ThDP Model Calculations

In a first set of theoretical calculations, the isolated cofactor was considered. The objec-tive was to understand the influence of specific geometries adopted in the acobjec-tive site and free in solution. At the same time, different electronic structure methods for the compu-tation of the electronic excicompu-tation spectra were benchmarked. Given that the dominant tautomer of free ThDP in solution is the AP form, this one was considered in greater detail.

The first step was to compare different functionals for the treatment of the charge-transfer excitation of the ThDP cofactor in the AP form. The inclusion of the phosphate group tail with its negative charge can generally lead to ghost states in gas phase cal-culations, because this is not compensated by the environment (be it in solution or at the active site by protein residues). Therefore, to facilitate the comparison between the environments, the diphosphate moiety was replaced with an OH group. The re-sulting model molecule was first optimized in the V conformation, which is the one adopted in the active sites of enzymes. CC2 calculations were taken as a reference and compared to TD-DFT/TDA excitation energies employing the CAM-B3LYP,^[65] M06-2X,^[128] BH&HLYP^[61] and B3LYP^[61;62] functionals. The results are listed in Table 4.1.

The TD-DFT/TDA calculations with the CAM-B3LYP, M06-2X, and BH&HLYP functionals yield consistent excitation energies for the charge-transfer state, where an electron is transferred from the pyrimidine to thiazolium ring (see NTOs in Figure 4.3).

Table 4.1.: Vertical excitation energies for the AP and IP-ThDP model compounds in theV conforma-tion, considering different levels of theory. All energies are given in electronvolt (eV). The corresponding wavelengths in nanometers (nm) are listed in parentheses.

ThDP character CC2^a CAM-B3LYP^b M06-2X^b BH&HLYP^b B3LYP^b AP CT 4.41 (281) 4.26 (291) 4.34 (286) 4.39 (282) 3.10 (400)

n→π^∗ 4.25 (292) 4.58 (271) 4.66 (266) 5.01 (247) 4.35 (285) IP CT 4.36 (284) 4.33 (286) 4.39 (282) 4.47 (277) 3.39 (366) π→π^∗ 4.80 (258) 4.93 (251) 4.99 (248) 5.15 (241) 4.51 (275)

a Basis: A’VDZ

b Basis: def2-TZVP

(a) (b)

Figure 4.3.: Dominant CAM-B3LYP/def2-TZVP NTOs for the charge-transfer excitation of (a) AP and (b) IP-ThDP model compounds in theV conformation.

In contrast, B3LYP excitation energies show the typical underestimation of charge-transfer excitations for common DFT functionals.^[66;67] The inclusion of a large fraction of exact exchange (M06-2X and BH&HLYP) or the application of range-separated func-tionals (CAM-B3LYP) is necessary for the accurate treatment of such excitations.

In the case of AP-ThDP, the reference CC2 calculation yield an n→π^∗ transition at the pyrimidine ring (4.25 eV, 292 nm) as lowest transition. At slightly larger energies (4.41 eV, 281 nm), the charge-transfer excitation from the pyrimidine to the thiazolium ring was found. The DFT calculations result in a different order of the two states. Here, the charge-transfer excitation comes first, followed by the n → π^∗ transition. In a first attempt to include environmental effects, CAM-B3LYP calculations were performed using the COSMO model, with toluene as the solvent. The latter is often used to replicate the conditions found in enzymatic active sites.^[129] The n → π^∗ transition is only slightly increased to 4.67 eV (265 nm). Opposed to this, the charge-transfer state is shifted by 0.25 eV to lower energies, resulting in an excitation energy of 4.01 eV (309 nm). When the environmental effect computed at the CAM-B3LYP level is added to the CC2 values as a correction, the charge-transfer excitation corresponds again to the lowest excited state with a transition energy of 4.16 eV (298 nm) compared to a value of 4.34 eV (286 nm) for the n → π^∗ state. Furthermore, the oscillator strengths differ significantly between the two states. The charge-transfer excitation is 4 times as intense as then →π^∗ transition (CC2 oscillator strength of 0.016 compared to a value of 0.004). The absorption spectrum of AP-ThDP in the low-energy region is therefore expected to be dominated by this charge-transfer excitation.

The lowest transition in IP-ThDP corresponds to a similar charge-transfer state as for AP-ThDP with an excitation energy of 4.36 eV (284 nm). The second excited state, a

Results and Discussion 59

π →π^∗ transition located at the pyrimidine ring, is well separated with an energy gap of roughly 0.5 eV to the charge-transfer state. All the applied DFT functionals (except B3LYP) perform well in comparison to the CC2 calculations. Altogether, the agreement between the reference values and the CAM-B3LYP results was satisfactory.

Having established a reliable level of theory, the focus was on the impact of the cofactor conformation on the electronic spectra. In contrast to the spectra in enzymes, no ab-sorption was observed for free ThDP in aqueous solution at wavelengths >300 nm.^[130]

In order to clarify this observation, the first excited states of the AP tautomer were calculated in the gas phase and with the COSMO continuum model in the V and F conformation, which differ in the orientations between the aminopyrimidine and thia-zolium rings.^[131] The F conformation is the most stable conformation of free ThDP in solution. The structures and gas phase excitation energies are shown in Figure 4.4a and 4.4b for the V and F conformations, respectively. Spectra in different conformations and environments were simulated as Gaussian bands with a full width at half maximum (FWHM) of 0.3 eV (Figure 4.4c).

The lowest transition is as above mentioned, the charge-transfer excitation. However, the excitation energy is found to be highly dependent on the the medium and confor-mation. In the gas phase, the energy is lower in the V conformer (4.26 eV, 291 nm) than in the F conformer (4.41 eV, 281 nm). Moving to the COSMO results in toluene, which should approximately mimic the environment of a hydrophobic enzyme pocket, the energy of the V conformation drops significantly to 4.01 eV (309 nm) and shows a prominent band in the spectrum (blue curve in Figure 4.4c). This is well separated from a very strongπ→π^∗ band of the thiazolium ring at about 4.96 eV (250 nm). However, moving to an aqueous solution for theF conformer of free ThDP, the excitation energy is strongly increased. The first transition is found at 4.66 eV (266 nm) and falls into the region of the much stronger π→π^∗ transition located at the thiazolium ring. Con-sequently, there was no significant absorbance in the spectra at wavelengths >300 nm, where ThDP-dependent enzymes show their typical CD band structures.

The previous results roughly confirm the nature and general features of the first absorp-tion band for the AP tautomer of ThDP. However, the first results for the IP tautomer hint at a similar excitation as in the AP, of a charge-transfer nature. This finding dis-agrees with the currently accepted assignment. The model compound studies of Jordan and coworkers pointed toward an n → π^∗ assignment.^[30] The latter authors made use of singly substituted pyrimidine compounds to assert the position of the IP band. The

0 1000 2000 3000 4000 5000

✏/M1 ·cm1

250 300 350

/ nm

5.0 4.5 4.0 3.5

! / eV

Vconformer Fconformer

in toluene in water

(a)

(b)

(c)

!^gas_F = 4.41 eV

!^gas_V = 4.26 eV ^gas_V = 291 nm

gas

F = 281 nm

Figure 4.4.: B3LYP-D3(BJ)/def2-TZVP optimized structures for the AP-ThDP model compounds in the (a)Vand (b)Fconformation. Additionally, the lowest gas phase excitation energies and the corresponding wavelengths at the CAM-B3LYP/def2-TZVP level of theory are given for both tautomers, associated with a charge-transfer from the pyrimidine to thiazolium rings.

(c) Simulated absorption spectra for the AP-ThDP model compounds for theV conformer (blue curve) and theFconformer in aqueous solution (red curve). The peak positions were represented as Gaussians with a FWHM of 0.3 eV.

nature of the latter was deduced from the measured solvatochromic shifts and the fact that only the pyrimidine ring is in fact represented in the model compounds used. In order to understand this disagreement, these compounds were studied in light of the recent calculations.

TD-DFT/TDA calculations were carried out on one of the IP analogues, N¹,N⁴ -dimethyl-1,4-iminopyrimidine (dmIP), featured in the study of Jordan and coworkers (see Figure 4.5a).^[30] The results are shown in Figure 4.5b, considering the same three solvents as in the latter work and the two possible isomers of the analogue. No agreement between the computed values for both isomers can be found. The largest deviations are found with THF as the solvent. The relative trends for both lowest transitions (π →π^∗ and n → π^∗) are also inconsistent with the measured data for varying solvents. The computed values show almost negligible solvatochromic shifts, while experimentally

de-Results and Discussion 61

termined absorption bands are shifted as much as 0.24 eV (comparing DMSO and water).

Even if the band positions were not in agreement with the measurements, one should at least expect the shifts to be consistent. This raises serious questions about the band assignment. The failure also does not seem to stem from the level of theory used. EOM-CCSD/A’VDZ, PBE0,^[132] and CAM-B3LYP results in the gas phase all agree closely in terms of the computed excitation value (282, 302, and 283 nm, respectively).

Another open possibility would be the formation of other species in solution, which would then be responsible for the recorded UV−vis signals. In particular, the forma-tion of dimers in soluforma-tion was considered as possible candidates, which could result in excitations similar to those observed in the previous section for the IP cofactor. The most promising candidate for the compound under study would be a protonatedN¹,N⁴ -dimethyl-4-aminopyrimidinium (similar to APH⁺), building a dimer in solution with an unprotonated molecule, effectively sharing the charge (which in turn reduces the pKa in solution). An electron transfer from the unprotonated ring to the protonated species could then occur in solution. The geometry was optimized in a π-stacked conformation at the B3LYP-D3/def2-TZVP level of theory, including the COSMO solvation model with the corresponding solvents. One of these π-stacked dimer structures is shown in

N

Figure 4.5.: (a) Structural formulas of two isomers ofN¹,N⁴-dimethyl-1,4-iminopyrimidine (dmIP) fea-tured in the study of Jordan and coworkers.^[30](b) CAM-B3LYP/def2-TZVP vertical ex-citation energies of the two isomers of dmIP including the COSMO continuum model.

The experimental band maxima were taken from Ref. [30]. (c) B3LYP-D3(BJ)/def2-SVP optimized structure of aπ-stacked dimer between dmIP and its conjugated acid.

Figure 4.5c. The values for the first electronic transitions are 3.82, 3.93, and 4.04 eV (325, 315, and 307 nm, respectively), in THF, DMSO, and water, respectively. The agreement is striking. An analysis of the NTOs reveals that it is in fact, as expected, an electronic transition from a ring to the other, with the protonated species effectively mimicking the thiazolium ring of ThDP. This could explain the overall coincidence of this study with the spectra recorded in functional enzymes. The trend in solution could also be understood through the charge-transfer character.