Acid-base properties of the N 3 Ruthenium ( II ) solar cell sensitizer : A combined experimental and computational analysis

Single Value Decomposition techniques, followed by Global Fitting procedures, allowing us to identify four separate acid base equilibria and their corresponding ground state pKa values. DFT/TDDFT calculations were performed for the N3 dye in solution, investigating the possible relevant species obtained by sequential deprotonation of the four dye carboxylic groups. TDDFT excited state calculations provided UV-vis absorption spectra which nicely agree with the experimental spectral shapes at various 15


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In the last two decades, dye-sensitized solar cells (DSSCs) 1,2 have attracted a wide interest as potential low-cost photovoltaic systems endowed with high efficiency.In these devices, a dye sensitizer absorbs the solar radiation and transfers the photoexcited electron to a wide band-gap semiconductor (usually TiO 2 ) electrode consisting of a mesoporous oxide layer, while the concomitant hole is transferred to the redox electrolyte, typically iodide/triiodide in solution or a hole-transporting material in the solid state.Recently, the DSSCs field has been revolutionized by Cobalt-based electrolytes, 3 which led to a new efficiency record close to 13%. 4,5 e [Ru(dcbpyH 2 ) 2 (NCS) 2 ] (dcbpyH 2 = 4,4'-dicarboxyl-2,2' bipyridine) dye and its doubly deprotonated TBA salt, N3 and N719, respectively, have maintained a clear lead in DSSCs technology, with efficiencies exceeding 11%. 6,7 or this family of dyes, it was found that the photocurrent obtained from TiO 2sensitized films decreased when the fully protonated to fully deprotonated dyes were used to dye the semiconductor film. 8The DSSCs open circuit voltage, on the other hand, showed an opposite trend, increasing from the fully protonated to the fully deprotonated dye.An optimal product of photocurrent and open circuit voltage was found for an intermediate number of protons, which allowed further device optimization leading to efficiency exceeding 11%. 7his marked dependency of the DSSCs performance on acid-base 45 chemistry was attributed to the dye protons, initially residing on the dye carboxylic groups, being released to the TiO 2 surface during the sensitization process, thus charging the semiconductor positively. 9,10 he position of the TiO 2 conduction band is known to be dependent from the pH (it becomes more negative by 0.06 50 V for pH unit increase). 11,12 he dependence of the injection kinetics upon protonation of the sensitizer dye most probably thus derives from the influence of protons in determining the potential of the TiO 2 conduction band. 13Binding of the fully protonated dye is likely to result in larger proton adsorption to the metal 55 oxide than for the corresponding TBA salts.Indeed, measurements of electron injection rates as function of the pH of the dye sensitizer solution, demonstrated that the component of ultrafast injection (<100 fs) increases upon decreasing the dye solution pH from 8 to 2, 14  N3 and N719 sensitizers on TiO 2 showed that these dyes anchor onto the TiO2 surface using two to three of their four carboxylic acid groups. 8,13,15,16 Th increased open circuit potential observed with the deprotonated dye is, at least in part, the result of the negative shift of the TiO 2 conduction band due to iodide/triiodide redox couple and the DSSCs quasi-Fermi level under illumination.The decrease in the photocurrent density observed for the fully deprotonated dye compared to that of the fully protonated dye is possibly due to the influence of protons on the energetics of the TiO 2 conduction band and therefore on the energetics of electron injection, which depend on the density of acceptor semiconductor states.An alternative reason could be the slower regeneration of the dye by the redox couple because of the decreased driving force between the dye and the redox couple.Indeed, studies of N3 in solution indicated a less positive dye 10 oxidation potential by decreasing the number of dye protons. 17ver the years, motivated by the great interest in the photovoltaic applications an increasing number of groups have investigated the acid-base properties of Ru(II) polypyridyl complexes, including the N3 dye.pK a values of 1.85 and 2.90 have been reported for Ru(bpy) 2 (dcbpy) 2+ (bpy= 2,2' bipyridine, dcbpy = 4,4'dicarboxybipyridine), which were related to the concomitant deprotonation of almost equivalent carboxylic groups. 18,19 zeeruddin et al. 20 characterized the electrochemical and photochemical properties of several Ru(II) complexes.In 20 particular they investigated the complexes of the series [Ru(bpy) n (dcbpy) 3-n ] (bpy= 2,2' bipyridine, dcbpy = 4,4' dicarboxybipyririne, n =1-3).For n=1 they found two pKa values at 1.75 and 2.85 indicating that two carboxylic groups are independent.For n= 2 and 3 they found again two pK a , so they 25 proposed that the dissociation is simultaneous occurring with 1.80-2.50and 1.70-2.20 pK a values, respectively.Nazeeruddin et al. have then reported two studies regarding two fundamental dyes, i.e. the Black Dye 21 and N3, 22 which are amongst the most efficient solar cells sensitizers.In the Black 30 Dye, [Ru(H n tcterpy)(NCS) 3 ] x-with n=3, 0 and x = 1, 4 (tcterpy = 4,4',4''-tricarboxy-2,2':6',2''-terpyridine), there are three carboxylic groups on the 4,4',4''-positions of the terpyridine ligand.The titration curves obtained by plotting the absorbance as a function of pH showed a clear inflection point at pH = 3.3 giving the ground state pK a value of 3.3±0.1.A second inflection point was observed at pH 5. The pK a at 3.3 was assigned to the concurrent dissociation of two protons of the peripheral pyridines, while the second pK a value,  5, was assigned to the deprotonation of the central pyridine carboxylic group.
In the N3 complex there are four carboxylic groups in two 4,4'dicarboxy-2,2'-bipyridine ligands that could potentially give four separated acid-base equilibria.Nazeeruddin et al. 22 determined the N3 pK a values by UV-Vis spectroscopy measurements.The titration curves showed two inflection points, providing pK a values of 3.0 ± 0.1 and 1.5 ± 0.1 for the concomitant double deprotonation.The observation of two pK a values again suggested that there are two separate acid-base equilibria involving the simultaneous dissociation of two protons.Motivated by the established impact of the dye/semiconductor 50 acid-base chemistry interactions in solar cells devices, in this paper we report a joint experimental and computational reinvestigation of the acid-base properties of the N3 dye.On the experimental side, we report a spectroscopic characterization of the N3 complex with different degrees of protonation and a 55 systematic study of its acid base properties.We have then carried out DFT/TDDFT calculations to extensively investigate the protonation effect of the terminal carboxylic groups, and also computed the pK a values to be compared with the experimental data.Thanks to our combined investigation, we are able to 60 distinguish and tentatively assign the pK a s of the four carboxylic groups of the N3 dye, allowing for a deeper insight into the acidbase properties of this important dye sensitizer.

65
The investigated compound N3 was a Solaronix product used without further purification.Ethanol (EtOH) was purchased from Fluka, while nitric acid (HNO 3 ) was a Sigma-Aldrich product and NaNO 3 salt was furnished by Carlo Erba.

Photophysical measurements 70
Absorption spectra were recorded with a Cary 4E Varian spectrophotometer.A dye stock solution (≈10-5 M) was prepared in 1:1 H 2 O/EtOH mixture containing 0.1 M NaNO 3 .Ethanol was used to enable compound solubilization in aqueous solution, while NaNO 3 keeps the ionic strength constant.The solution pH 75 was initially adjusted to a value of 12 by addition of 0.2 N NaOH and then lowered with concentrated HNO 3 .Notice that the pH scale is defined in aqueous solution, so the in mixed waterethanol solutions a different pH scale is expected.However, the differences in the pH scale 23 and consequently in the resulting 80 pK a values 24 are considered marginally significant for the aim of the present work.The UV-vis spectrum of each solution was recorded after adding a negligible acid volume and allowing the solution to equilibrate for 5 minutes.In order to establish the pK a of the acid-base equilibria as well as the concentration profiles 85 and the spectra of intermediate species, the global fitting of multivariate spectrophotometric data was carried out by the ReactLab Equilibria software (Jplus Consulting). 25The parameters sum-of-squares (ssq) and deviation standard for the residuals (σ r ) were used to evaluate the goodness of the fits.For 90 the analysis of the absorption spectra with a model of four acidbase equilibria, ssq = 0.13 and σ r = 0.009 were obtained.Typical experimental errors on the pK a values were estimated to be smaller than ± 5%.

Quantum−mechanical calculations
complexes.Following the 100 experimental titration studies, we considered five different protonation states related to the different solutions pH values.In particular, the optical data, measured in a pH range 9-0.5, were compared with the nonprotonated species (N3 4-), the monoprotonated (N3H .Here, the free energy of deprotonation in water is computed as , derived from the 110 thermodynamic cycle described in Ref. 26.For the proton we adopted values of -6.28 kcal/mol 27 and -263 kcal/mol 28 for the free energy in gas phase, G gas,H+ , and for the free energy of solvation, G solv,H+ , respectively.For the calculation of the free energy terms in gas phase (G gas,HA and G gas,A-), it is necessary to perform single point calculations at the optimized geometries of the protonated and deprotonated species in vacuum, followed by frequency calculations in order to include the vibrational contribution to the total partition function.G isolv is obtained by single-point calculation in water and reference calculations in gas phase at the optimized geometries in solution.All the calculations were performed using the Gaussian03 (G03) 29 program package.
Geometry optimizations of all complexes were performed in vacuum and aqueous solution, using the B3LYP exchangecorrelation functional, 30 using LANL2DZ basis set 31 for all atoms along with the corresponding pseudopotentials for Ru.Frequency calculations have been performed at the same level of geometry optimization in gas phase.For the single point calculations in gas phase and in solution we adopted a LANL2DZ basis set and pseudopotential for Ru augmented with a 6-31+G* basis sets 32,33 for N, C, S, O and H atoms. Solvation effects were included by means of the polarizable continuum model (CPCM), 34,35 as implemented in G03.To determine the pK a values, geometry optimizations were performed in water solution by means of the conductor-like polarizable continuum model (CPCM) using three different options: the default UA0 solvation radii, specific spheres (SPH) added on the carboxylic hydrogens, and UAHF solvation radii. 36he pKa is then calculated according to the following equation: TDDFT calculations of the lowest singlet-singlet excitations were performed for all considered species in aqueous solution on the structure optimized in vacuum and using a DGDZVP basis set.To simulate the optical spectra, the 70 lowest spin-allowed singlet-singlet transitions were computed on the ground state geometry.Transition energies and oscillator strengths were interpolated by a Gaussian convolution with an σ value of 0.15 eV, corresponding to an FWHM of  0.4 eV.

UV-vis Spectroscopic Properties and pKa determination
The UV-vis absorption spectra of N3 in 1:1 H 2 O/EtOH mixture (buffered at pH = 0.5-9) were recorded in the 250-700 nm range at room temperature (Figure 1).The absorption spectra are characterized by three bands in the investigated region whose position changes significantly with pH (λmax ≈ 310, 370-400 and 510-530 nm, respectively).These bands are typically assigned as π  π* transitions of the bipyridine ligands, and MLCT excitations involving a partial NCS ligand contribution, respectively. 37The spectral changes show three quasi isosbestic points at ca. 380, 460 and 515 nm, thus indicating that multiple species contribute to the absorption spectra.In order to characterize quantitatively the N3 acid-base equilibria, the absorption spectra of N3 recorded at various pH values were 55 analyzed by SVD analyses followed by Global Fitting procedures.We thus obtained five significant spectral components which describe the experimental data (Figure 2 and Table 1), together with the pK a of the associated acid-base equilibria 1-4: The molar absorption coefficients of the various protonated forms 65 of N3 are also provided by the analysis (Figure 2 and Table 1).The titration curves obtained at relevant wavelengths of analysis (at 385, 510, and 530 nm, where absorbance changes significantly with pH) are shown in Figure 3.The obtained pK a values were then used to calculate the concentration of each species during the titration experiment.Figure 4 shows the concentration profiles obtained for the five 80 differently protonated species of N3.In particular, at pH > 7 only the completely deprotonated form is found in solution, while, owing to the close pK a s, in acidic solutions at least two species are concomitantly present.

Computational analyses
Molecular and electronic structures.
We considered five different protonated form, named N3H x , with x = 4-0.For N3H 2 2-we have four different isomers, named N3H 2 2-_A, N3H 2 2-_B, N3H 2 2-_C and N3H 2 2-_D, while for N3H 3 -and N3H 3-we have two different isomers, N3H 3 -_A-B and N3H 3-_A-B, respectively (Figure 5).A schematic orbital energy diagram of the more stable investigated complexes is reported in Figure 6, while isodensity plots of the frontier orbitals of N3 4-are shown in Figure 7.A similar study was already reported by some of us, 7 here we just update this information at the presently employed level of theory and briefly summarize the results.The set of quasi-degenerate HOMO, HOMO-1 and HOMO-2 of all the investigated complexes have essentially Ru t 2g character.The LUMOs of the complexes are bipyridine π* orbitals, with different electronic localization depending on the pronation.The main difference with respect to the protonated species is that the HOMO-LUMO gap increases from 2.49 to 2.88 eV, going from N3H 4 to N3 4-, due to a larger destabilization of the unoccupied with respect to the occupied orbitals. 7This is the reason for the observed blueshifted absorption bands with increasing pH.

Acid-base properties
We simulate now the acid-base properties of the various protonated forms of the N3 dye.We computed four different pK a values with all the investigated solvation models (UA0, SPH and UAHF, see computational details).To tentatively define the stability of different isomers we resort to both Gibbs free energy values employed to calculate the pK a s and the so-called total free energy in solution, from SCF calculations, see Table 2.
Table 2 Relative free energies (including thermal contributions), first _A, see Figure 5, are the most stable tautomers among the species with 3 and 2 protons, respectively, while the monoprotonated N3H 3-_A and 50 N3H 3-_B species are essentially isoenergetic.By using SCF energy values, an opposite trend is found.We need to notice, in any case, that the calculated differences are very small so that the assignment of the deprotonation pathway should be considered with some caution.

55
A summary and comparison of the experimental and computed pK a s involving the most stable tautomers is reported in Table 3.We note that the values obtained using specific spheres (SPH) added on the carboxylic protons provide results which are in closer agreement with the experimental data, while the default 60 UA0 and the widely employed UAHF solvation radii tend to overestimate the experimental values, Table 3.On overall, our calculated SPH values agree within 0.31 to 1.06 units of pK a with the experimental values.We also notice that the agreement with the experiment tends to decrease by increasing the negative 65 charge of the investigated species, which can be related to the need of explicit solvent effect, e.g.interaction with water molecules, to properly describe the highly negatively charged N3H3-and N34-species.Having in mind the limitations of the model employed, we can draw a deprotonation pathway, see 70 Figure 8.With reference to Figure 8, we notice that the most acidic protons are predicted to be those lying on the pyridine ligands cis to the NCS ligands, which are less influenced by the anionic NCS ligands than those in the pyridine ligands trans to the NCS groups.Based on calculate free energies, the second deprotonation should involve the second carboxylic group of the already deprotonated bipyridyne ligand, leading to N3H the presence of the tetrabutylamonium counterions might however induce some slight changes in the tautomers stability order.As mentioned above, the performance of the pK a calculation tends to decrease, compared to the experimental values, by increasing the negative charges of the species involved in the third and fourth deprotonation steps.

Absorption spectra
The UV-vis properties of the N3 dye and of its deprotonated forms have been extensively investigated by DFT/TDDFT, 7, 37-40 20 In this paper, we simulated the absorption spectra of all the considered species to provide a direct connection to the measured UV-vis properties.In order to obtain the global spectrum which might be observed for each species, we calculated the averaged spectrum, weighted by the respective stabilities, of the different 25 A, B, C and D tautomers, see Supporting Information.In order to reproduce the experimental spectra at various pH values, we used the concentration profile obtained from the titration experiment.In particular we considered the global spectrum as a sum of contribution of the five species involved in the acid-base 30 equilibria, as reported in equation 1: where α pH , β pH , γ pH , δ pH and ε pH represent the concentration coefficient at each pH values, while 4H, 3H, 2H, 1H and 0H represent the computed spectrum for the different species.The 35 results are reported in Figure 9 for three representative pH (3.83, 5.35 and 7.74).As it can be noticed, our results are in good agreement with the experimental values, confirming the potential of the employed methodological set-up.

Conclusions
We have presented a combined experimental and theoretical study on the acid-base properties of the prototypical [Ru(dcbpyH 2 ) 2 (NCS 2 ) 2 ] N3 solar cell sensitizer.On the experimental side, the single value decomposition of the absorption spectra measured at various pH provided a number of five significant spectral components which describe the 50 experimental data, corresponding to four separate pK a values.In particular, at pH > 7 only the completely deprotonated form is present while, owing to the close pK a s, in mildly acidic solutions, at least two differently protonated species are present at the equilibrium.We have then carried out DFT/TDDFT calculations 55 in vacuum and water solution of molecular and electronic structures, optical and acid base properties.The calculated pK a values were in excellent agreement with experimental data for the first two deprotonation steps, allowing for a tentative assignment of the deprotonation pathways occurring in the N3 dye.A slight 60 deterioration of the calculated pK a s is found for the subsequent deprotonations, due to the highly negative charge of the involved species.The employed theoretical and experimental approach also allows us to reproduce the N3 UV-vis spectral shape at different pH values.We believe this study to constitute a 65 benchmark for the important acid-base properties of Ru(II)polypyridine solar cells sensitizers.
in relation to the energy down-shift of 60 the TiO 2 conduction band.From an experimental standpoint, information on the semiconductor/dye interfaces is usually accessed by vibrational spectroscopy [Fourier Transform InfraRed (FT-IR) spectroscopy].A quantitative analysis of the adsorption mode of 65 95 <Figure1>

60 <Scheme1> Scheme 1
Acid-base equilibria and pKa values of N3 obtained by SVD Analysis and Global Fitting.

Fig. 6
Fig.6 Schematic representation of the energy levels and the molecular structures of the more stable N3Hx complexes, considering Gibbs free energies in water solution. <Figure7>
the second proton in cis to the NCS groups is found very close in free energy (0.19 kcal/mol) or favored considered SCF energies.As a matter of fact the NMR spectrum of the N719 salt shows couples of equivalent aromatic signals, ruling out the possibility of the asymmetric structures N3H 7] The different solvent employed and 10 <Figure9>

Table 1
Absorption maxima and molar coefficients of the various protonated forms of N3.

Table 3
Comparison between experimental and calculated pKas using different computational methods.For calculated pKas the, the lowest values obtained among the various tautomers for each deprotonation step are reported.Schematic representation of deprotonation path of N3H4 together with the pKa values calculated by SPH method.