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The nature of the donor motif in acceptor-bridge-donor dyes as an influence in the electron photo-injection mechanism in DSSCs Ximena Zarate, Stephan Schott-Verdugo, Angela Susana Rodriguez-Serrano, and Eduardo Enrique Schott J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.5b12215 • Publication Date (Web): 22 Feb 2016 Downloaded from http://pubs.acs.org on February 27, 2016

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The Journal of Physical Chemistry

The Nature of the Donor Motif in Acceptor-BridgeDonor Dyes as an Influence in the Electron PhotoInjection Mechanism in DSSCs Ximena Zarate,*a Stephan Schott-Verdugo,b Angela Rodriguez-Serrano,c Eduardo Schottd a

Instituto de Ciencias Químicas Aplicadas, Facultad de Ingeniería, Universidad Autónoma de

Chile. Av. Pedro de Valdivia 641, Santiago, Chile. e-mail: [email protected] b

Centro de Bioinformática y Simulación Molecular, Universidad de Talca, 2 Norte 685, Casilla

721, Talca, Chile. c

Grupo de Fotodinámica Molecular, Universidad de los Andes, Carrera 1E No. 19A - 40, Bogotá

D. C., Colombia. d

Departamento de Química Inorgánica, Facultad de Química, Pontificia Universidad Católica de

Chile. Avda. Vicuña Mackenna 4860, Santiago, Chile.

ACS Paragon Plus Environment

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ABSTRACT: The combination and balance of acceptor(A)-bridge-donor(D) architecture of molecules confer suitable attributes and/or properties to act as efficient light-harvesting and sensitizers in dye sensitized solar cells (DSSCs). An important process in a DSSC performance is the electron photo-injection (PI) mechanism which can take place either via type I (indirect), that consists in injecting from the excited state of the dye to the semiconductor, or type II (direct), where the PI is from the ground state of the dye to the semiconductor upon photoexcitation. Here, we present a computational study about the role of the donor motif in the PI mechanisms displayed from a family of eleven A-bridge-D structured dyes to a (TiO2)15 anatase cluster. To this end, different donor motifs (D1-D11) were evaluated while the A and bridge motifs were remained the same. All the computations were carried out within the DFT framework, using the B3LYP, PW91, PBE, M06L and CAM-B3LYP functionals. The 6-31G(d) basis set was employed for non-metallic atoms and the LANL2DZ pseudopotential for Ti atoms. The solvation effects were incorporated using the polarized continuum model (PCM) for acetonitrile. As benchmark systems, alizarin and naphthalenediol dyes were analyzed as they are known to undergo Type I and Type II PI pathways in DSSCs, respectively. Donors in the studied family of dyes could influence to drive Type I or II PI since it was found that D2 could show some Type II PI route, showing a new absorption band although with CAM-B3LYP this shows a very low oscillator strength, while the remaining dyes behave according to Type I photo-injectors. Finally, the photovoltaic parameters that govern the light absorption process were evaluated as the use of these criteria could be applied to predict the efficiency of the studied dyes in DSSCs devices.

KEYWORDS: Solar cell, electron injection mechanism, organic dyes, DFT.


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INTRODUCTION Dye-sensitization technique dates back to the 19th century, when photography was invented. The work made in 1873 by Vogel can be considered the first significant study of dye-sensitization semiconductors, where silver halide emulsions were sensitized by dyes to produce black and white photographic films. More than 100 years after those studies, Professor Grätzel and his coworkers showed the study of efficient charge injection from a molecule to a semiconductor material.1-7 This injection was successfully obtained by combining nanostructured electrodes and dyes under sunlight. These devices called dye sensitized solar cells (DSSCs) are composed by a transparent conducting glass electrode covered with a film of porous nanocrystalline semiconductor usually TiO2 (band gap ∼3 eV) where the dye molecules are bonded as depicted in Figure 1.

Figure 1. Scheme of a Dye-Sensitized Solar Cell (DSSC). The adsorption of the dye to the TiO2 surface is usually done through anchoring groups containing oxygen such as hydroxyl (OH), phosphoric acid (PO(OH)2) and carboxylic acid (CO2H) groups.8-9 These groups in their deprotonated form show a mixed covalent and ionic bond with the oxide surface where the protons are donated to the TiO2 lattice. This DSSC device


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is immersed within an electrolyte containing the redox couple, e.g. I-/I3-, and a glass covered with platinum acts as the counter-electrode. Upon irradiation the dye strongly harvests solar energy, gets photoexcited and promotes the injection of electrons into the conduction band of the semiconductor. Before the charge recombination occurs, the oxidized sensitizer is regenerated to the native state by the electrolyte or a p-type hole conductor. The photocurrent is therefore generated by the injected charge which passes through the external load to the counter-electrode and the circuit is completed by the reduction of I3- which restores the I- ion.1-4 The operation of the cell is regenerative, since no chemical substances are consumed or produced during the working cycle. The semiconductor absorbs a small amount of light in the UV-Vis region of the solar spectrum which illuminates the device.8-9 A condition to ensure an efficient photo-conversion is that the adsorbed dyes show absorption in the UV-Vis region of the electromagnetic spectrum, which is mainly the radiation received on Earth.1 Consequently, nowadays DSSCs are viewed as a low cost alternative of energy resource, where the challenge remains in exploring new components to obtain better efficiencies.8-11 In terms of performance, a DSSC can display type I or II electron photo-injection (PI) mechanisms (Figure 2(a)). Type I (indirect) pathway involves, at first place, photon absorption by the dyes, which induces their excitation from the ground state to the excited state followed by an electron transfer to the conduction band of the semiconductor. Type II (direct) process is referred to one-step electron injection from the ground state of the dye to the semiconductor upon photo-absorption. In both cases, the net result of the injection process is an oxidized dye.2,12-13 Of these two types of PI, the Type II (direct) mechanism is considered very efficient because every absorbed photon creates an interfacial TiO2(e-)/Dye+ state that could be easily converted to electrical power. Also, after the electron injection, the dye is regenerated to the


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ground state faster than in the Type I pathway. Thus, this process leads to an increased the lifetime for the electron injection to the TiO2 and competes with the undesirable recombination.89,12-13

Figure 2. a) Scheme describing PI mechanism in a DSSC. b) Acceptor-bridge-donor (A-bridgeD) molecular structure. A and bridge structures are not varied while D is changed by different motifs. Theoretical investigations are useful to improve the understanding of the photophysical and electronic properties of variety of systems that can be used for DSSC, but surprisingly these studies focus on differentiating the undergoing PI mechanisms mainly for small compounds.12-16 In this framework, it has been shown that small structural differences in the sensitizer can induce a change of PI mechanism, e.g. naphthalenediol (two fused rings) and alizarin (three fused rings) display Type II and Type I PI mechanisms, respectively.13,17-19 As the demand of new solar cells design has grown, the synthesis of different molecules has increased and, currently, the most famous architecture of dyes adopts an acceptor-bridge-donor (A-bridge-D) arrangement. This dye architecture exhibits good efficiencies and properties as a high molar extinction coefficient, low cost of production, diversity, among others.20-25 In this


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sense, the combination and balance of the fragments that give suitable attributes and properties to the dye are valuable aspects, and, on the other hand, the specific PI mechanism as driven by the Type I or II pathways. Motivated by this behavior, the present theoretical study investigates the PI mechanisms of a family of A-bridge-D dyes (Figure 2(b) and Scheme 1).

Scheme 1. Molecular structures of the donors (D). The architecture of the studied systems is composed by the cyanoacrylic acid group as A, which combines the electron withdrawing properties of the cyano group with the binding character of the carboxylic group. A recent review reports that more than 50% of the organic dyes contain the cyanoacrylic acid as a binding group and thiophene as bridge.4 Therefore, our interest lays into analyze the effects on varying the D-fragment (motifs in Scheme 1) which may lead to a specific PI pathway depending on its structural and electronic properties. A family of 11 donor motifs (D1-D11) have been chosen displaying different structural properties and heteroatoms. Alizarin (Ali) and naphthalenediol (Naph) were chosen as models for analyzing the PI mechanisms as have been extensively studied and have been classified as Type I and Type II dyes, respectively.12-13,15-16 Furthermore, the assessment of the physical-chemical aspects, free energy of injection (-∆Ginj), light-harvesting efficiency (LHE), dipolar moment, that govern the


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light absorption process and efficiency of the different families of dyes in DSSCs have been also studied.26-28 THEORETICAL METHODS Composition of the family of donors. The following eleven donor motifs (Scheme 1) were selected for the analysis of the PI mechanisms and their photoelectronic properties within the Abridge-D arrangement: triphenylamine (D1), ullazine (D2), phenyl-hexahydrocyclopenta[b]indole (D3), free porphyrin (D4), phenyl carbazole (D5), perylene (D6), coronene (D7), pyrene (D8), anthraquinone (D9), coumarin (D10) and a phenoxazine-based dye (D11). The dyes are also labeled as their donor motifs. For the family of A-bridge-D dyes, the bidentate bond of the dye to the semiconductor was chosen since authors have reported that this mode is superior to monodentate in stability and provides better interfacial quantum yields due to the better contact with the oxide surface.3 The electronic properties of the selected dyes as strong donors in DSSC studies and the wide range of reports based in these molecular motifs make them suitable for the analysis. D1 is wellknown in the design of high efficient light harvesting dyes in DSSCs.20,29-35 D2 is a nitrogencontaining heterocycle whose derivatives have shown remarkable applications in photovoltaic devices and have been well-studied by Grätzel´s group and proved in optoelectronic devices showing electron donor and acceptor character under different conditions.36-38 On the other hand, studies of new indole dyes as D3 with different additional donors have reported high-efficiency up to 9.52%39-40 and regarded as promising for DSSCs. Porphyrin frameworks (as D4) are also emerging, where recently a solar-energy-to-electricity conversion efficiency of 13% has been


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reported.7,41 D5 is also an arylamine based donor with great interest due to its excellent hole transport capability.42-43 D6, D7 and D8 are polycyclic aromatic hydrocarbons (PAHs). D6 has been employed to demonstrate a retardation of the electron injection process and a loss of recombination by coadsorbing inert gases and solvents on a TiO2/perylene interface.44 And, through substituted perylene derivatives, this donor has improved its performance as light-harvesting dye.45 D7 and D8 are donors with thermal stability and extensive electron delocalization which is optimal for DSSCs.46-48 D9 and D10 are oxygenated ligands. The former, D9, is the molecular basis of Ali. D10 includes a coumarin as donor4,15 which has been tested in a DSSCs device containing a methine unit (–CH=CH–) between the coumarin and the thiophene bridge, and showed solarenergy-to-electricity conversion efficiency of 5.8%.49 D11, also already used in DSSCs, exhibits a high power conversion efficiency (6.5%) under standard illumination (Global Air Mass 1.5).50-54 Geometry optimizations and absorption energies. Density functional theory (DFT) and Gaussian 09 were employed within the computations.55 Several functionals were tested for assessing to their effects in the calculated properties such as: the hybrid Becke-3-parameter-LeeYang-Parr functional (B3LYP) and its long-range corrected version (CAM-B3LYP), the generalized gradient approximation with the Perdew-Wang 1991 functional (PW91) and the Perdew–Burke–Ernzerhof functional (PBE) and, the pure meta GGA functional of Truhlar and Zhao (M06L).56-59 The 6-31G(d) basis set60 was used for the non-metallic atoms and, as the relativistic effects are important in heavy atoms, the LANL2DZ pseudopotential61-63 was employed for the Ti atoms. This is the standard basis sets used in the literature for modeling this type of big size systems as it provides a reasonable compromise between speed and accuracy.


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We are interested to analyze in a qualitative way the PI mechanisms of the A-bridge-D dyes to the (TiO2)15 cluster. Therefore, we have elected the functionals mentioned above taking into account that B3LYP would add a fixed amount of exact (Hartree Fock) exchange (20%) to the xc-functional, which just smoothly improves the results while its GGA counterparts PBE and M06L do not add exact exchange. The CAM-B3LYP functional was also employed to compute the vertical excitation energies of the systems since this long-range dispersion correction treatment of the charge transfer excitations has shown good results.58 The latter were treated as single-point energy calculations performed at the minima obtained with the B3LYP functional. The molecular structures of the isolated dyes and the dyes anchored to the (TiO2)15 cluster were fully optimized without symmetry constriction and the frequency calculations were performed to confirm that all the optimized geometries are stationary minima points. The absorption wavelengths and oscillator strengths were computed by means of time-dependent density functional theory (TD-DFT).64 The implicit solvent–systems interactions were modeled using the polarizable continuum model for acetonitrile (PCM, ε = 35.7).65 The computations provided the character of transitions involved in the studied systems. Once the optimized geometries were obtained, the adsorption energies (Eads) of dyes onto the (TiO2)15 cluster were calculated. The Eads is calculated according to equation (1) where positive energy values indicate a stable adsorption: Eads = Edye + ETiO2− Edye+TiO2

(1)

where Edye is the total energy of free dye, ETiO2 is the total energy of (TiO2)15 cluster, and Edye+TiO2 is the total energy of dye-(TiO2)15 system.


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Dipole moments. Electrochemical studies suggest that the interfacial dipole moment contributes to the measured open-circuit photo-voltage.20 To determine the dipole moment, it has to rely on the standard finite-field method (FF) which is based on the expansion of the total energy of the perturbed system in terms of the applied external electric field (F):

1 1 E = E0 − µi Fi − αij Fi Fj − βijk Fi Fj Fk −... 2 6

(2)

Where µ, α and β denote the dipole moment, the dipole polarizability and the first hyperpolarizability, respectively. Indices i, j, k are cartesian components, and the summation over repeated indices is assumed. This is an important parameter which refers to the deviation of charge distribution and points from negative to positive charge. Therefore, the dipole moments might be so sensitive to the structure of the dyes. This parameter was determined for the isolated dyes and over the dyes anchored to the cluster. It is expected that good dyes display dipole moment perpendicular to the semiconductor surface and the difference in the dipole moments will reflect the significant charge transfer trends in the systems.50-54 Free energy change for electron injection. In the PI mechanism, the electron transfer speed is studied via a general classical Marcus theory: 1/ 2

K inj

 2 π = [VPR ]  × T  h  λk B 

 (∆G inj + λ ) 2  exp − ×T 4λ k B  

(3)

In the equation, Kinj is the rate constant (in s−1) of the electron injection from dye to TiO2, kB is the Boltzmann constant, h is the Planck constant, ∆Ginj is the free energy change of injection and λ is the reorganization energy of the system. The value of VPR is the coupling constant between


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the product potential curves and reagent.26-27 In this expression, the ∆Ginj (in eV) for the current process of electron injection can be expressed as: TiO2 dye* ∆G inj = EOX − ECB

(4)

TiO2

where ECB is the reduction potential of the semiconductor conduction band (-4.0eV vs vacuum) and

dye* EOX

is the excited state oxidation potential of the dye. The latter can be estimated using

equation (5), where

dye EOX

is the oxidation potential energy of the dyes in the ground state, which is

based on the Koopman’s theorem. This is related to the ionization potential energy that can be estimated as the negative of the HOMO energy. And,

E00

is vertical excitation of lowest energy.

Negative values of ∆Ginj show that the electron injection from the dyes to the semiconductor is spontaneous. dye * dye E OX = E OX − E 00

(5)

Light harvesting efficiency (LHE). The light-harvesting efficiency (LHE) of a dye should be high to upgrade the photocurrent response. LHE is related to the oscillator strength (f) at a given (λmax) maximum wavelength. While f is large, LHE is strong due to the relationship: LHE = 1 - 10-A = 1 - 10-f

(6)

In the equation, A (or f) is the absorption (or oscillator strength) of the dye related to the λmax. This data can be directly obtained from the TD-DFT calculations.28 Open-circuit voltage (VOC). The following relationship for calculating the VOC as displayed in equation (7) is based on the fact that the electron transfer occurs from the lowest energy


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unoccupied molecular orbital (LUMO) of the dye to the conduction band of the semiconductor (ECB).26-28 Therefore, if the ELUMO is high, the VOC will be as well. eVOC = ELUMO − ECB

(7)

It should be noted that experimental data for VOC is in units of voltage but the approximation in equation (7) gives the values eV. Electron density difference maps (EDDMs). The EDDMs are a representation of the changes in the electron density upon a given electron transition. Generating these maps involves the use of the given information in the single-excited state calculations and uses the configurations that contribute to the transition of interest.40,66 These can be plotted for the electron density obtained of the systems before and after excitation, which give information in a more explicit manner about the probability of the electron transfer from one fragment to another one. The visualization and plots of the EDDMs were performed using GaussSum (v. 2.2.6).67 RESULTS AND DISCUSSION Ground-state properties. To analyze the role of the D in dyes built with A-bridge-D architecture in the electron injection processes in solar cells, we started by considering Ali as a Type I (indirect) electron injector, Naph as Type II (direct) injector and, finally, the eleven selected donors (D1 - D11). Here, the A-bridge-D structure is composed by cyanoacrylic acid as A and thiophene as the bridge. The configurations of Ali and Naph directly bounded to the (TiO2)15 cluster are displayed in Figure 3 as well as the D3 and D2 donors built within a Abridge-D arrangement as exemplars of the family of dyes. In the latter case, the A-bridge-D


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system is bounded to the anatase (TiO2)15 cluster through a bidentate bond with the carboxylic acid group of A and one proton transferred to an oxygen atom of the cluster.

Figure 3. Molecular structure of some selected dyes adsorbed to the (TiO2)15 cluster. On the other hand, the size of the TiO2 cluster plays an important role on the appropriate description of the PI mechanism. In this framework, the effects on the size of the TiO2 clusters on the description of the electronic properties by analyzing clusters with 2, 3, 5, 9, 15 and 38 units has been evaluated in previous works.14-19 The results suggested that the cluster with 15 TiO2 units is the smallest (optimal) cluster that can reproduce the electronic and energetic features of the system, as good as the cluster with 38 TiO2 units. Therefore, the last spherical structure model of (TiO2)15, used also in this work, was chosen as an equilibrium between the suitable form of the semiconductor and the computational cost. The magnitudes of the dipole moments (µ) of the isolated (free) dyes and bounded to the TiO2 cluster as well as the adsorption energies (Eads) calculated with the B3LYP functional are listed in Table 1. Moreover, in Figure 4 we present a comparison of the results obtained for the other functionals. Ali and Naph display lower dipole moments compared to A-bridge-D dyes. The dyes with coumarin (D10) and perylene (D6) donors showed the largest dipole moments of the


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family. For all functionals as presented in Figure 4, it is observed the same trend of the magnitudes of the dipole moments and the differences among them are negligible. The plots of the dipole moments in the free and anchored dyes are reported in the Supporting Information (SI), see Figs. S1-S2. It is seen that all the systems display the vectors pointing toward the A fragment and towards the cluster. Besides, it is noted that within all the functionals, the D10 adsorbed on the cluster shows clearly the dipole moment pointing inwards the semiconductor in a perpendicular orientation. As the computations are performed at ground state geometries, it is assumed that the dipole moments point from negative to positive charge which indicates a tendency of charge transfer after photoexcitation of the systems.

Figure 4. Effects of the DFT functional (B3LYP, PW91, PBE, M06L and CAM-B3LYP) in the calculated a) adsorption energies (Eads [kcal mol-1]), b-c) dipole moments (µ, [Deybe]), and d-e) vertical excitation energy (∆Ev [eV]). f) Dipole moment vectors for the A-bridge-D dye where D=D10 free and anchored to the TiO2 cluster. The calculated values of Eads are also reported in Table 1 and they were calculated according to equation (1) by subtracting the energies of the free dyes and the TiO2 cluster, to the energy of the adsorbed dyes onto the cluster. Here, all the positive values of Eads of the systems indicate a


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stable adsorption of the A-bridge-D dye to the TiO2 cluster. The Eads for the smallest dyes (Ali and Naph) result very similar when employing the B3LYP and purely-GGA functionals (see Figure 4). Nevertheless, as the size of the dyes increases, the differences of the Eads values becomes smoothly higher (5 - 14 kcal·mol-1). Table 1. Calculated Adsorption Energies (Eads, [kcal·mol-1]), the Dipole Moments (µ, [Debye]), Maximum Absorption Wavelengths (∆Ev, [nm (eV)]) and Oscillator Strengths (f(L)) of the Free A-Bridge-D Dyes and Anchored to the (TiO2)15 Cluster at the (TD-)B3LYP/6-31G(d) Theoretical Level.

D

Eads

µ dye µ dye@TiO2

∆Ev (Calc.) dye

f(L) dye@TiO2 f(L)

∆Ev (Exp.) dye

dye@TiO2 a

502(2.47)a

47.19 1.24

10.68

438(2.83) 0.150 465(2.66) 0.236

428(2.90)

Naph 48.86 2.61

12.45

313(3.96) 0.072 581(2.14) 0.045

335(3.70)a

4̴ 00-1000 (3.2−1.2)a

D1

42.06 7.37

15.34

560(2.21) 0.849 565(2.20) 0.123

404(3.07)b

404(3.07)b

D2

37.93 6.51

12.42

444(2.79) 0.926 496(2.50) 0.229

D3

43.28 8.84

17.13

557(2.22) 1.004 573(2.16) 0.818

486(2.55)c

420(2.95)c

D4

28.34 9.89

9.6

576(2.15) 0.215 601(2.06) 0.261

D5

40.75 4.53

10.48

515(2.41) 0.461 568(2.18) 0.430

D6

31.79 10.45

10.52

607(2.04) 0.550 666(1.86) 0.408

D7

30.57

9.8

9.38

497(2.49) 0.407 541(2.29) 0.445

D8

42.64 5.64

10.67

424(2.93) 1.270 554(2.728) 0.521

D9

43.32

8.36

477(2.77) 0.688 477(2.77) 1.146

D10 47.14 14.65

25.04

542(2.29) 1.341 552(2.25) 0.616

507(2.45)d

D11 25.70 8.59

21.27

392(3.16) 0.777 440(2.82) 0.304

465(2.67)e

Ali

a

4.9

Ref 12, bRef 34, cRef 40, dRef 24 in acetonitrile. eRef 54 in THF.

The D10 with coumarin donor is the only system that display a significant difference of Eads among the hybrid and the GGA functionals of about 20 kcal·mol-1. On the other hand, we obtained, using PBE, a Eads of 22.70 kcal·mol-1 for the D1 (triphenylamine donor) within our


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model (A-bridge-D-(TiO2)15), and this value correlates well with a reported value for a substituted D1 as a donor (same A and bridge) with a bigger anatase model ((TiO2)38).30 For getting deeper insight into the electronic properties of the systems, the calculated energy levels of the molecular orbitals of the TiO2 cluster, the free and adsorbed dyes were analyzed. For four of the donors (Ali, Naph, D3 and D2), these energy levels are displayed in Fig 5 while for the other systems are provided in the SI (Figs. S3-S6). Although M06L has been found suitable for modeling of diverse chemical phenomena, B3LYP reproduces in excellent agreement the experimental band gap of the TiO2 of 3.2 eV,68 where this gap is found to be smaller when calculated with GGA functionals. A common trend found for all the employed functionals is that the energies of the HOMO and LUMO of the free and adsorbed dyes lie above the corresponding ones of the isolated (TiO2)15 cluster. Moreover, the LUMO energy levels are placed within the conduction band of the TiO2 and the HOMOs are immersed in the band gap of the TiO2. A closer look to Figure 5 shows up that the energies of the HOMO are maintained at almost the same energy before and after they bind onto the (TiO2)15 cluster. Besides, the LUMOs of the adsorbed systems are strongly stabilized after the binding to the TiO2 lying almost at the conduction band energy edge. The results clearly show a dependency of the energy levels distribution and the HOMO-LUMO gaps with respect to the functional employed in the calculation. The HOMO calculated with PBE functional are blueshifted while the LUMO are redshifted with respect to the B3LYP values. This results in an underestimation of the HOMO-LUMO gaps not only for the PBE functional but also found for those calculated with the M06L functional. Not surprising, PBE shows the higher deviations among the four functionals where M06L performs better for most of the dyes


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(as compared to PBE), fact that may be attributed to the partial inclusion of non-local exchange effects through the dependency of the functional in the kinetic-energy density.

Figure 5. Diagrams of the MOs energy levels for the free (TiO2)15 cluster, free and anchored Abridge-D dyes computed at the B3LYP/6-31G(d) level. Photophysical properties. The excitation energies corresponding to the λmax of the absorption spectra of the free dyes and anchored in (TiO2)15 are listed in Table 1. Besides, a detailed information of the obtained results is presented in Figure 4 and in the SI. As commented above, Ali and Naph were studied with the aim of obtaining benchmark models for the electronic properties inherent of a Type I (indirect) and Type II (direct) electron PI mechanisms. The photoinjection mechanism can be analyzed by comparing the UV-Vis spectra of the dyesemiconductor system and of the free dye. The appearance of a new band in the UV-Vis spectrum for the dye-semiconductor system as compared with the spectrum of the free dye suggests that the system undergoes a Type II (direct) mechanism. This new band corresponds to a metal-to-particle charge-transfer (CT) in case of the dye has a metallic center or donor-toparticle CT if the system is metal free.12-13 On the other hand, when the anchored dye shows a


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Type-I injection route, the absorption spectrum does not exhibit any new band upon adsorption, but a shift of the λmax. The B3LYP functional provided excitation energies for the bright transition (λmax) in acetonitrile in a reasonable agreement with the experimental values of the already synthesized and characterized systems Ali and Naph. These excitation energies are seen to be slightly underestimated for D1,31 D340 and D10.49 This is an expected behavior of this functional as related to the charge transfer character of the transitions and the size of the dyes.37-38 One exception is presented by D11 where experimental report is performed using THF. The vertical excitation energies displayed in Figure 4 demonstrate the large wavelengths computed when using the PW91 and PBE functionals which do not include a corrected 1/R asymptotic behavior (R is the charge separation length). Certainly, in most of the cases may affect their performance for reproducing the excitation energies in spatially extended systems that could involve intramolecular charge transfer. The composition of the B3LYP functional displays in our study an improvement of this results, as well as M06L functional that also provides a reasonable concordance with the experimental data for the free and anchored dyes. On the other hand, the excitation energies calculated with the CAM-B3LYP functional display a better agreement with the experimental reports for the family of A-bridge-D dyes when compared to the B3LYP results. Nevertheless, this statement does not apply to the Ali and Naph dyes where the results obtained with CAM-B3LYP are strongly overestimated compared either with the experimental reports and also the B3LYP data. For all the systems, the values obtained with the B3LYP functional behaves with an acceptable precision for the reference models (Ali and Naph) and the A-bridge-D dyes.


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The simulated UV-Vis absorption spectra of some selected A-bridge-D as well as of Ali and Naph dyes using the TD-B3LYP functional are presented in Figure 6. The absorption spectra computed using the four functionals is presented in the SI (Figure S11). After the adsorption of Ali onto the semiconductor, the λmax band undergoes a bathochromic shift. While, the spectra profiles of Naph are characterized by the formation of a new broad band at lower energies after the adsorption on the TiO2 cluster. These differences in the behavior of the absorption spectrum after adsorption on the cluster let us to classify these dyes as Type II (direct) and Type I (indirect) PI mechanisms, respectively.


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Figure 6. Simulated UV-Vis spectra through TD-B3LYP(6-31G(d) vertical excitations for the A-bridge-D dyes. a) Ali, b) Naph, c) D3 and d) D2. Solid lines correspond to the results for free dyes and dotted lines correspond to the dye-(TiO2)15 systems. By assessing this same parameter for the dyes, for all systems the adsorption onto TiO2 leads to a redshift of the λmax compared to the spectra profiles of the free A-bridge-D dyes. A special case is the D2 where the absorption spectrum presents a new excitation in the visible region when employing not only the B3LYP functional but also with the other three functionals. Interestingly, this result is in agreement with a Type I (direct) PI pathway for the D2 donor. In fact, Meng and co-workers38 have studied the injection and recombination in a A-bridge-D2-TiO2 surface system via electronic dynamics and first principles designing a method for accurately predicting energy conversion efficiencies of DSSCs and other electronic properties. For this case, the first excited state (HOMO→LUMO) is invoked for starting the dynamic simulations and, therefore, the PI mechanism is forced to a Type I (indirect) pathway. As the authors found a good correlation with experiments for the recombination processes but much discrepancies for the injection, our results infer that this deviations might be happening because (among other factors) the dye would display a PI mechanism consisting in the Type II (direct) route. The UV-Vis absorption profiles for the A-bridge-D3 dye show a clear redshift of the wavelengths to lower energies. For the other A-bridge-D dyes, it is also observed that the absorption is redshifted even when employing GGA functionals with respect to the spectra obtained from the (CAM)B3LYP and M06L functionals. Moreover, it is important to mention that as implicit solvation interactions were modeled via PCM, explicit solvation interactions were not taken into account which may be affecting, in terms of accuracy, the calculated excitation energy values. On the other hand, the Ali, Naph, D1, D3, D5, D6, D7, D9, D10 free


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dyes show that the nature of the first band corresponds mainly to an HOMO → LUMO excitation, unlike for the dyes constituted by the D2, D8 and D11 donors that start with the HOMO-1. Only the dye built with the D4 donor presents a mixture of configurations describing the λmax. This last phenomenon is more frequently found in the states computed with the GGA and M06L functionals (see Tables S1-S4 in the SI). The amplitudes of the HOMO orbitals involved in the corresponding electronic transitions are localized in the donor motifs and for the LUMO in the acceptor fragments, respectively, indicating a donor-acceptor charge transfer character in all the cases. For the Dye-(TiO2)15 systems, the electronic states corresponding to λmax in the UV-Vis spectra start the electronic transition from the HOMO and end in several unoccupied MOs at higher energy. This behavior is seen for the results calculated using the four functionals. As our interest is to assess the localization of the MOs in these excitations, in the SI (Figs. S7-S10) we report the isosurfaces plots of the active MOs involved in the transitions assigned to the λmax for all the adsorbed dyes on the cluster. The B3LYP MOs isosurfaces of Ali-TiO2 and Naph-TiO2, analyzed as finger prints for studying the PI mechanism among the selected family of dyes, show substantial differences. The HOMO for the Ali-TiO2 system are mainly localized in the ring containing the anchoring group (with PBE is found also a small contribution of the HOMO-1 localized in the center of the Ali). While, the HOMO of the Naph-TiO2 system (and by using the four functionals) is extended over the aromatic dye showing some contributions of the A group. For the unoccupied orbitals, it can be observed that for the Ali-TiO2 system the LUMO+2 is localized over the dye and over a part of the cluster bonded to the dye, hence, the transition is


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directed to the dye with some mixture of cluster orbitals (using the B3LYP and CAM-B3LYP functionals). By using the PW91, PBE and M06L functionals, the unoccupied orbitals of lower energy where the transition is directed present most of the amplitudes localized in the dye. Nevertheless, this localization decreases as the MOs are placed at higher energies indicating that the composition of them consists mainly of TiO2 cluster contributions. On the other hand, those unoccupied MOs for Naph-TiO2 are composed mainly by d orbitals of the Ti atom and a few contribution of the p orbitals of the O atoms. The observed behavior in this study is consistent with the proposed Type I (indirect) and Type II (direct) PI mechanism for Ali and Naph, respectively. To analyze the charge transfer via photon absorption, the plots of the electron density differences maps (EDDMs) between the ground state and the first computed excitation of the Ali, Naph, D3 and D2 binding onto the TiO2 cluster are presented in Figure 7. The EDDMs for the other systems are reported in the SI (Figures S12-13). In this manner, it was possible to elucidate the localization of the occupied MOs of the systems that would show a depopulation and the unoccupied MOs which would be populated at the excitation. The EDDM has become very useful to evidence the character of excitations as it resumes the charge migration in the adsorbed dyes upon photoabsorption. This is an important feature for solar cells referring to the charge separation that generates donor-acceptor systems. Therefore, the results would help to be able to attribute a PI route for dyes. With all the functionals, it is observed that the orbitals where the electrons are coming from (blue densities in Figure 7) show p orbital delocalization spatially extended over the dye. Whereas, the orbitals where the electrons are going (orange densities in Figure 7) are located mainly on the acceptor fragment and a strong contribution of the TiO2 cluster orbitals. In this


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sense, D9 shows a slight difference as it also shows contribution of the donor motif and of the cluster orbitals which is rather weak using the B3LYP and M06L functionals.

Figure 7. EDDMs for the A-bridge-D-(TiO2)15 systems (D = Ali, D3, Naph and D2) upon photoexcitation to the first singlet excitation. The blue densities represent the source of electrons and the orange densities represent the target location after electron transfer. The dye with the D2 donor constitutes an exception in the described trend (using B3LYP). The EDDMs indicate that the region where the electrons are coming from is over the dye unit and the region where the charge is going is located over the whole cluster, since LUMO+3 represents the biggest contribution (around 90%) in the electronic transition (Figure S7). Albeit it is worthy to mention that the calculated EDDMs using GGA and M06L functionals show a small contribution of dye MOs. In spite of this feature, this describes a new band observed at low energy, upon adsorption of the dye on the cluster, in the UV-Vis spectra profiles computed using the four methods. These results enable us to propose that D2 is the only donor motif of the A-bridge-D dyes that exhibits Type II (direct) PI mechanism in the studied family. In general terms, a


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redistribution of the MOs where the electron density increases is observed after photoexcitation and when the dyes are anchored onto the semiconductor. Photovoltaic performance. The energy level diagrams for all the studied systems computed using the B3LYP functional show that the HOMOs of the free and anchored dyes are aligned under the potential energy of -4.8 eV of the electrolyte I-/I3- which indicates the possibility of charge regeneration of the dyes after the photooxidation. In the cases of the computations using the GGA functionals, only a few dyes display HOMO energies under the electrolyte energy, which is expected as these functionals have shown a detrimental underestimation of the HOMOLUMO energy gaps (Figures S3-S5) but using the M06L functional, the D11 shows a HOMO energy slightly lying over the electrolyte potential energy (Figure S6). For the LUMO counterparts, it is observed that for the free dyes they are aligned over the conduction band (CB) edge of the semiconductor and that they suffer a mixture with the semiconductor MOs after adsorption. This condition is propitious to promote a spontaneous electron transfer from the excited dye to the CB of the TiO2 cluster. The estimated thermodynamic properties -∆Ginj, LHE and eVoc are reported in Table 2. The negative of the obtained ∆G of injection establishes the described phenomenon of spontaneous charge transference from the dyes to the semiconductor. Taking into account only the A-bridgeD dyes, the -∆Ginj [eV] calculated using the B3LYP functional increases from 0.42 for D9 to 2.12 for D11, being D2 the second among the best injector. The trends calculated with the other functionals are very similar as the variation of the computed values is very small from one functional to the other. Using the PW91 functional the ascending trend follows from 0.34 for D10 to 2.14 for D1 with D2 placed in the fourth place. With the PBE functional the -∆Ginj [eV]


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limits vary from 0.43 for D9 to 2.18 for D11, being D2 the second among the best and finally with the M06L functional it is observed 0.52 in D9 to 2.3 in D1 being D2 the third best. Table 2. Calculated Negative Free Energy of the Injection (-∆Ginj, [eV]), Light-Harvesting Efficiency (LHE, [eV]) for the Lowest Singlet Excited State, the Open-Circuit Voltage (eVOC [eV]). B3LYP D

inj

-∆G

PW91

LHE

eVOC

inj

-∆G

PBE

LHE

eVOC

inj

-∆G

M06L

LHE

eVOC

inj

-∆G

LHE eVOC

Ali

0.65

0.29

1.07

0.87

0.23

0.39

0.91

0.23

0.44

0.98

0.25

0.55

Naph

2.46

0.15

2.96

2.72

0.11

2.23

2.75

0.11

2.26

2.86

0.13

2.4

D1

0.96

0.86

1.41

2.14

0.8

0.86

1.09

0.77

0.76

2.3

0.84

0.81

D2

1.68

0.88

-

1.57

0.55

-

1.65

0.55

-

1.71

0.61

-

D3

1.08

0.90

1.54

1.23

0.85

0.99

1.35

0.85

0.86

1.38

0.88

0.91

D4

0.71

0.39

1.12

0.72

0.52

0.51

0.76

0.51

0.55

0.8

0.55

0.6

D5

0.88

0.65

1.20

0.73

0.5

0.58

0.76

0.5

0.62

0.84

0.58

0.68

D6

0.86

0.72

1.18

0.82

0.62

0.56

0.85

0.61

0.6

0.91

0.66

0.66

D7

0.85

0.61

1.23

0.76

0.44

0.59

0.79

0.43

0.62

0.85

0.47

0.69

D8

1.2

0.95

1.28

1.31

0.87

0.67

1.44

0.87

0.63

1.46

0.9

0.68

D9

0.47

0.79

0.82

0.34

0.46

0.09

0.43

0.45

0.18

0.52

0.56

0.25

D10

1.01

0.95

1.46

1.81

0.73

0.74

1.25

0.88

0.78

1.27

0.91

0.82

D11

2.12

0.83

1.43

2.11

0.59

0.89

2.18

0.59

0.77

2.26

0.69

0.81

The eVoc represents the maximum voltage available from a solar cell which occurs at zero current, whose calculated values are listed also in Table 2, where in general it is observed that they agree in a good manner with the shown ranges by experiments. A similar pattern as for the ∆Ginj is observed for the eVoc [eV] parameter assessed here where D9 in all cases shows the lowest eVoc and D2 although is not the dye with the highest value, it occupies always one of the highest places in the trend. The dye with a D9 donor did not present significant interfacial interaction between the dye orbital and the TiO2 orbitals in the lowest excited state. Therefore,


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based on these results it is possible to affirm that this interaction is necessary to reach a spontaneous charge transfer with a subsequent enhanced open circuit voltage. The LHE refers to the fraction of light intensity absorbed by the dyes and their values (also in Table 2) should be large to achieve good photocurrent response. The studied dyes with A-bridgeD architecture display LHE values within the range of 0.29-0.95 using the B3LYP functional. These values are very similar when calculated with the PW91, PBE and M06L functionals, where the computed limits for the family of dyes are within 0.2-0.73, 0.2-0.88, and 0.23-0.91, respectively. In all cases, the D4 has the lowest LHE values while with the D8 donor presents the highest LHEs. These LHE ranges and the -∆Ginj intervals cover the calculated values reported by Amornkitbamrung et. al for a family of monascus dyes.28 Moreover, it is worthy to mention that these values of these metal free dyes are significantly larger than the LHE reported recently for a family

of

metal

complexes

consisting

in

tricarbonylrhenium(I)

compounds

with

tetrathiafulvalenes.69 CONCLUSIONS In the context of dye-sensitized solar cells (DSSCs), the electron photo-injection (PI) mechanisms and photovoltaic properties of Acceptor-bridge-Donor (A-bridge-D) dyes adsorbed onto a (TiO2)15 cluster (anatase like) are analyzed in this work by using (time dependent-) density functional theory ((TD-)DFT). Within the A-bridge-D architecture, the A and bridge motifs were fixed to cyanoacrylic acid and thiophene, respectively. As the aim was to evaluate the electronic properties of the D motif and their subsequent role in the PI mechanism, a set of 11 donors was analyzed. Moreover, two dyes, Alizarin (Ali) and naphthalenediol (Naph), were


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chosen as benchmark models for analyzing the PI mechanisms as their behaviors have been extensively studied as Type I (indirect) and Type II (direct) dyes, respectively. Due to the size of the systems (A-bridge-D-(TiO2)15), the selection of the DFT functional was done taking into account a balance between computational cost and qualitative agreement with available experimental measurements. It is known that charge transfer interactions (as occurring in the electron PI process) may influence the accuracy of the calculated electronic properties, and more when the DFT functional does not contain a desirable amount of exact (Hartree-Fock) exchange. The electronic properties were calculated and analyzed using the B3LYP, PW91, PBE, M06L and CAM-B3LYP functionals. In this context, the B3LYP functional has reproduced in a very good agreement the experimental band gap of the TiO2. In relation of the stability of the dyes supported onto the TiO2, the computed energy for the adsorption process (Eads) displayed positive values for all the systems. This indicates a stable adsorption of the dyes into the semiconductor. It was found that the Eads for Ali and Naph are the largest compared with the A-bridge-D dyes. Differences were observed using the four functionals, being the M06L results the largest data followed by B3LYP and GGA methods, although PBE correlates in a good manner the results with computations performed with an increased size of the semiconductor model. On the other hand, it was observed that the LUMO orbital energies are immersed within the conduction band of the semiconductor. While, the HOMO energies of all the systems are aligned within the semiconductor band gap. This fact suggests that the coupling of the dye to the semiconductor induces the energetic destabilization of the HOMO in all cases. All systems show the dipole moment (µ) vectors pointing towards the A fragment (except Ali) and toward the


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(TiO2)15 cluster and their magnitude increases in some cases after adsorption of the dye. This points out the possible direction that charge can drive after an incident luminous energy source, which in this case is directed to the semiconductor. In general, changing the donor fragment of the A-bridge-D structured dyes could be a factor that induce a different PI routes in DSSCs. The UV-Vis absorption spectra profiles of the D dyes (except D2) suffer a red shift of the maximum absorption band (λmax) after adsorption to the TiO2 cluster. This behavior shows the same trend as found for Ali, a dye well known to display a Type I (indirect) PI mechanism model in DSSCs. For the adsorbed Naph and D2 donors, their absorption spectra are characterized by the formation of a new absorption band with very low oscillator strength for CAM-B3LYP calculations. The elucidation of the character of the transitions were supported by the EDDM plots which are nowadays a worthy tool to study charge differences in photochemical processes. The photovoltaic parameters that govern the light absorption process and the energy photoconversion were also assessed, which suggest that the employment of the donor groups D2, D3, D8, D10 and D11, would make an improvement of the DSSC efficiency as they show the highest values of free energy of injection and light harvesting properties. A point that has to be highlighted here is that the proposed approximation to obtain the eVoc is not recommended to be employed for dyes behaving as Type II (direct) injectors, as the equation consists in injecting charge from the excited dye to the CB of the semiconductor. Therefore, according to our results the D2 dye could act as direct injector or a mix of direct and indirect and could give high photoelectric conversion efficiency in concordance with the high values obtained for the photovoltaic parameters. It is interesting to mention that the difference of D2 with the


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other dyes consists in that it contains an ullazine core substituted by phenyl rings which show the electron-donating ability. Thus, a relationship between the dye structure and the PI pathway is a difficult task that has to be in continuous study since at this point is difficult to state if there is a specific structural feature that carries the mechanism to follow a determinate route, either of Type I or Type II. Nevertheless, the use of these criteria could be applied to predict the sensitization performance of dyes for DSSC, in order to design new and more efficient sensitizers, reducing economical cost and synthetic efforts. ASSOCIATED CONTENT Supporting Information. Supporting Information Available: Dipole moment vectors of the free dyes and the dye-(TiO2)15 systems, energy levels diagram of the free cluster (TiO2)15, free dyes and dye-(TiO2)15 systems. Results of the time dependent computations for the description of the vertical excitations of all dyes and dye-(TiO2)15 systems using the B3YP, PW91, PBE, M06L and CAM-B3LYP functionals with their corresponding EDDMs. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *(X.Z.) E-mail: [email protected] Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENT The financial support of Fondecyt 11140563 and Fondecyt 1130707 is gratefully acknowledged.

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