. The corrin ring was truncated by replacing the side chains with hydrogen atoms, and DBI with imidazole (Im). The resulting overall charge of the system was +1 due to removal of the PO − 4 nucleotide loop from below the plane. Previous studies have demonstrated that such simplified structural models accurately reproduce the electronic and spectroscopic properties of the full B 12 structure (Jaworska and Lodowski, 2003;Ryde, 2003, 2009;Stich et al., 2003Stich et al., , 2004Jaworska et al., 2005Jaworska et al., , 2007Kuta et al., 2006Kuta et al., , 2009Liptak and Brunold, 2006;Kozlowski et al., 2007Kozlowski et al., , 2012Rovira and Kozlowski, 2007;Galezowski et al., 2008;Lodowski et al., 2009Lodowski et al., , 2011. More inclusive structural models

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February 2014 | Volume 1 | Article 41 | 3 of coenzyme B 12 will be employed in future studies utilizing multiple levels of theory. Optimized RibCbl structures correspond to equilibrium geometries where Co-C Rib = 2.02 Å and Co-N Im = 2.21 Å in the gas phase, and Co-C Rib = 2.02 Å and Co-N Im = 2.19 Å in water (PCM). Optimized axial bond lengths are in reasonable agreement with X-ray data of Randaccio et al. (Ouyang et al., 2004) with corresponding experimental bond lengths of 2.04 Å for Co-C Ado and 2.23 Å for Co-N DBI , respectively. Molecular orbital (MO) energies and fragment contributions of RibCbl are collected in Table S5 for the gas phase, and Table S6 for water (PCM). The relevant MO diagram can be found in supporting information as Figure S2.
Frontier orbitals of RibCbl were determined by fragment analysis to be mainly corrin π, π * , and metal d orbitals.
In particular, HOMO, HOMO−2, −4, −6, and LUMO+1, +2, +3 show major contributions from d Co and π * while HOMO−3, −5, −8, −9, −10, and LUMO+3 have increased weights from the Rib group. On the other hand, LUMO and LUMO+4 are composed of nearly pure π orbitals of the corrin ring. Finally, HOMO-7 and LUMO+5 are both composed of excitations from the imidazole group. The change of environment from gas phase to water solution (Table S6) did not influence the character of the MOs significantly, differences being attributed to reversion of energies between the HOMO-5 and −7 in the gas, and HOMO-3 and −4 in the PCM model.

ELECTRONICALLY EXCITED STATES OF RibCbl
Simulated absorption (Abs) spectra generated from TD-DFT/BP86/TVZP vertical excitation energies with transition dipole moments, using corresponding optimized RibCbl geometries in the gas phase and in water, are shown in Figures 2, 3 respectively. Since hybrid B3LYP functional underestimates BDE as well as produce low-lying states as pure π corrin → π * corrin excitations, we employed BP86 throughout this study which has been proved to produce correct BDE for both MeCbl and AdoCbl (Kuta et al., 2006;Kozlowski et al., 2007Kozlowski et al., , 2012Galezowski et al., 2008;Kornobis et al., 2011Kornobis et al., , 2013. BP86 functional was also frequently applied in QM/MM calculations for the enzyme-active cofactors . In both the gas phase and solvent-based calculations, forty excited states were calculated to cover a range appropriate for electronic states potentially involved in coenzyme B 12 photolysis. The lowest ten singlet states are listed in Table 1, and the lowest ten triplet states are listed in Table 2 for the gas phase. In addition, the corresponding solvent-based calculations are listed in Table 3 for singlet states and Table 4 for triplet states. Complete lists of the forty excited states for each system can be found in the supporting information (Tables S1-S4).
Taking into account that light exposure used in experimental studies was no shorter than 400 nm to induce Co-C cleavage (Walker et al., 1998a,b;Shiang et al., 1999;Yoder et al., 2001;Cole et al., 2002;Sension et al., 2004Sension et al., , 2005aHarris et al., 2007), in further discussion we will focus on the low-energy region.
Since the studied RibCbl model is a truncated form of full coenzyme B 12 , no direct comparison to the experimental spectrum can be made. However, the predicted spectra can be correlated to that of AdoCbl with good agreement (Shiang et al., 1999). Several calculated electronic transitions can be assigned to experimental spectral bands. Specifically, the S 2 at 2.36 eV and the S 3 at 2.37 eV agree well with the experimental transition at 2.35 eV (528 nm), the S 6 at 2.87 eV agrees with the experimental transition at 2.90 eV (428 nm), and the S 10 state at 3.10 eV can be assigned to absorption observed at 3.07 eV (404 nm). The same trend applies to PCM geometries (Table 3). Namely, the S 2 , S 3 , S 6 , and S 9 can all be correlated with experimental absorption bands for AdoCbl observed at 2.35 eV (528 nm), 2.90 eV (428 nm), and 3.07 eV (404 nm), respectively. Furthermore, the simulated RibCbl Abs spectra are also in reasonable agreement with the simulated AdoCbl spectra published by Andruniow et al. (2009) further supporting the ability of the truncated AdoCbl model, (i.e., RibCbl) to accurately reproduce the experimental spectroscopic features of AdoCbl.
The absorption spectrum of RibCbl calculated in the gas phase at the BP86/TZVP level is shown in Figure 2, and assignments for the lowest forty singlet states are collected in Table S1. Based on these results it can be deduced that the α/β bands are located in the low energy region from 2.00 to 2.80 eV, covering first five calculated singlet transitions, the D/E band ranges from 2.80 to 3.30 eV and is composed of multiple excitations, and the high-energy region, or so-called γ band, has significant intensity covering several transitions from 3.30 to 4.40 eV. Based on the nature of the calculated electronic excited states (Table 1), the α/β bands involve primarily d Co /π → π * contributions, the D/E bands result from various electronic transitions with more contributions from the Rib group, and the same tendency is observed in the γ band, where oscillator strength increases significantly. It should be noted that ribose increases its role in photoelectronic transitions in the high energy region, i.e., the D/E and γ bands, respectively. Table 1 summarizes the ten lowest calculated excited singlet states of RibCbl in the gas phase. As shown in Table 1, the S 1 excitation present at 2.24 eV, carries only a small oscillator strength (0.008). The major contribution from the S 1 state is an excitation from HOMO-1 to LUMO, in which π + d xz /d z 2 → π * is dominant. The MO diagram ( Figure S2), shows that S 1 excitation also involves a transition from a σ orbital of axial bonding to the π * of the corrin ring, and is identified as SBLCT  is the transition from HOMO-2 to LUMO, identified as π + d xz → π * . Based on the MO diagram it is apparent that LUMO is a pure corrin π * orbital, to which all the excitations in the α/β band generally take place. The next two states, the S 2 and S 3 , are adjacent closely in energy. The most significant components of the S 2 and S 3 states are HOMO → LUMO and HOMO-2 → LUMO, where HOMO is a mixture of π and d yz and HOMO-2 refers to π and d xz . Therefore, the d to π * transition is dominant in this region, and should be described as MLCT transition (Cole et al., 2002;Jaworska et al., 2007;Lodowski et al., 2009Lodowski et al., , 2011. The S 4 state has even less oscillator strength intensity compared to that of S 1 , in which both HOMO-3 and HOMO-4 contribute almost evenly to excitation at 2.58 eV. HOMO-3 derives from ribose, according to MO diagram, while HOMO-4 is composed from the Co d x 2 −y 2 orbital. Coincidently, the S 5 involves the same set of orbitals which contribute to the S 4 state. The only difference, considering their specific characters, is that the S 5 state mixes a minor contribution from the HOMO-1→ LUMO transition. However, the larger oscillator strength of the S 5 state makes it the strongest component of the α/β band. Electronic transitions in the D/E band are more complex than those in the α/β band, and the oscillator strengths are noticeably smaller. This region can be represented by electronic transitions from the S 6 to S 14 with three strong excitations occurring at 2.87 (S 6 ), 3.10 (S 10 ), and 3.21 eV (S 12 ) (Figure 2). The S 6 and S 10 have d Co /π → π * character while the S 12 shows a d Co /π → σ * Co−C nature. The other small intensity transitions in this region are of similar character.
More than twenty singlet states can be associated with γ band ranging from 3.31 (S 15 ) to 4.23 eV (S 40 ) (Table S1). Among them, the S 25 and S 27 have the largest transition dipole moment and are composed of n Rib /σ Rib + d xz /d z 2 + π →d xy −n + π * transitions with a minor d Co /π → π * contribution. The S 29 is dominated by d Co /π → π * transitions, while the S 32 has d Co /π → π * Im character. Near the end of the simulated spectrum, another noticeable transition of n Rib /σ Rib + d xz /d z 2 + π → σ * (d z 2 ) + n type is found at 4.14 eV corresponding to the S 37 state (Table S1).
Since triplet excitations have zero transition dipole moments, we will not take them into account for spectral analysis. The first three triplet states are energetically below the S 1 (2.24 eV), where the T 1 occurs at 1.72 eV from an electronic transition of HOMO→LUMO, while T 2 and T 3 are transitions at 1.94 and 2.15 eV, originating from HOMO-1→LUMO and HOMO-2→LUMO, respectively. All three electronic transitions can be described as d Co /π → π * type (see Table 2 and Table S2).
The Abs spectrum of RibCbl calculated in water solution using the same level of theory was plotted in Figure 3. The energy of the γ band remains unchanged in comparison to gas phase calculation. However, the α/β band is narrowed due to the blue shift of the S 5 to the D/E region. The S 1 , S 2 , and S 3 are assigned to d Co /π → π * transition. A significant contribution to S 1 state is composed of a π + d xz /d z 2 → π * excitation and, like in the gas phase, is characterized as SBLCT. The S 4 has pure d x 2 −y 2 → π * character. The D/E band covers states S 5 -S 13 . The states S 5 and S 7 are identified as d/π → π * /d−n excitations with a small admixture of long range CT (LRCT) type transitions (n Rib /σ Rib → π * ) . The S 6 state at 2.90 eV is a mixture of a dominant LRCT, and minor d/π → π * /d−n character. In contrast, the S 7 state is mainly composed of a d Co /π → π * transition, with minor contributions from SBLCT. The other intense singlet transitions in this region are assigned to the d Co /π → π * transition, which is consistent with singlet excited states observed in the gas phase calculation. The complete assignment of electronic transitions is presented in Table S3. In water solvated system, the T 1 -T 4 states are below the S 1 state (Table 4), and all possess contributions from the d Co /π → π * transition.

MECHANISM OF PHOTOLYSIS
In order to simulate the photodissociation of AdoCbl, the Co-C Rib bond in RibCbl was elongated to mimic the light induced bond scission. The length of the Co-C Rib bond was systematically stretched with the increment of 0.05 Å in a range from 1.90 to 2.65 Å. For each constrained distance, the ground state geometry was optimized at the BP86/TZVP level, followed by TD-DFT calculations for both singlet and triplet states. Figure 4 depicts the potential energy curves of a manifold of excited states computed as a function of Co-C Rib bond length. The S 1 -S 5 singlet states, which belong to α/β band, have nonrepulsive character, and the gap between the S 1 and higher states gets larger when the bond length increases. States denoted as S 2 and S 3 are parallel at short Co-C Rib distance but cross at ∼2.50 Å. On the other hand the S 4 and S 5 keep similar energy but visibly separate from the first group of transitions (S 1 -S 3 ). However, at ∼2.30 Å these two states show avoiding crossing, and the S 4 approaches the S 2 at long length bond region. The excited states higher in energy (S 6 -S 10 ), display multiple crossings at even short Co-C distances. According to the TD-DFT data, low-lying singlet states do not participate in photodissociation because there is no 1 (σ Co−C → σ * Co−C ) dominant. Most likely such a transition requires an energetically high excitation and none of singlet states with predominant 1 (σ Co−C → σ * Co−C ) character are in a reasonable transition region. Additionally, it is expected that such states would not dissociate to the cob(II)alamin and ribosyl radicals, but rather to ionic fragments. However, the low-lying triplet states appear to have σ Co−C → σ * Co−C character in the achievable energy region. By connecting the energy points of σ Co−C -featured triplet states at different dissociation distances, the 3 (σ Co−C → σ * Co−C ) state with repulsive character can be located (black curve in Figure 4). At 2.35 Å, this state becomes the lowest level in terms of energy, and displays an avoided crossing with T 1 state, that typically accounts for d Co /π → π * excitation. Together with an increasing Co-C Rib distance, the energy of the triplet state drops dramatically above a Co-C bond distance of 2.40 Å, indicating that dissociation may not be properly described with a single-determinant wavefunction approximation at long Co-C Rib distances (Kumar et al., 2011a,b). It is also reasonable to postulate that there is a conical intersection existing between the two states. Although the current study has limitations on the longer bond distances, it is expected that the photolysis happens at much shorter bond lengths, where 3 (σ Co−C → σ * Co−C ) excitation is described properly. Further multi-configuration wave functions would be required to obtain a more detailed picture.

POTENTIAL ENERGY SURFACES OF LOW-LYING EXCITED STATES
Since the photoexcitation of B 12 derivatives involves primarily the structural changes of the axial ligand involved in N-Co-C bonding, this investigation was extended to the PESs computed as a function of both Co-C Rib and Co-N Im distances. The S 1 and S 2 PESs were constructed from the equilibrium structure of the RibCbl (S 0 state), and systematically stretching the two axial bonds with an increment of 0.05 Å. Geometries at each grid point were optimized by BP86/TZVP, and the vertical excitations were calculated by TD-DFT at the BP86/TZVP level of theory (Figures 5, 6).
In gas phase PES contours (Figure 5), the S 0 shows an equilibrium geometry with the lowest energy at 2.02 Å for Co-C Rib and 2.21 Å for Co-N Im , while for the S 1 PES, the minimum occurs at the longer Co-C Rib bond (∼2.17 Å) but shorter Co-N Im (∼2.00 Å) distance. According to pump-probe time resolved experiments, an intermediate state of AdoCbl is populated through photoelectronic excitation, leading to a partial mixture of adenosyl radical and cob(II)alamin. It is therefore reasonable to postulate that such an intermediate state can be identified as the S 1 , which according to TD-DFT calculations has the Co-C Rib bond elongated and Co-N Im shortened due to an electron density shift from the metal to the equatorial bonds of the corrin ring. The PES plot of the S 2 is nearly parallel to the S 0 surface. Estimates based on PES projections (Figure 5) predict the energy minimum of the S 2 surface is located at Co-C Rib ≈ 2.04 Å, and Co-N Im ≈ 2.23 Å, ± 0.02 Å, compared to the equilibrium geometry. This indicates no significant change of axial bond distances occur from the S 0 to S 2 transition. If this is true, the energy difference between the S 0 and S 2 states are mainly attributed the geometry changes of the corrin ring.
At this point, the distortion of the corrin ring, mainly due to π → π * electronic transitions, increases the potential energy of the system. Since the geometry change in the S 1 state involves Co-C Rib bond stretching, it is likely that the S 1 state is the most involved in the photolytic cleavage of Co-C, and thus the formation of the radical pair generated when the Co-C bond is stretched.
The PES of RibCbl in water retains nearly all of the general features of the gas phase PES (Figure 6). However, although the equilibrium geometry of RibCbl in water has similar axial bond lengths to those obtained in the gas phase calculation (with the exception of a slightly reduced Co-N bond distance of 0.02 Å), there remain subtle differences in energies between the S 0 and S 1 , and S 0 and S 2 states. The energy gaps between S 0 and S 1 , as well as S 0 and S 2 , are larger for the solvated geometry than those of the gas phase. The vertical energy gaps between the minimum point of solvated ground state and the lowest two excited states are ∼2.30 eV (S 0 -S 1 ), and ∼2.40 eV (S 0 -S 2 ) respectively, while the vertical energy gaps in the gas phase calculation are ∼2.20 eV (S 0 -S 1 ) and ∼2.35 eV (S 0 -S 2 ). It can be reasoned that the larger vertical energy gaps from the ground state to the first two excited states in the PCM calculation, that the polar effect of solvent tends to increase the energies required for RibCbl excitation.

SUMMARY AND CONCLUSIONS
The purpose of this study was to explore the mechanisms of Co-C bond scission in AdoCbl upon light exposure using the TD-DFT method. To accomplish this we used a simplified RibCbl model to mimic the molecular features of photoexcited AdoCbl. The optimized RibCbl geometry at the DFT/BP86/TVZP level of theory was very close to the X-ray structure of AdoCbl with respect to the Co-C and Co-N ax bond distances, within the deviation of 0.02 Å. Electronically excited states were calculated with TD-DFT, and both low-lying singlet and triplet states were analyzed. Calculated singlet states of RibCbl were used to generate electronic spectra that agree well with the experimental UV-Vis for AdoCbl, especially considering the characteristic low energy α/β band. In addition, PESs were generated as a function of both Co-C Rib and Co-N Im distances for singlet excited states using TD-DFT. The S 1 state was identified as the key state of RibCbl photoexcitation, with contributions from both MLCT and SBLCT. Similar to the analysis of low-lying excited states of MeCbl, a repulsive 3 (σ Co−C → σ * Co−C ) triplet state was found to facilitate photon induced dissociation of the Co-C bond in RibCbl.