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Absorption Spectra and Excited State Energy Levels of the N719 Dye on TiO2 in Dye-Sensitized Solar Cell Models Filippo De Angelis,*,† Simona Fantacci,†,‡ Edoardo Mosconi,† Mohammad K. Nazeeruddin,§ and Michael Gr€atzel§ †
Istituto CNR di Scienze e Tecnologie Molecolari (ISTM-CNR), c/o Dipartimento di Chimica, Universita di Perugia, Via elce di Sotto 8, I-06213, Perugia, Italy ‡ Italian Institute of Technology (IIT), Center for Biomolecular Nanotechnologies, Via Barsanti, I-73010, Arnesano, Lecce, Italy § Laboratory for Photonics and Interfaces, Station 6, Institute of Chemical Sciences and Engineering, School of basic Sciences, Swiss Federal Institute of Technology, CH - 1015 Lausanne, Switzerland
bS Supporting Information ABSTRACT: We have investigated the absorption spectrum and the alignment of ground and excited state energies for the prototypical N719 Ru(II) sensitizer adsorbed on an extended TiO2 model by means of high level DFT/TDDFT calculations. The calculated and experimental absorption spectra for the dye on TiO2 are in excellent agreement over the explored energy range, with an absorption maximum deviation below 0.1 eV, allowing us to assign the underlying electronic transitions. We find the lowest optically active excited state to lie ca. 0.3 eV above the lowest TiO2 state. This state has a sizable contribution from the dye π* orbitals, strongly mixed with unoccupied TiO2 states. A similarly strong coupling is calculated for the higher-lying transitions constituting the visible absorption band centered at ca. 530 nm in the combined system. An ultrafast, almost instantaneous, electron injection component can be predicted on the basis of the strong coupling and of the matching of the visible absorption spectrum and density of TiO2 unoccupied states. Surprisingly, this “almost direct” injection mechanism, corresponding to excitation from the dye ground state to an excited state largely delocalized within the semiconductor, is found to give rise to almost exactly the same absorption profile as for the dye in solution, despite the drastically different nature of the underlying excited states. On the basis of our calculations it seems therefore that no sizable lower bound to an “injection time” exists, rather the timings of electron injection are mainly ruled by electron dephasing in the semiconductor.
1. INTRODUCTION Dye-sensitized solar cells (DSSCs) are currently attracting large academic and industrial interest as a low-cost and highly efficient approach to the direct conversion of light into electrical power.18 In DSSC devices, sunlight is absorbed by a molecular dye sensitizer anchored on the surface of a moseporous semiconducting TiO2 film made of synthered nanoparticles. Upon light absorption by the dye, a charge-transfer excited state is generated, from which an electron is transferred to the manifold of unoccupied semiconductor states, it diffuses toward the transparent conductive oxide film and reaches the electrical contact. At the same time, a charge hole is transferred from the oxidized dye to a the redox electrolyte (usually based on the I/I3 couple in organic solvents) or to a hole conductor. Electrolyte regeneration at the cathode eventually closes the circuit.18 Ruthenium(II) polypyridyl complexes maintained a clear lead as the most efficient dye sensitizers to date,9,10 particularly the prototype [cis-(dithiocyanato)-Ru-bis(2,20 -bipyridine-4,40 -dicarboxylate)] complex (N3) and its doubly protonated tetrabutylammonium salt (N719).9,10 In these complexes, the thiocyanate r 2011 American Chemical Society
ligands ensure fast regeneration of the photooxidized dye by the I/I3 redox mediator, while the two equivalent bipyridine ligands functionalized in their 440 positions by carboxylic groups ensure stable anchoring to the TiO2 surface, allowing at the same time for the strong electronic coupling required for efficient excited-state charge injection.10,11 Despite showing only relatively intense absorptions in the blue and green spectral regions (400 and 535 nm, ε ≈ 14000 M1 cm1),9,10 the N719 dye has shown an efficiency exceeding 11% when employing the most commonly used I/I3 liquid electrolyte.10 Part of the reason for this success is due to the high open circuit potential obtained in optimized cells based on N719, which is so far unmatched by other dyes under comparable conditions.12 A further interesting and almost unique peculiarity of the N3/ N719 dye is the ultrafast electron injection occurring after light absorption;1318 see also Ardo and Meyer for a recent review.19 Obviously, the efficiency of the electron injection step is a Received: December 16, 2010 Revised: March 28, 2011 Published: April 08, 2011 8825
dx.doi.org/10.1021/jp111949a | J. Phys. Chem. C 2011, 115, 8825–8831
The Journal of Physical Chemistry C fundamental requisite for functioning DSSCs, so as to avoid parasitic excited state deactivation pathways which would decrease the cell efficiency. Upper limits for injection times in N3/ N719-sensitized TiO2 have been estimated by various authors to be in the 1025 fs range,14,16,18 which has led to assign the ultrafast electron injection component as occurring from a highlying, nonthermalized singlet excited state prior to vibrational relaxation and intersystem crossing to a lower-lying triplet state.14,16,18 To attain electron injection on such a short time scale, strong electronic coupling through the dye anchoring groups needs to exist together with a high density of unoccupied semiconductor states “surrounding” the dye excited state. Under these circumstances, the limiting phenomenon ruling the injection time is possibly the electron dephasing occurring in the solid,18,20 which in related systems has typical time scales of ∼10 fs.20 Interestingly, the ultrafast injection dynamics has also been found to occur along with slower injection components on the picosecond time scale,1318 which have been interpreted as being due to injection from a lower lying triplet state16 and/or from the heterogeneous dye interaction with the TiO2 nanostructured electrode.18 The relative weights of short and long injection components have been observed to depend upon the laser excitation wavelength, with the shorter time component being increased from 56 to 75% of the total injection yield when using 620 and 440 nm laser sources, respectively.17 This observation further confirms the idea of injection from a nonthermalized singlet state: assuming a constant electronic coupling, the higher semiconductor density of unoccupied states sampled by the higher-energy excitation wavelength would be responsible of the increased ultrafast injection yield. If the system’s excited state were to decay to the lowest excited state and thermalize before injecting, a negligible wavelength dependency would in principle be expected. A related phenomenon, observed by the same authors, was the ultrafast injection component dependence on the buffered pH of the sensitizer solution used to dye the electrodes, which led to a 44 to 73% ultrafast injection increase upon decreasing the solution pH from 8 to 2.17 The position of the TiO2 conduction band is indeed known to be dependent from the pH (it becomes more negative by 0.06 V for pH unit increase).21 Since the sensitizers protons are mainly transferred to TiO2 upon dyeing the semiconductor electrode,22,23 the TiO2 conduction band energy downshift associated to the increased number of dye protons would lead to a higher density of unoccupied semiconductor states in correspondence of the dye excited state, increasing the ultrafast injection component. Notably, this behavior is perfectly paralleled in DSSC devices, whereby increasing the dye protons content was found to lead to increased photocurrent densities and decreased open circuit voltage,22 reflecting the TiO2 conduction band shifts discussed above. Thus, the energetic position of the dye excited state relative to the TiO2 conduction band and the electronic coupling are the fundamental parameters to use to interpret the various experimental results and possibly to design new and more efficient dye sensitizers. Along with the dye molecular/electronic structure and adsorption mode, which determine the electronic coupling, a key parameter for efficient dyes is the energetic position of the dye excited state relative to the TiO2 conduction band edge, which formally sets the “driving force” for excited state electron injection into the manifold of TiO2 unoccupied states. The dye excited state oxidation potential (ESOP), rigorously corresponding to the Gibbs free energy
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difference between the neutral and oxidized dye in its excited state, is usually approximated by3 ESOP ðG0 Gþ ÞGS E0-0 where (G0 Gþ)GS is the ground state oxidation potential and E00 is the adiabatic lowest excitation energy. Electrochemical measurements of the ground state oxidation potential along with the spectroscopic evaluation of E00 for the dyes in solution allow therefore to estimate the ESOP which, compared to the position of the TiO2 conduction band energy, provides an estimate of the formal injection driving force. These measurements are usually performed for the dye in solution, i.e., not adsorbed onto the TiO2 semiconductor; thus the alignment of interacting dye/semiconductor energy levels and the associated driving force for injection efficiency for the dye on TiO2 remain rather elusive quantities. Theoretical and computational modeling can thus provide fundamental atomistic information which are scarcely accessible by experimental tools. In this respect, we recently calculated the adsorption mode of N719 on extended TiO2 models, and systematically evaluated the role of protonation and counterions on the combined systems electronic structure.24 In this paper we move beyond such ground state picture and present extended TDDFT excited state calculations on the absorption spectrum and alignment of energy levels for the prototype N719 dye on TiO2, to provide a unified picture of the joint dye/semiconductor excited states, thus providing hitherto inaccessible information about the alignment of the energy levels for the interacting dye/ semiconductor system. Starting from the recently reported N719 adsorption geometry, we calculate the absorption spectrum of the combined dye/TiO2 system by TDDFT calculations in solution up to an energy of ca. 2.5 eV (500 nm), thus allowing us to explore the nature and energy distribution of the excited states of the joint system in the energy range typically accessed by pumpprobe spectroscopic techniques. To check the possible role of triplet states in the injection process, for the same system we also calculate a large number of singlettriplet excitation energies. These extended models and the employed high-level computational setup represent so far the most advanced and realistic simulations of dye/TiO2 excited state interactions relevant for DSSC devices, thus allowing us to gain unprecedented insights into the detailed factors governing their efficiency.
2. MODELS AND COMPUTATIONAL DETAILS To model the TiO2 surface, we consider a (TiO2)82 cluster, obtained by appropriately “cutting” an anatase slab exposing the majority (101) surface.25 Following the work by Persson et al.,26 we consider a neutral stoichiometric TiO2 cluster with no saturating atoms or groups at the cluster border. These models have been shown to accurately reproduce the electronic and structural properties of TiO2 anatase.26 The calculated dipole moment for our (TiO2)82 cluster is correctly found to be almost vanishing in all directions (0.5, 0.7, and 0.8 D for x, y, and z, the latter corresponding to the surface normal). The employed (TiO2)82 model is an almost square TiO2 (101) two-layer anatase slab of ∼2 nm side, with three rows of five- and sixcoordinated surface Ti sites, which is large enough to avoid possible spurious dye/titania interactions at the cluster border due to the finite cluster size. This is possibly the largest TiO2 model which can be employed in the present case, where a large number of excited states for the combined dye/TiO2 system 8826
dx.doi.org/10.1021/jp111949a |J. Phys. Chem. C 2011, 115, 8825–8831
The Journal of Physical Chemistry C
Figure 1. Optimized geometrical structure of the N719 dye with two protons and no counterions (N719-2H/0TBA) adsorbed on the (TiO2)82 extended model. The dotted circles denote the position of the two protons.
need to be calculated. Furthermore, a recent paper by Martsinovich et al. has pointed out that TiO2 anatase surface models are rather insensitive to the thickness of the TiO2 layer,27 with twolayer slabs accurately reproducing the electronic and structural features of larger models. In addition to the vanishing dipole moment, the adequacy of the employed cluster model against periodic surface slabs has been further checked here by performing comparative CarParrinello (CP) calculations employing the same GGA functional employed for geometry optimizations, see below. We report in Figure S1 and S2 of the Supporting Information the optimized geometries and the calculated density of states (DOS) for the (TiO2)82 cluster and for a periodic (TiO2)32 surface slab. The two DOS curves are very similar, with maximum deviations within 0.1 eV. Thus, within the necessary size limitations, we can be confident of the accuracy of the employed TiO2 model. The geometry of the combined dye/ semiconductor system was previously optimized24 by ab initio molecular dynamics simulations based on the CP method,28 using the PBE exchange-correlation functional29 together with a plane wave basis set and ultrasoft pseudopotentials.30 Comparative calculations performed on the N3 dye have shown that the GGA-based CP method can provide comparable geometries to those obtained by hybrid functionals and localized basis sets.11,31 TDDFT calculations were performed on the GGA-optimized geometries, employing the hybrid B3LYP functional32 with a 3-21G* basis set. The effect of the surrounding water solvent is included by employing a polarizable continuum model of solvation (C-PCM),33 as implemented in the Gaussian03 program package.34 Calculations were limited to the system bearing two protons with no counterions, which was found to represent a realistic description of N719.24 Simulation of the absorption spectra has been performed by a Gaussian convolution with σ = 0.17 eV.
3. RESULTS AND DISCUSSION 3.1. Absorption Spectrum of N719 on Titania. The optimized geometry of N719 on titania is reported in Figure 1. Of the three carboxylic groups involved in dye binding to TiO2, one is attached to two surface Ti atoms in a bidentate bridging mode, while the other two are bound in a monodentate mode.24 The
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Figure 2. Comparison between the experimental (red) and calculated (blue) absorption spectra of N719 on TiO2. The intensity of the experimental spectrum has been rescaled so that the absorption maxima match. Blue vertical lines represent unbroadened transition wavelengths and oscillator strengths. The inset shows the calculated density of singlet (black) and triplet (magenta) excited states (energy in electronvolts) for the same system.
optimized structure also shows one proton firmly bound to a surface oxygen close to the bidentate-bound carboxylic group (OH distance 1.02 Å) and a second proton to be bound to a surface oxygen (OH distance 1.06 Å), hydrogen bonding the uncoordinated oxygen of the monodentate carboxylic group. A subsequent paper by Schiffmann et al. has confirmed that this adsorption mode is the more stable when protons are present in the combined dye/semiconductor system.35 A comparison between the experimental and calculated absorption spectra for N719 bound to TiO2 is reported in Figure 2. To calculate the absorption spectrum up to ca. 2.5 eV, corresponding to the entire first visible absorption band, a large number of excited states were computed (the 50 lowest transitions) with an associated large computational overhead. It is therefore crucial at this stage to exploit the suitable trade-off between the size and the realistic description of the investigated system offered by our (TiO2)82 cluster. Obviously, we cannot rule out some sensitivity of the obtained results to the employed model, especially concerning the size of the TiO2 cluster, even though we can gauge the quality of the model a posteriori, by comparison with available experimental quantities. Considering the limitations of the model, the agreement between the calculated and experimental spectra in Figure 2 is excellent over the investigated energy range. The calculated spectral profile shows a comparable shape to the experimental one, with the absorption maximum being calculated at 552 nm (2.25 eV), to be compared to an experimental band maximum of 531 nm (2.34 eV). The small discrepancy between theory and experiment (
