Spectra of DHEThDP

The broad absorption band in the range of 2.25–3.55 eV (350–550 nm) observed in UV-vis measurements ofE. coli TK after addition ofβ-hydroxypyruvate is most likely linked

Results and Discussion 93

to the formation of the DHEThDP intermediate. The spectra of this key intermediate were studied in the active site of the enzyme, using an amino acid shell of roughly 5 Å around the cofactor. Hereby, the pyrimidine ring of DHEThDP was set to its APH⁺state with a deprotonated (negatively charged) canonical glutamate based on the information from the electron density map of the X-ray measurements. Two different setups were employed for the protonation state of the substituent of DHEThDP in connection to a hydrogen bonded histidine residue (His473). In the first case, the oxygen atom of the enamine moiety was protonated (enol-DHEThDP), forming a hydrogen bond to the deprotonated Nϵ atom of the (neutral) His473 residue. In the second case, the oxygen atom was deprotonated (enolate-DHEThDP), whereby the His473 residue was assumed to serve as proton acceptor and set doubly protonated (positively charged). Otherwise, the same setup for the enzyme environment was considered for both systems. After a QM/MM optimization of the intermediates at the B3LYP-D3(BJ)/def2-TZVP QM level of theory, vertical excitation energies were obtained with TD-DFT/TDA employing the CAM-B3LYP functional with the def2-TZVP basis set. The optimized structures and calculated excitation energies are shown in Figure 6.3.

(a) enol-DHEThDP (b) enolate-DHEThDP

His473 His473

Glu411 Glu411

!1 = 2.92 eV

!2 = 3.33 eV

!1 = 1.86 eV

!2 = 2.25 eV

1= 424 nm

2= 372 nm

1 = 668 nm

2 = 552 nm f1 = 0.006

f2 = 0.004

f1= 0.022 f2= 0.003

Figure 6.3.: QM/MM optimized structures of (a) enol and (b) enolate-DHEThDP in the active site of E. coliTK. The His473 residue is assumed to serve as proton acceptor/donor for their inter-conversion. The pyrimidine ring was set to its APH⁺ state with a deprotonated canonical glutamate (Glu411). Furthermore, TD-DFT/TDA with CAM-B3LYP/def2-TZVP vertical excitation energies, their associated wavelengths and oscillator strengths are given for the first and second excited states for each system.

The spectra calculations revealed two low-energy excited states for enol and enolate-DHEThDP which could contribute to the observed band at 2.25–3.55 eV (350–550 nm).

In particular, these excitation energies are found at the limits of the absorption band.

In the high energy regime (2.9–3.3 eV) the enol-DHEThDP absorbs, whereas the exci-tation energies are strongly red shifted for enolate-DHEThDP to 1.86 and 2.25 eV. This large shift of about 1.1 eV roughly corresponds to the broadness of the measured band (≈ 1.3 eV). The origin of this energy gap can be explained by inspection of the excita-tion characters. The dominant NTO pairs for the first and second excited states of enol and enolate-DHEThDP are shown in Figure 6.4. Equivalent excitation characters are observed for both states of DHEThDP. All excited states correspond to charge-transfer excitations from the π-system of the thiazolium-substituent moiety to the aminopy-rimidinium ring. This is an opposite charge-transfer character compared to the spectral characteristics of unsubstituted ThDP and AcThDP featured in the preceeding chapters.

In the case of DHEThDP the electronic structure is reversed, so that the electron rich thiazolium-substituent moiety acts here as electron donator and the positively charged

(a) enol-DHEThDP (b) enolate-DHEThDP

Figure 6.4.: Dominant CAM-B3LYP/def2-TZVP NTO pairs for the (a) enol and (b) enolate-DHEThDP.

The NTO pairs for the first and second excited state are shown on the top and on the bottom, respectively.

Results and Discussion 95

pyrimidine ring (APH⁺) being the electron acceptor. According to this excitation char-acter, the introduction of a negative charge at the thiazolium-substituent moeity by moving from enol to enolate-DHEThDP facilitates the donation of an electron in the excitation process. This results in a significantly lower excitation energy for the enolate-DHEThDP intermediate.

The information of the first set of calculations can be summarized as follows. Both pro-tonation states of the DHEThDP intermediate show excited states with similar charge-transfer characters in the energy range of the measured UV-vis band. These are found at the limits of the band, whereby the excitation energies of enol and enolate-DHEThDP are located in the high and low-energy regime, respectively. The connection between the two limits of the band could arise from a dynamical equilibrium of the interme-diates or from a rather weak O–H bond in the enol case. For this reason, the 1D-potential for the hydrogen movement was calculated. Thereby, the optimized structures of enol-DHEThDP was used as reference. The O–H distance was then incrementally increased/decreased. The hydrogen position was then reoptimized with a restraint for its distance to the oxygen atom through a harmonic potential. All other atoms were constraint in their Cartesian coordinates. For these calculations the side chains of the His473 residue as well as the canonical glutamate (Glu411) were included in the QM region. An anharmonic frequency analysis followed in order to determine the probability of presence of the hydrogen atom along the calculated path. This was applied to scale the oscillator strengths of the excited states from TD-DFT/TDA calculations (CAM-B3LYP/def2-TZVP). A spectrum was then simulated by convolution of Gaussian bands (FWHM= 0.3 eV). The results are shown in Figure 6.5.

The potential for the hydrogen movement reveals a common shape for an anharmonic O–H stretch vibration. Employing this reaction coordinate, no minimum could be ob-served at large O–H distances, where the enolate-DHEThDP intermediate with a doubly protonated His473 residue would be expected. The anharmonic frequency analysis shows significant probability of presence in the O–H distance range of 0.9–1.1 Å with a maxi-mum at 1.01 Å for the lowest quantum state. This distance is, as expected, somewhat larger than the determined minimum of the potential (0.99 Å), but still refers to a enol-DHEThDP intermediate. The first excited vibrational state is well separated by about 2800 cm⁻¹ from the ground state. According to Boltzmann statistics, only the latter is significantly populated at a temperature of 300 K. Therefore, the probability of presence of the hydrogen position from the vibrational ground state was employed for the

simu-lation of the UV-vis spectrum (blue curve in Figure 6.5b). This includes only the two charge-transfer transitions since these are the ones contributing to the measured band.

The simulated spectrum shows absorbance in the spectral range of 2.91–3.81 eV (325–

425 nm). Similar to the single point calculations, this corresponds to the high-energy regime of the measured UV-vis band. In this model, the broadness of the band cannot be explained. However, there are important information resulting from these calculations.

The observed band cannot solely originate from the enol-DHEThDP intermediate. For that case, a much sharper band at about 3.26 eV (380 nm) would be expected. In order to obtain such a broad band the enolate-DHEThDP intermediate has to be involved.

The simple model of a moving hydrogen atom in a rigid environment is not enough to describe this system. A coupling to other degrees of freedom is required for their interconversion. This could be other proton transfers or conformational changes in the enzyme environment. This effect was, however, not investigated in further detail.

-200

300 350 400 450 500 550

/nm

Figure 6.5.: (a) QM/MM potential energy curve for the hydrogen movement connecting the enol-DHEThDP intermediate with its enolate form in the active site ofE. coliTK. Furthermore, the vibrational ground and first excited state levels are depicted together with the resulting probability of presence (|ψ_v|²) of the hydrogen position. Dashed lines indicate the positions of the minumum of the potential and the maximum of|ψ₀|². (b) Simulated absorption spec-trum for the charge-transfer states of DHEThDP in comparison to the measured difference absorbance.

Results and Discussion 97