Ground-State Redox Potentials Calculations of D-π-A and D-A-π-A Organic Dyes for DSSC and Visible-Light-Driven Hydrogen Production

The prediction of ground-state redox potentials by quantum chemical methods has a prominent role in the rational design of novel organic photosensitizers both for dye-sensitized solar cells (DSSCs) and photocatalytic systems for the production of H2. Indeed, the ground-state redox potential of the photosensitizers is one of the key parameters to identify the most promising candidates for such applications. Here, the ground-state redox potentials of 16 organic donor-π-acceptor D-π-A and donor-acceptor-π-acceptor D-A-π-A dyes having a medium to large size of the conjugated scaffold are evaluated, using the methods of the Density Functional Theory (DFT), in terms of free energy differences between their neutral and oxidized ground-state forms. These results are compared to the available experimental data and to the computed highest occupied molecular orbital energy −ε(HOMO) values as an approximation of ground-state redox potentials according to Koopmans’ theorem. Using the MPW1K functional in combination with the 6-31+G* basis set, the strategy based on the free energy cycle, including solvent effects, reproduces with a good level of accuracy the observed values (mean absolute error (MAE) < 0.2 eV) and trend of redox potentials within related families of dyes. On the other hand, the −ε(HOMO) values are only able to capture the experimental trends in redox potential values.

The use of synthetic organic push-pull dyes is becoming increasingly popular [6]. In particular, donor-acceptor D-π-A architectures, have been found able to establish an efficient charge separation: indeed, due to the wide diversity of suitable D, A and π fragments a huge number of different sensitizers can be accessed, allowing a fine-tuning of their chemical, optical, energetic, and stability properties. In addition, recently, the use of sensitizers based on the D−A−π−A architecture has been investigated, finding that the additional acceptor is useful for modulating the energy levels, extending the light harvesting ability, as well as improving photovoltaic performances and photostability. Indeed, the additional electron acceptor unit can enhance the intramolecular electronic push−pull effect, thus significantly affecting the energy levels and absorption properties of sensitizers [8].
In DSSCs, the dye absorbs light and, upon excitation, it transfers an electron to the conduction band of the semiconductor, which carries it to a glass electrode (transparent conducting oxide layer); at the same time, the resulting hole is transferred from the dye/sensitizer to the redox mediator (usually an I -/I 3 redox couple) which, through an oxidation-reduction interchange, carries it to the counter-electrode, thereby closing the circuit and generating a current (See Figure 1a). The photocatalytic systems, on the other hand, are dye-sensitized Pt/TiO 2 photocatalysts in which the dye, as in DSSCs, harvests visible light and injects the electron in the TiO 2 conduction band (See Figure 1b). Electrons are then transferred to Pt 0 nanoparticles, which are adsorbed on the TiO 2 surface and here protons are reduced to H 2 . The regeneration of the oxidized dye occurs by using a sacrificial electron donor (SED) agent. Triethanolamine (TEOA), ethylenediaminetetraacetic acid (EDTA), ascorbic acid (AA) and, more recently, ethanol, have been employed as SEDs [4].
Energies 2020, 13, x FOR PEER REVIEW 2 of 11 indeed, due to the wide diversity of suitable D, A and π fragments a huge number of different sensitizers can be accessed, allowing a fine-tuning of their chemical, optical, energetic, and stability properties. In addition, recently, the use of sensitizers based on the D−A−π−A architecture has been investigated, finding that the additional acceptor is useful for modulating the energy levels, extending the light harvesting ability, as well as improving photovoltaic performances and photostability. Indeed, the additional electron acceptor unit can enhance the intramolecular electronic push−pull effect, thus significantly affecting the energy levels and absorption properties of sensitizers [8].
In DSSCs, the dye absorbs light and, upon excitation, it transfers an electron to the conduction band of the semiconductor, which carries it to a glass electrode (transparent conducting oxide layer); at the same time, the resulting hole is transferred from the dye/sensitizer to the redox mediator (usually an I -/I3 -redox couple) which, through an oxidation-reduction interchange, carries it to the counter-electrode, thereby closing the circuit and generating a current (See Figure 1a).
The photocatalytic systems, on the other hand, are dye-sensitized Pt/TiO2 photocatalysts in which the dye, as in DSSCs, harvests visible light and injects the electron in the TiO2 conduction band (See Figure 1b). Electrons are then transferred to Pt 0 nanoparticles, which are adsorbed on the TiO2 surface and here protons are reduced to H2. The regeneration of the oxidized dye occurs by using a sacrificial electron donor (SED) agent. Triethanolamine (TEOA), ethylenediaminetetraacetic acid (EDTA), ascorbic acid (AA) and, more recently, ethanol, have been employed as SEDs [4]. Among other requirements, the correct alignment of the relative energy levels of the dye and the redox couple in DSSCs or the SED in the Pt/TiO2 photocatalysts is a key issue that affects the overall efficiency of both dye-sensitized systems. Indeed, the effective regeneration of the oxidized dye is pivotal for both devices to obtain good performances in terms of efficiency. Thus, a key parameter for an efficient dye to be employed is the ground-state redox potential (GSRP) since this value, especially when compared to the redox couple or SED energy levels, is a measure of the dye regeneration driving force.
The prediction of GSRP by quantum chemical methods is of outstanding importance for the rational design of novel organic sensitizers and greatly contributes to the development of more efficient devices. Indeed, the calculations of these photoelectrochemical properties along with the modeling of other key parameters such as the excited state redox potential, the vertical excitation and emission energies, the charge transfer nature of the excitation process and the electronic coupling between the dye and the semiconductor, would indicate the most promising dye candidates for solar energy and fuel (H2) devices. This strategy has been intensely applied in literature for the molecular engineering of the organic sensitizer for DSSC [9][10][11][12][13][14], mostly using the methods of the density functional theory (DFT) and its time-dependent extension (TDDFT).
The accurate evaluation of GSRP is hard to achieve, especially because it has been shown that the accuracy deteriorates as the conjugation length of the molecule increases [15]. In the present Among other requirements, the correct alignment of the relative energy levels of the dye and the redox couple in DSSCs or the SED in the Pt/TiO 2 photocatalysts is a key issue that affects the overall efficiency of both dye-sensitized systems. Indeed, the effective regeneration of the oxidized dye is pivotal for both devices to obtain good performances in terms of efficiency. Thus, a key parameter for an efficient dye to be employed is the ground-state redox potential (GSRP) since this value, especially when compared to the redox couple or SED energy levels, is a measure of the dye regeneration driving force.
The prediction of GSRP by quantum chemical methods is of outstanding importance for the rational design of novel organic sensitizers and greatly contributes to the development of more efficient devices. Indeed, the calculations of these photoelectrochemical properties along with the modeling of other key parameters such as the excited state redox potential, the vertical excitation and emission energies, the charge transfer nature of the excitation process and the electronic coupling between the dye and the semiconductor, would indicate the most promising dye candidates for solar energy and fuel (H 2 ) devices. This strategy has been intensely applied in literature for the molecular engineering of the organic sensitizer for DSSC [9][10][11][12][13][14], mostly using the methods of the density functional theory (DFT) and its time-dependent extension (TDDFT).
The accurate evaluation of GSRP is hard to achieve, especially because it has been shown that the accuracy deteriorates as the conjugation length of the molecule increases [15]. In the present study, the GSRP of 16 organic dyes having a medium to large conjugation length (see molecules in Figure 2) have been computed using DFT, and in particular the MPW1K functional [16,17], which has been shown to give the best accuracy before [15], and a polarizable continuum model (PCM) [18] to take into account solvent effects. To the best of our knowledge, this is the first work dealing with the calculations of GSRP of a relatively large set of organic dyes having a medium to large size of the conjugated scaffold. The DFT predicted values had been compared to the available experimental data showing that the employed strategy allows reproducing the GSRP with a mean absolute error <0.2 eV.

Methods
All quantum mechanical(QM) calculations were performed using density functional theory (DFT) and time-dependent DFT (TDDFT) [19] using the G09 program package [20]. The ground-state

Methods
All quantum mechanical(QM) calculations were performed using density functional theory (DFT) and time-dependent DFT (TDDFT) [19] using the G09 program package [20]. The ground-state redox potential was computed at the MPW1K/6-31+G* level of theory as free energy differences between the neutral and oxidized state of these dyes following the procedure described by Pastore et al. [15].
More specifically, GSRP = G 0 − G + solv where both G 0 solv and G + solv are obtained by adding the solvent effect to the free energies of the gas-phase optimized molecules: G 0 vac and G + vac are obtained by performing a single point calculation at the optimized geometry in vacuo, followed by frequency calculations. The free energies of solvation ∆G 0 solv and ∆G + solv are estimated as the free energy difference between the system in solution and in gas-phase, calculated at the geometry optimized in solution.
Neutral and oxidized ground-state geometries of all dyes were computed using the MPW1K [16,17] functional in combination with 6-31G* and 6-31+G* basis set both in gas-phase and in the presence of dichloromethane (DCM) as a solvent. The MPW1K functional choice was made as it was shown to be the method providing results closer to the experimental values when used for the calculations of GSRPs in smaller but related D-π-A dyes [15]. Solvent effects were added via PCM [18]. DCM is the solvent experimentally employed for the electrochemical measurements. Indeed, a rigorous way to obtain the ground state redox potential needs to consider in the calculation energy terms including geometry relaxation energy connected with changes of electronic structure and changes of the solvation energies.
Initial structures for the ground-state geometry optimization were built starting from their B3LYP/6-31G* optimized geometries, for which the most stable among the possible conformers had been identified in our previous papers (see References [10,12,[21][22][23]).
DFT frontier molecular orbitals and spin densities of the cation species were computed at MPW1K/6-31+G* level both in vacuo and using PCM.
Minus the value of the highest occupied molecular orbital (HOMO) energies, -ε(HOMO), were evaluated both in gas-phase and in DCM, for the neutral state of all dyes at their optimized geometry in DCM.
Vertical excitation energies (E exc ), absorption maxima (λ max ), and oscillator strengths (f ) were computed at the time-dependent DFT (MPW1K/6-31+G*) level on all the optimized structures. Again, the PCM was used to include the effect of the solvent. These results are shown in the Supplementary Materials.
Electrochemical experiments were conducted on N 2 -saturated solutions of the compound under study in freshly distilled dichloromethane, in the presence of electrochemical grade [Bu 4 N] [PF 6 ] (0.1 M) as supporting electrolyte (Merck). Cyclic voltammetry was performed in a three-electrode cell using a glassy carbon working electrode, a platinum counter electrode, and an AgCl/Ag (NaCl 3 M) reference electrode. A Bioanalytical Systems (BAS) 100 W electrochemical analyzer was used as polarizing unit. E S+/S values were obtained as standard potentials by averaging the values of the anodic and cathodic peaks and using the ferrocenium/ferrocene couple as an external standard. All the potential values were then referred to normal hydrogen electrode (NHE) by using a value of +0.63 V for ferrocene vs. NHE [24]. Typical analyte concentration was approx. 10 −3 M.

Results and Discussion
All the investigated dyes (see Figure 2) were based on fully conjugated D-π-A or D-A-π-A structures, the latter having an auxiliary acceptor group in the central part of the molecule. D5 and DF15 were triarylamine-thiophene derivatives bearing cyanoacrylic acid as anchoring group. The heterocyclic benzobisthiazole-and thiazolothiazole-systems constituted the central π scaffold of BBZ1,2 and TTZ1-7 sensitizers, respectively. The last group of molecules (BD1,2,6,7,8) contained an electron-poor bis-lactone moiety (Pechmann lactone) connected to thiophenes decorated with various donor and acceptor groups. With the only exception of compound D5 [25], the investigated dyes were selected based on reliable experimental data available, having been designed, characterized and synthetized in our laboratories, as described in our previous works [4,10,[21][22][23].
The neutral ground-state geometries of these dyes, computed at the MPW1K/6-31+G* level, are shown in Figure S1 (see Supplementary Materials). All the dyes assumed a largely planar structure along most of the conjugated system with a deviation from coplanarity (ranging from 27 • to 49 • ) between the triarylamine and the linked thiophene. To assess the quality of the MPW1K/6-31+G* optimized structures, their vertical excitation energies were computed at the TDDFT level and the comparison between these results and experimental values is shown in Table S1 of the Supplementary Materials. The mean absolute error was about 0.06 eV, which clearly indicates the accuracy of the optimized structures and the high degree of accuracy of MPW1K functional in dealing with the excited states of the analyzed D-π-A or D-A-π-A dyes. Table S1 (see Supplementary Materials) also shows that the main electronic transition was, in all cases, a HOMO→LUMO transition with a smaller contribution of a HOMO−1→LUMO transition. From the plot of the corresponding DFT frontier molecular orbitals collected in Table S2 of the Supplementary Materials, it is clear that the HOMO and LUMO were mostly localized on the donor and acceptor unit, respectively, albeit still with a sizable contribution of the conjugated scaffold.
Given the good performance of the MPW1K functional in reproducing the vertical excitation energies (this work) and in computing excited state geometries and vertical emission energies [12], the choice of MPW1K functional appears appropriate also to compute GSRP. Additionally, in a previous paper, the MPW1K has been demonstrated to be by far the method that provided computed GSRP values closer to the experimental ones [15].
The results of GSRP computed vs experimental E S + /S values on all the investigated dyes are shown in Figure 3. The graph is built from raw data of Table S3 (GSRP b-d ). The analysis of the computed values leads to some interesting considerations. At first glance, it is straightforward to observe that data covered two distinct regions of the graph: GSRP values calculated in the gas-phase overestimated the experimental value (black circles in the region above the diagonal, where y = x, i.e., calculated (y) = experimental (x)), while GSRP values calculated in the presence of the solvent slightly underestimated the experimental value (red and blue circles, below the diagonal). The use of high-quality basis sets in the geometry calculation visibly improved the agreement between the calculated GSRP and experimental potential values (red circles). From the quantitative point of view, the highest level of theory employed, i.e., computing frequencies at the MPW1K/6-31+G* on neutral and oxidized state geometries optimized at the same level (MPW1K/6-31+G*//MPW1K/6-31+G*) was the one that provided the most accurate values with a mean absolute error (MAE) of 0.18 eV (red circles). Higher deviations from experiments were found applying the MPW1K/6-31+G* combination on neutral and oxidized state geometries computed at the MPW1K/6-31G* level (MPW1K/6-31+G*//MPW1K/6-31G*). Indeed, the MAE was about 0.32 eV (blue circles). The highest deviations from experiments were provided by the GSRP calculations in terms of free energies using the MPW1K/6-31+G*//MPW1K/6-31+G* level in gas-phase (black circles). Thus, we may conclude that the difference of the free energy values allows, at least, to correctly reproduce the redox potential qualitative trend, while calculations using the use of the MPW1K/6-31+G*//MPW1K/6-31+G* level in the presence of the solvent is crucial to correctly reproduce the quantitative trend. According to Koopmans' theorem [26], related to the closed-shell Hartree-Fock theory and extended to Kohn-Sham orbital energies within the DFT [27,28], the negative of the HOMO energy is equal to the first ionization energy of a system, which is the minimum energy required to remove an electron from the HOMO of a molecule. The first ionization energy of a system can be related to the energy involved in the oxidation (loss of electrons) of a molecule and therefore to E S+/S . Thus, -ε(HOMO) values were also computed both in gas-phase (Figure 3, grey triangles and Figure  5, blue circles) and in DCM (Figure 3, grey asterisks and Figure 5, brown circles)) giving a MAE of 0.50 and 0.56 eV, respectively. The data provided by the computation of -ε(HOMO) values in gas-phase were slightly closer to the experimental values than the -ε(HOMO) values computed in solution. This evidence could be related to the fact that, for the investigated molecules in the gas-phase, the orbitals of the charged and neutral species are nearly identical and orbital relaxation is not expected. Since the difference ∆ε = ε (HOMO)vac − ε(HOMO)solv broadly varies from ∼ 0 to a few hundreds of meV, we further investigated three of the dyes, namely TTZ7 (a large molecule with the largest ∆ε), BD2 (a large molecule with ∆ε ≈ 0) and D5 (a small molecule with ∆ε ≈ 0). To probe the extent of the orbital relaxation, the HOMO of each neutral dye was compared with the spin-density surface calculated for its cation; orbital relaxation should produce visible differences in the space localization of these two surfaces. Figure 4 shows how, for D5 and BD2, the HOMO of the neutral dye and the spin density of its cation had a very similar shape and space distribution, both in the gas-phase and in DCM. Therefore, in this case, the orbital relaxation was minimal and Koopmans' theorem was expected to be valid, either in gas phase or in solution. On the other hand, the HOMO of TTZ7 and the spin density of TTZ7 + had a similar shape and space distribution in the gas-phase. In contrast, in solution, the spin density was much more localized on the donor region as an effect of the orbital rearrangement. Localization of the charge on a more restricted region was possible because of the stabilizing interaction with the solvent. In this case, there were not favorable conditions to apply Koopmans' theorem. In general, charge localization is driven by the presence of electronwithdrawing groups, facilitated by the larger size of the molecule and made possible by the presence of the solvent. At the same time, charge delocalization is favored by the relief of the interelectronic repulsion and made possible by the presence of an efficient conjugation path. Considering all these aspects, after having analyzed the conformation, the dimensions and the presence of electronwithdrawing groups, it has not been possible to univocally identify the reason why a more marked charge localization is observed only in some cases. Reasonably this interesting aspect will require a dedicated study and may be the subject of subsequent work, but we will have to settle for this further caveat against the uncritical use of Koopmans' theorem. Since the difference ∆ε = ε (HOMO) vac − ε(HOMO) solv broadly varies from~0 to a few hundreds of meV, we further investigated three of the dyes, namely TTZ7 (a large molecule with the largest ∆ε), BD2 (a large molecule with ∆ε ≈ 0) and D5 (a small molecule with ∆ε ≈ 0). To probe the extent of the orbital relaxation, the HOMO of each neutral dye was compared with the spin-density surface calculated for its cation; orbital relaxation should produce visible differences in the space localization of these two surfaces. Figure 4 shows how, for D5 and BD2, the HOMO of the neutral dye and the spin density of its cation had a very similar shape and space distribution, both in the gas-phase and in DCM. Therefore, in this case, the orbital relaxation was minimal and Koopmans' theorem was expected to be valid, either in gas phase or in solution. On the other hand, the HOMO of TTZ7 and the spin density of TTZ7 + had a similar shape and space distribution in the gas-phase. In contrast, in solution, the spin density was much more localized on the donor region as an effect of the orbital rearrangement. Localization of the charge on a more restricted region was possible because of the stabilizing interaction with the solvent. In this case, there were not favorable conditions to apply Koopmans' theorem. In general, charge localization is driven by the presence of electron-withdrawing groups, facilitated by the larger size of the molecule and made possible by the presence of the solvent. At the same time, charge delocalization is favored by the relief of the interelectronic repulsion and made possible by the presence of an efficient conjugation path. Considering all these aspects, after having analyzed the conformation, the dimensions and the presence of electron-withdrawing groups, it has not been possible to univocally identify the reason why a more marked charge localization is observed only in some cases. Reasonably this interesting aspect will require a dedicated study and may be the subject of subsequent work, but we will have to settle for this further caveat against the uncritical use of Koopmans' theorem. Figure 4. HOMO of the neutral species (top) and the spin density of its cation (bottom) in gas-phase (left) and DCM (right) for D5, BD2 and TTZ7 dyes computed at the MPW1K/6-31+G* level and plotted using Avogadro [29,30] and Chemcraft [31] softwares, respectively. Figure 5, which collects the computed GSRP vs dyes, reveals that, considering closely related compounds with similar scaffolds, computed GSRPs and -ε(HOMO) reproduced the same trends found for the experimental values. For example, GSRP and -ε(HOMO) values of DF15 were lower in energy than those of D5, due to the presence of a stronger hexyloxy-substituted donor group in DF15. Both dyes had more positive values than the redox potential of the conventionally and commonly used redox couple in DSSC, i.e., the iodide/triiodide redox couple (4.77 eV) [32], as well some Co-based redox systems (4.85-5.04 eV) [33] suggesting that regeneration of the sensitizer is feasible. Similar considerations apply to the Pechmann lactone containing molecules (BD1, 2,6,7,8) and to the benzobisthiazole-(BBZ1,2) and thiazolothiazole-systems (TTZ1-7). In particular, and again in agreement with the experimental values, the introduction of a stronger donor group in BD2 compared to the one present in BD1, and the substitution of the lactone moiety of BD1 with the less electron-withdrawing lactam in BD8, determined the lowering of the GSRP. Moreover, the substitution of the cyanoacrylic acid with a less electron-withdrawing acceptor (BD6 and BD7 vs BD2)
Inspection of Figure 5, which collects the computed GSRP vs. dyes, reveals that, considering closely related compounds with similar scaffolds, computed GSRPs and -ε(HOMO) reproduced the same trends found for the experimental values. For example, GSRP and -ε(HOMO) values of DF15 were lower in energy than those of D5, due to the presence of a stronger hexyloxy-substituted donor group in DF15. Both dyes had more positive values than the redox potential of the conventionally and commonly used redox couple in DSSC, i.e., the iodide/triiodide redox couple (4.77 eV) [32], as well some Co-based redox systems (4.85-5.04 eV) [33] suggesting that regeneration of the sensitizer is feasible. Similar considerations apply to the Pechmann lactone containing molecules (BD1, 2,6,7,8) and to the benzobisthiazole-(BBZ1,2) and thiazolothiazole-systems (TTZ1-7). In particular, and again in agreement with the experimental values, the introduction of a stronger donor group in BD2 compared to the one present in BD1, and the substitution of the lactone moiety of BD1 with the less electron-withdrawing lactam in BD8, determined the lowering of the GSRP. Moreover, the substitution of the cyanoacrylic acid with a less electron-withdrawing acceptor (BD6 and BD7 vs. BD2) provided experimental ground-state oxidation potentials similar to BD2. While the computed GSRP and -ε(HOMO) values for BD6 and -ε(HOMO) value for BD7 are in line with this observation, GSRPs of BD7 were instead predicted to be higher in energy although closer to the experimental values. Concerning the benzobisthiazole-(BBZ1,2) and thiazolothiazole-systems (TTZ1-7), the introduction of electron-rich methoxy-substituents on TTZ2 and BBZ2 led to a decrease in the ground-state oxidation potentials compared to TTZ1 and BBZ1, respectively, which is also evident in the computational results. In the series TTZ3-7, in line with experiments, the introduction of the electron-donating alkoxy groups on the triarylamine portion in TTZ4 and the presence of the terminal phenothiazine unit in TTZ7 resulted in lowering ground-state oxidation potential values. However, all BBZs and TTZs dyes had ground-state oxidation potentials more positive than that of the iodide/triiodide couple, thus assuring dye regeneration. The present results are consistent with the following final observations: (i) the frontier orbital approximations, according to Koopmans' theorem, might be used to reproduce the trend of standard potentials in closely related families of compounds but cannot be used as a method to predict quantitative values; (ii) to obtain GSRPs with a certain degree of accuracy sufficient to be comparable with experimental standard potentials, free energy differences computations including solvent effects need to be taken into account.
provided experimental ground-state oxidation potentials similar to BD2. While the computed GSRP 240 and -ε(HOMO) values for BD6 and -ε(HOMO) value for BD7 are in line with this observation, GSRPs 241 of BD7 were instead predicted to be higher in energy although closer to the experimental values.

242
Concerning the benzobisthiazole-(BBZ1,2) and thiazolothiazole-systems (TTZ1-7), the introduction 243 of electron-rich methoxy-substituents on TTZ2 and BBZ2 led to a decrease in the ground-state 244 oxidation potentials compared to TTZ1 and BBZ1, respectively, which is also evident in the

258
The present study shows that, using the MPW1K functional in combination with an appropriate 259 basis set, the prediction of GSRP of a relatively large set of D-π-A/D-A-π-A dyes having a medium

Conclusions
The present study shows that, using the MPW1K functional in combination with an appropriate basis set, the prediction of GSRP of a relatively large set of D-π-A/D-A-π-A dyes having a medium to large size of the conjugated scaffold can be obtained with a good level of accuracy. Moreover, the experimental trends in GSRP values of closely related compounds with similar scaffolds are well reproduced. Thus, the employed strategy should help researchers to identify sensitizers that can efficiently be used in DSSCs or in photocatalytic systems for the production of H 2 , allowing them to concentrate precious time and resources only on the preparation of the most promising candidates.