Absorption transition energies

If we compare the absorption transition energies computed using the LR, cLR and SS formalisms, we observe that the absorption energies are mostly underestimates compared to experimental ones, except for the energies of phenolate-keto form and its analogue which are slightly above the experimental ones, being the energy difference of less than 0.06 eV. The energy differences calculated between LR-PCM (𝐸_𝐿𝑅^𝑎𝑏𝑠) and cLR-PCM (𝐸_𝑐𝐿𝑅^𝑎𝑏𝑠) are small (≤ 0.1 eV).

However, the transition energies computed using SS-PCM (𝐸_𝑆𝑆^𝑎𝑏𝑠) are significantly different from the ones computed with LR-PCM and cLR-PCM, except for phenolate-keto, phenol-enol and their analogues.

In order to rationalise the energy differences found between LR-PCM (𝐸_𝐿𝑅^𝑎𝑏𝑠) and SS-PCM (𝐸_𝑆𝑆^𝑎𝑏𝑠), we computed the charge transfer (CT) character of the absorption transition (S0→S1) for the oxyluciferin natural forms and the analogues as it is known that the LR formalism is suitable for transitions characterised by low CT character, unlike the SS formalism which gives better results for transitions with large charge rearrangement.^146,147 In particular, we calculated the Mulliken charges of the thiazolone moiety (qS0thiaz and qS1thiaz) for the GS equilibrium geometry at the initial (S0) and final (S1) states, respectively. Then, we calculated the CT character as the difference of the Mulliken charges of the thiazolone moiety between the final state qS1thiaz and initial state qS0thiaz (CT = qS1thiaz – qS0thiaz) (Table 1). By analysing the calculated CT character for the absorption transition (Table 1), we can classify the chemical forms of the oxyluciferin and the analogues in three groups: (i) group with a low charge transfer (LCT group) where the CT character is almost negligible (|qS1thiaz – qS0thiaz|≤ 0.1e), (ii) group with a high charge transfer (HCT group) where the CT character is equal or larger than 0.25e and (iii) group with a medium charge transfer (MCT) presenting an intermediate CT character. Following these indications, phenol-enol and its analogue can be classified to the LCT group as the CT character of the transition is quite small. Phenolate-keto, phenolate-enol, phenolate-enolate and their analogues, presenting an intermediate CT character, can belong to the MCT group. Phenol-keto and phenol-enolate forms and their corresponding analogues can be classified to the HCT group as they show a large CT character.

Regarding LCT group, we observed that absorption energies computed within LR, cLR and SS formalisms are quite similar presenting energy differences less than 0.1 eV (Table 1). This can be explained by the negligible CT character of the absorption transition. For the HCT group, the energy differences between 𝐸_𝐿𝑅^𝑎𝑏𝑠 and 𝐸_𝑆𝑆^𝑎𝑏𝑠 calculated for the keto and phenol-enolate forms and their corresponding analogues are the largest ones, about 0.27–0.37 eV in

absolute value (Table 1) due to the large CT character of the transition. The absorption energy of the phenol-keto and phenol-enolate forms and their corresponding analogues (HCT group) is more sensitive to the solvation model. For the MCT group, we observe a halfway effect of the formalism chosen, finding out that the transition energies computed with SS formalism are always higher than the ones computed with LR formalism (energy difference around 0.13 to 0.24 eV).

Table 1 Absorption energies⁽⁴⁾ (given in eV (nm)) of oxyluciferin natural forms (coloured lines) and their analogues (uncoloured lines) computed in gas phase (GP), using implicit (LR-, cLR- and SS-PCM) and explicit⁽⁵⁾ (QM/MM) solvation models. Experimental absorption wavelength maxima (given in eV (nm)) from ref.¹⁶ are also presented. CT character is given as CT = qS1thiaz – qS0thiaz. Minus sign indicates that, during the transition, there is a fraction of the electronic charge transferred from the benzothiazole moiety to the thiazolone moiety. (Table reproduced from ref.¹³⁵).

Furthermore, we compared the absorption energies computed within LR, cLR and SS formalisms to the experimental results (Table 1). As previously mentioned for phenol-enol and its analogue (LCT group), the absorption energies computed with the LR, cLR and SS formalisms are quite similar. For LCT group, the absorption energies (𝐸_𝑐𝐿𝑅^𝑎𝑏𝑠) computed using cLR formalism is the closest to the experimental (𝐸_{𝜆𝑚𝑎𝑥,𝑒𝑥𝑝}^𝑎𝑏𝑠 ) values, with an energy difference about 0.05 eV.

Then for HCT and MCT groups where the CT character of the chemical compounds are large, the

(4) The transition energies have been computed using the B3LYP functional and the 6-311g(2d,p) basis set.

A benchmark with different DFT exchange–correlation functionals has been achieved. The obtained results show that the B3LYP functional gives transition energies closest to the experimental values within a shorter CPU time (Table A- 1).

(5) 𝐸_{𝑄𝑀𝑀𝑀}^𝑎𝑏𝑠 values correspond to the maxima wavelengths of the absorption spectra simulated considering 100 MD snapshots.

absorption energies (𝐸_𝑐𝐿𝑅^𝑎𝑏𝑠 and 𝐸_𝑆𝑆^𝑎𝑏𝑠) computed using both cLR and SS formalisms are closest to the experimental values (Table 1). Except for phenol-keto and its analogue which constitute a special case. In this case, the closest value to the experiment is obtained by when using LR formalism with an energy difference less than 0.08 eV. This can be explained by the fact that the simulated and experimental absorption spectra of phenol-keto (or of its analogue) are different from the ones obtained for the rest of chemical compounds. For most of chemical compounds, the absorption spectra are characterised by an intense band that corresponds to the S1 transition (described by a HOMO to LUMO mono-excitation) and by a less intense one that corresponds to S2 transition. However, the absorption spectral band of phenol-keto and its analogue is wide and structured because both S1 and S2 transitions are intense and close in energy, as we have discussed in the previous work (Chapter 6). In addition, the electronic nature of these S1 and S2

transitions results in a mixture of mono-excitations: HOMO to LUMO and HOMO–1 to LUMO.

Moreover, we also compared the absorption energies computed using explicit solvation model to the experimental results. For all the oxyluciferin forms and their analogues, the absorption energies⁽⁶⁾ (𝐸_{𝑄𝑀𝑀𝑀}^𝑎𝑏𝑠 ) computed using explicit solvation model match the experimental values, with an energy difference less than 0.1 eV (Table 1).

In summary, although different formalisms have been applied to account the solvent effect within PCM solvation model, the absorption transition energies of some of the oxyluciferin forms and their analogues are still far from the experimental values. In addition, the computed transition energies differ from one formalism to another, depending on the CT character of the chemical compound. For instance, the SS-PCM formalism is suitable to compute the absorption energies of the chemical compounds characterised by a significant CT character while, the LR-PCM formalism is appropriate for the compounds with negligible CT character.

Furthermore, the lack of explicit interactions between the solute and solvent molecules could also be the reason for the discrepancy between these energies. Indeed, the vertical transition energies computed considering explicit solvent model are in good agreement with experimental values.

(6) It is worthwhile to highlight that in order to explore a high enough conformational space it would have been desirable to perform thousands of conformations (snapshots) to simulate the absorption and emission spectra. This is due to the fact when considering the explicit water molecules in the system the degrees of freedom increase very rapidly. Because of the physical constraints (such as time and computational resources), we could only use one thousand snapshots. Looking further into the spectra convergence, we were able to demonstrate that with only one hundred snapshots reasonably accurate spectra can be simulated. Indeed, the spectra simulated with one thousand and with one hundred snapshots are similar (see Figure 36a in computational details).