Coupled Electron–Hole Quantum Dynamics on D−π–A Dye

Article pubs.acs.org/JPCC

Coupled Electron−Hole Quantum Dynamics on D−π−A DyeSensitized TiO2 Semiconductors Diego A. Hoff,†,§ Robson da Silva,‡,§ and Luis G. C. Rego*,† †

Department of Physics, and ‡Department of Chemistry, Universidade Federal de Santa Catarina, Florianópolis, SC 88040-900, Brazil S Supporting Information *

ABSTRACT: A quantum-mechanical description of the electron− hole charge separation and interfacial electron transfer, including the underlying nuclear motion and solvation dynamics effects, is presented for a prototypical class of D−π−A (electron donor−π conjugated bridge−electron acceptor) organic dyes sensitizing the TiO2 (101) surface. The dyes are comprised of a triphenylamine donor group and a cyanoacrylic acceptor anchoring group, connected by varying thiophene unit lengths (TPAn, n = 1, 2, 3). Simulations show that the electron−hole Coulomb coupling considerably delays charge separation and interfacial electron transfer. A comparative analysis demonstrates that the relevance of thermal nuclear motion, in this case, is secondary relative to electron−hole coupling during the ultrafast transfer from the D−π−A dyes. A dynamic atomistic method is used to describe the solvation effects and the optical properties of the dyesensitized interface. The solvation dynamics screens the dye molecule, decreasing its complexation with the semiconductor and delaying the electron injection.

1. INTRODUCTION Electronic charge transfer is a fundamental process that is relevant to a broad range of fields including solar energy conversion in organic1−4 and dye-sensitized solar cells,5−10 photoelectrochemistry,11 catalysis,12 and artificial photosynthesis.13−15 It has therefore been a subject of intense experimental and theoretical research, so much that a variety of frameworks have been developed to describe the process. In this Article, a combined time-dependent quantum mechanics/ molecular mechanics method is used to describe the interfacial electron transfer in dye-sensitized semiconductor interfaces, taking into account the interacting electron−hole quantum dynamics and the underlying effects of nuclear thermal fluctuations and solvation dynamics. Photovoltaic and photoelectrochemical solar cells have been considered promising alternatives for the production of electricity and fuels. In particular, dye-sensitized solar cells (DSSC) and organic photovoltaic devices rely on similar electronic mechanisms to produce electrochemical energy:13−15 light harvesting, energy transfer, charge separation, and electron transfer. Dye-sensitized solar cells have received widespread attention, as they offer the possibility of low cost and high solarto-electricity conversion efficiency. The dye-sensitized Grätzel cells16 currently attain conversion efficiencies a little over 12% in standard air mass 1.5 sunlight. Although DSSC based on transition metal complexes have achieved a remarkable effectiveness, particularly in the case of ruthenium dye complexes, the search for alternative sensitizers is underway. Many sensitizers have been tested experimentally, including © 2012 American Chemical Society

organometallic complexes, metal-free organic sensitizers, polymers, and supramolecular structures.17−19 Interest has been increasing toward metal-free dyes, because of their extremely low production costs and unlimited resources, which are essential for large-scale applications, and the possibility of engineering new molecular structures with the desired photophysical and electrochemical properties. The high molar extinction coefficients of the organic dyes (surpassing those of Ru dyes) are ideal for the use with thin TiO2 films in solid-state devices, where insufficient pore filling normally limits the photovoltaic performance. Several organic compounds have been synthesized and tested,20,21 including coumarins, indolines, triphenylamines, fluorenes, and perylenes. The photoconversion efficiency of the organic DSSC is normally in the range of 4−7%9,21−24 and, to date, can reach 9% under AM 1.5 irradiation.25,26 However, the lack of stability of the organic sensitizers under illumination and their tendency to form aggregates, which in most cases decrease the conversion efficiency, are aspects of major concern that still hinder the practical application of this new family of DSSC. Because of its potential to improve the viability of DSSC, we investigate the details of the interfacial electron transfer from a prototypical class of D−π−A dyes into a TiO2 semiconductor cluster. Research in organic dyes for solar cell applications suggests an optimal molecular design that comprises an Received: April 16, 2012 Revised: September 5, 2012 Published: September 12, 2012 21169

dx.doi.org/10.1021/jp303647x | J. Phys. Chem. C 2012, 116, 21169−21178

The Journal of Physical Chemistry C

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electrophobic donor (D), a π-conjugated bridge, and an electrophilic acceptor (A), constituting a D−π−A structure.8,9,21,27−31 The organic dye structure is engineered in a way that the acceptor moiety also functions as a stable anchoring group, and the photoexcitation of the electron−hole pair that happens by charge transfer (CT) mechanism is followed by a vectorial electron flow through the π-conjugated bridge into the conduction band states of the semiconductor. This D−π−A design provides great flexibility in tuning the optical properties of the dye by changing the length of the bridge; different bridge structures can also confer distinct mechanical and stability characteristics for the dye. The D−π−A organic dyes studied herein are comprised of an electron-rich triphenylamine donor, an electron-deficient cyanoacrylic acid acceptor, and n thiophene units that provide conjugation between donor and acceptor moieties. The chemical structure for the TPAn (n = 1−3) dyes is depicted in Figure 1a. Triphenylamine has been used widely in organic

In the realm of theory, the development of new theoretical formalisms and computational methods has improved the understanding of the interfacial electron transfer and its underlying dynamics in vacuum conditions,40−43 the electron−phonon relaxation processes,44,45 and the properties of the electrolyte/semiconductor interface in DSSC.46,47 The analogous electron transfer processes in the organic interfaces of polymeric devices2,4,48,49 are usually described within the Marcus−Levich−Jortner framework, where the nuclear reorganization plays a central role in determining the transfer rates. Furthermore, efficient QM/MM methods have been used to study the eletronic charge transfer processes and the nonadiabatic molecular dynamics of organometallic complexes in solution.50 However, there is still the need for a theoretical treatment that describes the coherent quantum mechanical electron−hole dissociation and charge transfer dynamics subject to the underlying effects of nuclear fluctuations and solvation dynamics, for realistic models of solar cell interfaces. Considering its significance for the new generation of organic DSSC, this Article investigates the quantum dynamics, the electronic, and the structural properties for a prototypical class of D−π−A organic dyes sensitizing the TiO2 anatase surface, both in vacuum and solvated by liquid acetonitrile. The results presented herein reveal structural and optical properties of such interfaces that can assist the interpretation of experimental results and guide new efforts to improve the quality of current dye-sensitized solar cells. This Article is organized as follows: Section 2 describes the theoretical and computational methods, section 3 presents results and discussions regarding the structural, electronic, and quantum dynamics simulations, and section 4 presents the concluding remarks.

2. THEORY AND METHODS Coherent quantum dynamics and molecular mechanics methods are combined to describe the electron−hole charge separation and the interfacial electron transfer dynamics from solvated D−π−A organic sensitizers to TiO2-anatase semiconductors. The fundamentals of the theoretical approach are introduced next, leaving the specific implementation details to the sections where they are used and the Supporting Information. Molecular dynamics (MD) simulations were performed at the molecular mechanics (MM) level of theory51 with two purposes. Initially, long time dynamics simulations (a few nanoseconds in duration) were performed to produce an ensemble of uncorrelated configurations, which were employed in the calculations of spectral properties and density of states (DOS). In addition, short trajectories (a few picoseconds in duration) were generated to be used as the underlying nuclear trajectories for quantum dynamics simulations. A detailed description of the MM procedures and force fields is provided in the Supporting Information. The electronic properties of the system are described by a quantum mechanical Hamiltonian based on the extended Hückel molecular orbital theory,52 H = H0 + HDP + Heh, where H0 is the ordinary extended Hückel (EH) Hamiltonian, HDP takes into account the long-range dipolar interactions between the dye and the solvent molecules as well as the solvent molecules among themselves, and Heh describes the Coulomb interaction between the photoexcited electron and hole wavepackets. All components of the system, including the

Figure 1. (a) Chemical structure of the D−π−A organic dyes studied in this Article: TPAn (n = 1, 2, 3). Molecular configurations for the TPA1 dye with the 2-cyano-3-(thiophen-2-yl) acrylic acid (TCA) moiety in the E (b) and Z (c) configurations.

sensitizers8,9,24,28−31,33 due to its excellent electron-donating capability and aggregation resistant characteristics. The distance between donor and acceptor moieties is varied according to the number of thiophene units in the bridge, allowing some control over the dye’s optical properties. The n-oligothiophenes form planar bridges that are approximately coplanar with cyanoacrylic acceptor group, yielding better conjugation and improved electron transfer within the dye. In addition, the cyanoacrylic acid binds strongly to the TiO2-anatase surface.34 It is wellknown that the electronic coupling between dye and semiconductor, via the acceptor group, is very important for the efficiency of the electron injection.35,36 We investigate, in addition, the adsorption issues associated to two conformations of the anchoring moiety that can be obtained during synthesis: the E-configuration (TPA1-E) and the Z-configuration (TPA1Z)37 shown in Figure 1b and c, respectively, which are not examined in the literature.9,27,28,30,38,39 21170



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solvent molecules, are treated at the quantum mechanical level of theory. The EH Hamiltonian is computed on the basis of Slater-type atomic orbitals (STO).53 The STO parametrization is performed for the system’s constituent molecules independently, that is, the TPAn dyes and the acetonitrile molecule (CH3CN), at their in vacuo ground-state geometry, as obtained from the DFT/B3LYP method with the 6-31G(d,p) basis set, with the Gaussian 03 package.54 No energy shifts or additional corrections were necessary for either occupied or unoccupied states of the total system. Complete details of the parametrization procedure can be found elsewhere.45,46 The plain extended Hückel matrix elements, H0ij, do not account for the long-range interactions between dye and solvent, both polar molecules, neither for solvent molecules interacting among themselves. Instead of using a continuum dielectric model for the solvent, which is not a good approximation for the immediate solvation shells in the vicinity of the dye and near the TiO2 surface,45−47,55 we use an atomistic quantum mechanical formalism described by Hoff et al.45 The Hamiltonian term Heh accounts for the Coulomb interaction between the photoexcited electron and hole pair. According to the formalism, both wavepackets are written as a linear combination of Slater-type atomic orbitals, |Ψel⟩ = ∑iAeli |i⟩ and |Ψhl⟩ = ∑kAhlk |k⟩, with {|i⟩} and {|k⟩} spanning the atomic orbitals of the entire system. To account for the quantum dynamics of the wavepackets, Ael and Ahl are complex coefficients that depend on the time (not explicitly represented for clarity sake). The Coulomb energy of the electron−hole pair can be written as Eel − hl =

Vijhl = −Ajhl ∑ Ak*el Alel ⟨i , k|Vcoul|l , j⟩ k ,l

= −Ai*hl Ajhl [∑ |Akel |2 ⟨i , k|Vcoul|k , j⟩ k

+ 2 ∑ 9e[Ak*hl Alel ]⟨i , k|Vcoul|l , j⟩] k>l

If only the two-center Coulomb integrals are taken into account, Vel and Vhl are block diagonal matrices. During the excitonic dissociation and interfacial electron transfer, the electron wavepacket evolves under the influence of the Coulomb potential produced by the evolving hole and vice versa. The electron−hole coupling is described within the timedependent Hartree approximation.58 Exchange interaction effects are negligible because the wavepackets describe independent particles in this framework. In general, Velij ≠ Vhlij because electron and hole undergo different dynamics; thus, we have two coupled Hamiltonians for the electron−hole pair:

(1)

k ,l

where ⟨i,k|Vcoul|j,l⟩ are multicenter (2, 3, and 4) Coulomb integrals over Slater-type orbitals: 2

⟨i , k|Vcoul|l , j⟩ =

∫ d r ′⃗ ∫ d r ⃗ χi*( r ⃗)χk*( r ′⃗ ) | r ⃗ −e r ′⃗ | χl ( r ′⃗ )χj ( r ⃗)

Hijel = Hij0 + HijDP + V ijel(Ael , Ahl)

(5)

Hijhl = Hij0 + HijDP + Vijhl(Ahl , Ael)

(6)

The molecular orbitals (MO) of the entire system, comprised of the TiO2 nanoparticle, adsorbed dye, and solvent molecules, are written as |ϕ⟩ = ∑iCiϕ|i⟩, with the coefficients Ciϕ obtained through the generalized eigenvalue equation HCϕ = εϕSCϕ. Transformation between the localized, {|i⟩}, and delocalized, {|ϕ⟩}, basis representations is performed via operators P̂ = ∑ϕ∑i,j|i⟩(S−1)⟨j|ϕ⟩⟨ϕ| = ∑i,ϕCi,ϕ|i⟩⟨ϕ|. The procedure for quantum propagation of the photoexcited electron−hole pair45 is summarized as follows. The nuclear coordinates gained from ground-state classical MD simulations, R⃗ n(t), yield time-dependent STO basis functions |i(t)⟩ that are used to compute the electron and hole time-dependent Hamiltonians, Hel/hl(t), and the corresponding adiabatic molecular orbitals |ϕ(t)el/hl⟩ for the entire system. The initial wavepackets are written as |Ψ(0)⟩ = ∑DYE Ai(0)|i(0)⟩, where i A(0) is obtained from HDYEA = εSDYEA. The electron wavepacket is initially assigned to an unoccupied molecular orbital within the dye and the hole wavepacket to its HOMO. The adopted procedure45 of time-propagating the wavepacket in the adiabatic (MO) basis, then projecting its coefficients onto the AO basis set before transferring them to the AOs of the next ionic configuration, is very robust and reliable, because it avoids numerical problems caused by MOs level-crossing and accidental degeneracies that mix the phases of the wavepacket and lead to unphysical results. Moreover, it always converges if the time-slice is small enough. The quantum dynamics results presented herein were obtained with δt = 0.25 fs, which provided a good convergence. The time-dependent electron and hole wavepacket populations within the dye (survival probabilities) are calculated as dye sys P(t ) = 9e[∑i ∑ j Ai*(t )Sij(t )Aj (t )].

∑ Ai*el Ajel ∑ Ak*hl Alhl ⟨i , k|Vcoul|j , l⟩ i,j

(4)

(2)

The Coulomb integrals, eq 2, are calculated by an efficient numerical algorithm adapted from the SMILES program for integrals with Slater-type orbitals, developed by Rico and collaborators.56,57 In our calculations, only the two-center Coulomb integrals are taken into account, because the threeand four-center integrals involving the electron−hole pair are much smaller and can be disregarded. The matrix elements for the electron wavepacket Hamiltonian, due to its interaction with the hole, are written as V ijel = −Ai*el Ajel ∑ Ak*hl Alhl ⟨i , k|Vcoul|l , j⟩ k ,l

=

3. RESULTS AND DISCUSSION 3.1. Electronic Structure of the Organic Dyes. The in vacuo ground-state molecular structures of the dye molecules were obtained with the Gaussian package,54 at the DFT/B3LYP level of theory, using the 6-31G(d,p) basis set. Such configurations were subsequently used as reference for parametrization procedures. The molecular geometries were

∑ |Akhl |2 ⟨i , k|Vcoul|k , j⟩

−Ai*el Ajel [

k

+ 2 ∑ 9e[Ak*hl Alhl ]⟨i , k|Vcoul|l , j⟩] k>l

(3)

and likewise for the hole wavepacket: 21171



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Figure 2. Frontier molecular orbitals for the (E)-TPAn (n = 1, 2, 3) dye molecules at the ground-state optimized geometry, calculated by the semiempirical extended Hückel method.

were performed for an ensemble of TPAn molecules (a set of 100 statistically independent dye configurations) gained from MM simulations at T = 298 K in vacuo. The averaged transition lines are shown in the top panel of Figure 4. As anticipated, the spectral bands are red-shifted and the height of the peaks increases as the bridge elongates. The oscillator strengths calculated for the dyes in vacuo agree with absorption spectra measurements performed for the same dyes in solution.28−30,33 3.2. Sensitization of TiO2-Anatase with TPAn Dyes. Several attachment modes between carboxylic linkers and the (101) surface of anatase are possible, for instance, the dissociative bidentate and the nondissociative molecular forms. The bidentate bridging is the most stable anchoring mode34,42,59 and, therefore, adopted in this study. Figure 3 presents typical configurations for the TPAn dyes adsorbed on the (101) surface of anatase; the dissociated H atom is placed in a nearby bicoordinated oxygen (O2c). In particular, notice the different adsorption geometries for the TPA1 sensitizer in the Z and E conformations. Although both conformers can be obtained during synthesis, our DFT/B3LYP/6-31G(d,p) ground-state energy calculations revealed that the (Z)-TPA1 conformer is ∼3.1 kcal/mol less energetically stable than the prevailing (E)-TPA1. As shown in Figure 3, the semiconductor is modeled by a [TiO2]512 cluster, with lateral dimensions 40.89 Å × 30.26 Å and periodic boundary conditions in the [10̅ 1] and [010] directions. Details of the supercell preparation are provided elsewhere.46 The use of large supercells is necessary in the present simulations due to the reasons: the size of the dye molecules, to avoid recurrences in the electronic injection,43 and to minimize spurious Coulomb attraction

also optimized by the molecular mechanics method, with the GROMACS package,51 using an all atom AMBER force field. Both methods produced very similar structures for all of the TPAn (n = 1, 2, 3) molecules. Having obtained the optimized geometries, electronic structure calculations were also performed with the EH method, and a single set of STO parameters was generated for all of the TPAn dyes. The resulting frontier orbitals for the TPAn molecules, presented in Figure 2, show good agreement with the corresponding ab initio calculations.27−29,33 The general characteristics of the molecular orbitals are common for the three dye species. The HOMO and HOMO−1 orbitals have a π character and are delocalized over the entire chromophore, particularly at the triphenylamine group. The LUMO and LUMO+1 orbitals have a π* character and concentrate on the oligothiophene bridge and the cyanoacrylic acid acceptor group, with very little contribution from the triphenylamine donor group (an exception is the LUMO+1 orbital of the TPA1 dye that is not well described by this set of STO parameters). The semiempirical calculations yield for the ground-state optimized geometries the following HOMO− LUMO energies: 2.5 eV (TPA1-E/Z), 2.4 eV (TPA2), and 2.42 eV (TPA3), whereas the calculated dipole moments are 8.8 D (TPA1-E), 11.6 D (TPA2), 8.2 D (TPA3), and 14.5 (TPA1-Z). A detailed comparison between DFT/B3LYP and semiempirical EH calculations is included as Supporting Information. Because of the charge delocalization effect, a red-shift of the transition lines is expected as the π-conjugated bridges elongate. Photoabsorption oscillator strength calculations 21172



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Figure 3. TPAn (n = 1, 2, 3) organic dyes adsorbed on the (101) surface of a [TiO2]512-anatase cluster via bidentate bridging mode. The dissociated hydrogen is bound to the closest O2c. Notice the different adsorption geometries for the Z and E configurations. Typical molecular configurations obtained from molecular dynamics simulations at T = 298 K in vacuo.

upon which the quantum dynamics calculations were carried out for the coupled electron and hole wavepackets. Figure 5 shows time-dependent survival probabilities, P(t), of the electron and hole wavepackets for each of the adsorbed TPAn (n = 1, 2, 3) dyes, including the (Z)-TPA1 conformer. At t = 0 the electron wavepacket is set to the LUMO of the TPAn molecule and the hole wavepacket to its HOMO. The initial ionic configuration is an arbitrary one, obtained from the MD simulations at T = 298 K, and the survival probability curves are not averages over distinct nuclear trajectories. Three situations were considered for the analysis. The blue dot−dash curve describes the electronic injection disregarding the presence of the hole but taking into account the ionic motion. In this case, because there is no electron−hole pair dissociation, the electron injection is extremely efficient and takes place in a few femtoseconds, corroborating the strong complexation observed in the photoabsorption oscillator strength results of Figure 4. The black and red curves describe calculations taking into account the electron and hole coupling interaction; however, nuclear dynamics is disregarded in the simulations described by the red curves. In this scenario, during the electron injection the hole remains stably inside the TPAn dye, with Phl(t) ≃ 1 (black

effects between the injected electron (that remains confined to the cluster) and the hole that dwells in the molecule. To preserve the symmetry of the TiO2 cluster, during the MD simulations only the Ti and O atoms at the surface, within a 6 Å radius from the anchoring site, as well as the dye molecules themselves and the dissociated H atom are allowed to move in the MD simulations. Figure 4b presents photoabsorption oscillator strength calculations performed with the EH method for the TPAn/ TiO2-sensitized nanostructures (as shown in Figure 3), averaged over 100 uncorrelated configurations obtained from MD simulations at T = 298 K. The strong chemical binding between the TPAn chromophores and the TiO2 surface renders the absorption bands broader, besides shifting them to lower energies. The strong complexation is an indication of fast electronic injection. In real devices, however, the formation of aggregates can also cause line width broadening, but in this case the electron injection is usually suppressed. 3.3. Electron−Hole Dissociation and Electronic Injection Dynamics. From the MD simulations performed for the combined TPAn/TiO2 system, short nuclear trajectories were generated to yield time-dependent nuclear configurations 21173



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despite their structural differences. The similarity of injection times is partly due to the fact that significant charge transfer toward the anchoring moiety is already accomplished through the photoabsorption process in such D−π−A dyes. In addition, the analysis demonstrates that nuclear motion plays a secondary role in such ultrafast electron transfer processes. In that respect, though, the situation differs from the cases that the LUMO of the dye is at the edge of (or just below) the conduction band of the semiconductor40,42,60 and the injection dynamics is modulated by the nuclear dynamics. Figure 8 shows that the unoccupied frontier orbitals of the dye lie well within the conduction band of the semiconductor. Anticipating possible approximations, the observed weak influence of the ionic dynamics reduces the need for averages over ionic trajectories. Furthermore, given that full dynamics calculations show that the hole remains in the dye during the electron transfer in such systems, we performed calculations keeping the charge of the hole static in the dye and obtained very similar dynamics for the electron wavepacket. Most dye-sensitized solar cells, nonetheless, are built to function in the presence of an electrolyte. Thus, in the following we study the effects produced by a solvent on the electronic injection. 3.4. Solvated Dye-Sensitized TiO2 Interfaces. Figure 6 shows typical configurations of the TiO2/TPAn/acetonitrile interface, obtained from molecular mechanics simulations performed at T = 298 K in the NVT ensemble. A simulation box of 30.67 × 30.26 × 55 Å3 was used for all systems, comprising a TPAn (n = 1, 2, 3) dye adsorbed on the (101) surface of a [TiO2]384 anatase cluster, solvated by 450 acetonitrile (CH3CN) molecules. Acetonitrile (ACN) is a nonviscous aprotic polar solvent used with excellent performance16,24,25 in most dye-sensitized solar cells. In the MM simulations, the CH3CN molecule is described by a six-site model, constituted by the atom types: three methyl hydrogens (HC), a methylcarbon (CT), carbon (YC), and nitrogen (YN). The force field (FF) parameters used for liquid ACN were derived by Nikitin and Lyubartsev,61 while the preparation of the system and the MD simulations followed standard procedures described elsewhere.46,62 The model potential includes electrostatic and Lennard-Jones pairwise interactions, as implemented in the AMBER molecular mechanics force field.63 The MM simulations were performed with a nonpolarizable force field; nevertheless, the electronic polarizability is built in the method, as described section 2. After equilibration, the average density ρ, the heat of vaporization ΔHvap, and radial distribution functions were calculated and compared to the experimental results, showing good agreement.46,61,62 Production runs were carried for 2 ns to generate statistically independent configurations of the system that were used to study the solvent structure and the electronic properties of the interface. The typical configurations presented in Figure 6 show a very organized solvation structure over the TiO2 anatase surface,46,47,64 as evidenced by the density profile curves in Figure 7. In the first ACN solvation layer, centered ∼2.4 Å above the surface, the ACN molecules are well aligned with each other, with their N atoms pointing predominantly toward a neighboring Ti4+ 5c ion on the surface. The second and third solvation layers are also present, respectively, at ∼3.0 and ∼6 Å, although with less organization. The neighboring solvation layers tend to anti-align with each other.

Figure 4. Photoabsorption oscillator strength calculations performed by the EH method, over an ensemble of 100 uncorrelated configurations. (a) Top panel calculations correspond to TPAn dye molecules in vacuo. (b) Bottom panel shows calculations for the TPAn/TiO2-sensitized nanostructures. The dashed curve describes the (Z)-TPA1 conformer.

Figure 5. Time-dependent survival probabilities P(t) of electron and hole wavepackets for the TPAn/TiO2-sensitized nanostructures and the (Z)-TPA1 conformer. Three situations are represented: el−hl interaction and nuclear motion taken into account (black curves), el− hl interaction but no nuclear motion (red curves), and independent electron with nuclear motion taken into account (blue dash−dot curves). For the holes, P(t) ≃ 1 throughout the simulation (black and red dashed curves).

and red dashed curves), whereas the electron is still effectively transferred to the semiconductor within ∼10 fs. As compared to the independent electron case, the electron−hole coupling delays the interfacial electron transfer for all TPAn sensitizers, 21174



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Figure 6. Typical configurations of the TiO2/TPAn/acetonitrile interface obtained from molecular mechanics simulations at T = 298 K in the NVT ensemble. TPAn dyes (n = 1, 2, 3) are adsorbed on the (101) surface of a [TiO2]384 anatase cluster and solvated by 450 acetonitrile molecules. Charge density isosurfaces for the LUMO state of the dye molecules are displayed. The Z conformer is indicated explicitly.

configurations. In comparison with the spectral curves for the in vacuo TiO2/TPAn interfaces, Figure 4b, the first feature to be noted is the narrowing of the spectral lines caused by the solvation mechanism that screens the dye and decreases its complexation with the semiconductor. From a more fundamental point of view, the fluctuating dipolar field produced by the solvation dynamics localizes the molecular orbitals of the chromophore, which impacts also on the electron transfer dynamics.45 Our calculations show that the narrowing of the absorption bands is more pronounced for the TPA1 dye, specially for the (Z)-TPA1 conformer that lies amidst the first and third solvation layers. Thus, in principle, it is expected a stronger influence of the solvent on the shorter sensitizers that stay close to the interface. 3.5. Interfacial Electron Transfer in Solvated DyeSensitized TiO2 Interfaces. This section explores, in Figure 10, the effects produced by the collective polarization field of the solvent molecules in thermal motion impinging on the interfacial electron transfer dynamics for typical TiO2/TPAn/ ACN interfaces.

Projected density of states (DOS) calculations, shown in Figure 8, were performed for an ensemble of TiO2/TPAn/ ACN interface configurations. The top panel of Figure 8 shows the occupied bands for both the TiO2 cluster (black) and the acetonitrile solvent molecules (red), on the left, as well as the conduction band of the TiO2 and the unoccupied band of the ACN solvent, on the right. For all calculations, the obtained semiconductor band gap was within the range of 3.1−3.4 eV. The lower panels emphasize the DOS of the TPAn molecules, clearly demonstrating the sensitization effect. The DOS curve for the (Z)-TPA1 conformer is also shown by a dashed curve. Notice that the broadening of DOS bands and peaks results from the configuration averaging. A few weak peaks located in the gap for TiO2 and ACN are due to the motion of surface and solvent atoms, because the curves were obtained for an ensemble of configurations at ambient temperature. The Fermi level of the system is located at the HOMO of the adsorbed dye molecule. Figure 9 presents photoabsorption oscillator strength calculations for an ensemble of TiO2/TPAn/ACN interface 21175



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Figure 7. Atomic density profile of the acetonitrile solvent as a function of the coordinate (z) perpendicular to the (101) anatase surface. The inset depicts the chemical structure of acetonitrile and its molecular mechanics atom types.

Figure 9. Photoabsorption oscillator strength calculations performed by the EH method, over an ensemble of 100 uncorrelated configurations for the TiO2/TPAn/acetonitrile interface. The dashed curve describes the (Z)-TPA1 conformer.

Figure 8. Projected density of states (DOS) calculations for the TiO2/ TPAn/acetonitrile interfaces (n = 1, 2, 3), averaged over a set of 100 uncorrelated configurations gained by MM simulations performed at T = 298 K in the NVT ensemble. The top panel presents the occupied (left) and unoccupied (right) bands of TiO2 anatase and liquid acetonitrile. The lower panels show the TPAn sensitizer states (blue) around the energy band gap of the semiconductor. The DOS curve for the (Z)-TPA1 conformer is shown by an orange dashed curve. Figure 10. Time-dependent survival probabilities P(t) of electron and hole wavepackets for TiO2/TPAn/acetonitrile interfaces and the (Z)TPA1 conformer. Two situations are considered: taking solvation effects into account (black curves) and disregarding the solvent molecules in the calculations (red circle curves); solid lines describe electrons, and dashed lines designate holes.

To analyze the effects produced by the solvent dynamics alone, two types of simulations were performed employing the same underlying nuclear trajectories: in one case the acetonitrile solvent molecules were taken into account (black), whereas they were disregarded (red ○) in the other. Solid lines designate the survival probabilities for electrons and dashed lines for the holes. As expected, the hole survival probabilities remain very close to unit during the electron injection, for all cases considered in Figure 10. By comparing the electron injection curves calculated with the same underlying nuclear trajectories, but including (black) or disregarding (red ○) the presence of the solvent, we verify that its influence can delay the interfacial electron transfer, even for such ultrafast injection events. In accordance with the

oscillator strength calculations of Figure 9, the influence of the solvent is more pronounced for the electronic injection from the (Z)-TPA1 dye that is amidst the solvation layer. According to the results, the solvation dynamics screens the dye and decreases its complexation with the semiconductor at the anchoring site, leading to a slower interfacial electron injection process. 21176



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In the adiabatic transfer regime, a broad electronic coupling between the photoexcited states in the dye and the conduction band states in the semiconductor improves the interfacial electron injection, because the process relies on quantum coherences to take place efficiently, by taking advantage of the superexchange mechanism.65,66 That electronic coupling and the inherent quantum coherences are weakened by the fluctuating dipolar field and by the direct interaction of the complex with the neighboring solvent molecules. It has been shown, in another instance, that the solvation dynamics localizes the photoexcited electronic states in solvated [Ru(bpy)3]2+ complexes,45,50 changing the interligand electron transfer mechanism from wave-like (delocalized) to hopping. To conclude, experimental realization of DSSCs employing the TPAn dyes30,33 reveals that the TPA2 molecule yields conversion efficiencies a bit higher than the others. Because the electron injection kinetics is equally efficient for all of the dyes, we conclude that the better performance of TPA2 is due to a combination of factors: its good absorption, particularly at longer wavelengths; its efficient electronic injection; and the appropriate length of its conjugated bridge that keeps the triphenylamine donor group just outside the ACN solvation layer, which prevents recombination and eases the regeneration of the dye, still not being prone to aggregation and degradation.

is reflected on moderately slower electronic transfer rates for the solvated interface. For ultrafast interfacial electron transfer processes, such as those studied herein, it was verified that it is a good approximation to assume a static hole and just propagate the electronic wavepacket. In addition, although an atomistic solvent model is necessary to describe the dye-sensitized interface properly, one could simplify the model by using a procedure that treats only the dye and the TiO2 by quantum methods, whereas the solvent could be described by classical point charges, as in the regular QM/MM approach. However, both approximations may be inaccurate to describe charge transfer in supramolecular structures, large-scale polymeric systems, or protein systems, where electron and hole exhibit similar dynamics and there is strong coupling with the dielectric (solvent) environment.

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ASSOCIATED CONTENT

S Supporting Information *

Details of (i) molecular and electronic structure optimization by ab initio and molecular mechanics methods, (ii) procedures for molecular dynamics simulations, and (iii) technical documentation on computational methods and parametrization regarding the Extended Hückel method. This material is available free of charge via the Internet at http://pubs.acs.org.

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4. CONCLUSIONS We have analyzed the quantum dynamics, the electronic, and the structural properties of typical D−π−A organic dyes sensitizing the TiO2 anatase surface, both in vacuum and solvated by liquid acetonitrile (ACN), by means of efficient atomistic quantum mechanics/molecular mechanics combined methods. The organic dyes studied herein represent a broad class of D−π−A sensitizers used in prototypical organic DSSC. In addition, the present quantum dynamics simulations take into account the real conditions impinging upon the dyesensitized interface of solar cell devices. Quantum calculations reveal details of the sensitization process for an ensemble of TiO2/TPAn/ACN interface configurations, by means of density of state diagrams, Figure 8, and photoabsorption bands, Figures 4 and 9. The oscillator strength results show very good agreement with experimental absorption spectra.8,29,30,33 A strong complexation is produced by the adsorption of the dye onto the anatase surface, leading to an ultrafast electronic injection within 10 fs. The electron−hole pair dissociation is described quantum mechanically within the time-dependent Hartree approximation. For all cases considered, the hole remains stably confined to the dye, while the electron is effectively transferred to the semiconductor. It is demonstrated that the electron−hole coupling delays the electronic injection. Furthermore, the ultrafast electron transfer events studied in this Article occur well within the adiabatic regime, and the effects produced by nuclear motion are secondary to the electron−hole Coulomb interaction, because the unoccupied states of the dye lie well within the conduction band of anatase. We describe the solvent by a quantum mechanical atomistic model. By solvating the interface with acetonitrile, the short dye molecules, particularly the (Z)-TPA1 conformer, interact more intensely with the well-structured ACN solvation layers. Photoabsorption oscillator strength calculations show that the polar solvent screens the dye, localizing the molecular orbitals of the chromophore and decreasing its complexation with the anatase surface. That effect

AUTHOR INFORMATION

Corresponding Author

*E-mail: lrego@fisica.ufsc.br. Author Contributions §

These authors contributed equally.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We acknowledge helpful discussions with Professor H. Gallardo. Financial support was provided by the Brazilian research agencies CNPq and CAPES.

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Coupled Electron–Hole Quantum Dynamics on D−π–A Dye

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