Computational Insight on the Working Principles of Zinc

Article pubs.acs.org/JPCC

Computational Insight on the Working Principles of Zinc Porphyrin Dye-Sensitized Solar Cells Ming-Gang Ju† and WanZhen Liang*,‡ †

Department of Chemical Physics, University of Science and Technology of China, Hefei 230026, People’s Republic of China State Key Laboratory of Physical Chemistry of Solid Surfaces, Collaborative Innovation Center of Chemistry for Energy Materials, Fujian Provincial Key Laboratory of Theoretical and Computational Chemistry, and Department of Chemistry, College of Chemistry and Chemical Engineering, Xiamen University, Xiamen 361005, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: A step-by-step theoretical protocol based on the density functional theory (DFT) and time-dependent DFT (TDDFT) at both the molecular and periodic levels have been performed to study a zinc porphyrin complex (named YDoc) sensitized TiO2 solar cell including dye excitations, electron injection, the regeneration of photooxidized dyes and the effect of electrolyte additives. Our study reveals the possibility of a favorable electron transfer from the excited dye to the semiconductor conduction band (CB) and suggests three possible pathways of the electron injection from the dye to the nanoparticle (TiO2)38. One is the direct one-step injection by photoexcitation, and the other two are from the different parts of the excited dye to the nanoparticle. The influence of the electrolyte composition on the geometric and electronic features of the dye/TiO2 system has also been studied. It is found that, with the additive of the lithium ion, the energy gap between the LUMO of dye and the TiO2 CB edge increases, which subsequently increases the driving force for the ultrafast excited-state electron injection, contrary to the effect of 4-tert-butylpyridine additive. The computational results of the oxidized dye interacting with I− and I2− reveal that there are a few possible mechanisms for the regeneration of oxidized dye. The effective mechanisms of the regeneration are suggested. transferred to I3− to yield I− at the cathode. Finally, iodide ions reduce the photooxidized dye molecules to their original ground state.3,4 In a way, the device operates in a regenerative mode. Therefore, to improve DSSC performance, the three aspects of light absorption, electron injection, and regeneration of the dye should be promoted and the recombination of injected electrons by interactions with the dye and by interaction with the electrolyte should be hampered. The dyes are able to adsorb on the semiconductor surface firmly, to absorb in the near-IR region as well as over the entire visible region of the solar spectrum, to inject electrons into the CB of the semiconductor, and to maintain a sufficient thermodynamic driving force for both the processes of electron injection and the sensitizer regeneration. The charge injection from the

I. INTRODUCTION Due to the immense potential impact of their successful massmarket application, dye-sensitized solar cells (DSSCs) have attracted a considerable amount of attention since O’Regan and Grätzel published their pioneering work in 1991.1,2 A basic DSSC consists of three fundamental components: a sensitized photoanode, which is a transition metal complex or an organic dye-sensitized nanocrystalline TiO2 film on a transparent conductive oxide (TCO) glass; a redox mediator in the electrolyte (typically I−/I3−) to facilitate electronic communication with the counter electrode; and a cathode, which is typically platinized TCO glass. Illuminating a DSSC with light causes the electrons in the ground state of the dye to pump to the higher-energy excited states. Next, the excited electrons are injected from the photoexcited dye into the TiO2 conduction band (CB). The injected electron percolates through the porous TiO2 layer into the TCO glass, passing the enterable load to the counter electrode. Subsequently, an electron is © XXXX American Chemical Society

Received: December 20, 2012 Revised: June 24, 2013

A

dx.doi.org/10.1021/jp3125445 | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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geometry of YDoc at the bare and modified surface of the bulk TiO2([101]) and (TiO2)38 nanoparticle, the UV−visible absorption spectroscopies of isolated dye and dye/TiO2 complex, and the energy alignment of molecular levels with respect to the substrate band edges. The interactions between the YDoc dye and TiO2, as well as the influences of the electrolyte on the electronic structure of the YDoc/TiO2 and the mechanisms for the oxidized dye by the I−/I3− redox couple, will be revealed. Especially, the mechanisms of interface electron separation of the YDoc-sensitized TiO2 system will be revealed.

excited dyes into the semiconductor nanoparticles is required to occur very rapidly, often requiring less than 1 ps.5−7 The electron donor member of the redox couple must reduce quickly and quantitatively the oxidized sensitizer, etc. Due to extensive research and development during the past decade, the highest authorized efficiency for DSSCs has recently reached 12.3% under standard test conditions.8 A widely used approach is to modify the dye in the hope of increasing the light-harvesting and charge-injection efficiencies. A variety of dye sensitizers for TiO2 have thus been suggested, such as the metal−organic or fully organic dyes and porphyrin derivatives. To date, the most efficient and stable dyes are based on ruthenium polypyridyl complexes,9,10 such as N3 and N719 dyes, the best of which have been reported to convert solar energy to electrical energy with an efficiency of around 11%.11 The high energy conversion efficiency of the widely used N3 sensitizer and other related Ru(II) polypyridyl complexes derives from the spatial separation of the donor lowest unoccupied molecular orbital (LUMO), which is closed to the TiO2 surface, resulting in electron injection which is much faster than recombination. Although these intrinsic properties of Ru(II) are based on dyes, many efforts have been devoted for a long time to replace these rare and expensive Ru(II) complexes with cheaper and environmentally friendly natural dyes. Porphyrin sensitizers were among the first examined natural types of dyes,12,13 and to this day they continue to be some of the most frequently studied sensitizers.14−21 A zinc porphyrin is substituted with a π-conjugated linker that attaches to the TiO2 semiconductor with a carboxyl group, which is a common motif. A structural design of this group of dyes taking the form of donor−π-conjugated bridge−acceptor zinc porphyrin has been done by Diau and co-workers over the past several years.22−24 It has been found that the particularly successful donor group is the diarylamino moiety. Based on Znmetalated porphyrin dye and cobalt(II/III)-based redox electrolyte, the power conversion efficiency of the best DSSC device has reached a record of 12.3% recently.8 However, substantial progress is still required to reach higher conversion efficiencies to make the DSSCs applicable at an industrial scale, and the improvement based on the atomistic understanding from both the time-resolved experiments and theory as well as modeling is crucial for further breakthroughs. In this respect, microscopic examinations of dye and dye-sensitized systems are of great importance. In recent years, many works have been devoted to atomistic simulation of DSSCs25−36 and most of them focus on Rucomplex dyes, such as N3-type dyes.37−41 To our knowledge, accurate first-principles calculations, based on density functional theory (DFT) and its extension to excited states (timedependent DFT), have not been used to simulate the interactions of porphyrin dye/semiconductor and porphyrin dye with the redox mediator. Herein we perform a step-by-step theoretical protocol based on DFT and TD-DFT at both the molecular and periodic levels to study porphyrin-sensitized DSSC devices including dyes and electrolyte additives. The most efficient DSSC device, a zinc porphyrin complex (named YD2-o-C8 (YDoc)) dye-sensitized DSSC device,8 will be studied. Through the studies on the atomic and electronic structures of isolated dyes and the dye/TiO2 complex, and the influence of the electrolyte part of the DSSC as well as the regeneration mechanism of the oxidized dye about the DSSC, we give a deeper insight into the working principle of a YDocsensitized DSSC device. In detail, we show the adsorption

II. COMPUTATIONAL DETAILS A step-by-step theoretical protocol based on DFT and TDDFT at both the molecular and periodic levels will be performed to study porphyrin-sensitized DSSC devices including dye excitations, electron injection, the regeneration of photooxidized dyes and electrolyte additives, etc. Molecular calculations were carried out with the Gaussian 09 program package.42 The geometries were fully optimized at the DFT level with the B3LYP functional and the long-range-corrected DFT (LRC-DFT) exchange-correlation (XC) functionals, camB3LYP (α = 0.19, β = 0.46, ω = 0.33 a0−1),43 and ωB97X-D (ω = 0.2 a0−1, CHF = 0.22).44 The LanL2DZ basis set45−47 is adopted. The solvent effects were taken into account by means of the integral equation formalism for the polarizable continuum model (IEFPCM).48 To understand the nature of electronic excitations, we analysis the excited states by constructing the natural transition orbitals (NTOs)49 within the Gaussian program package. The NTOs are defined by transformations U and V obtained by singular value decomposition (SVD) of the transition density matrix T, i.e., UTV† = λ. The matrixes U and V are unitary and λ is diagonal, with the latter containing at most O nonzero elements. To have a clearer picture on the mechanism of photoinduced electron injection in YDoc/(TiO2)38 complex, we then perform a calculation on the density of states (DOS) of the coupled dye−TiO2 complexes along with their projection onto the individual constituents of the dye. DOS and projected DOS (PDOS) are defined as50 DOS(E) =

∑ δ(E − εi)

(1)

i

and PDOS(subsys)(E) =

∑ ∑ ∑ CμiSμνCνiδ(E − εi) μ ∈ subsys

v

i

(2)

where εi represents the energy of the ith molecular orbital, C and S denote the MO coefficient matrix and the overlap matrix, respectively. The index μ (ν) denotes the indices of atomic orbitals. To analyze the efficiencies of suggested regeneration mechanisms of the oxidized dye by the I−/I3− redox couple, we calculate the binding energy of the complex ([dye·In]q; n and q denote the number of iodine atoms and the total charge of the complex, respectively) which corresponds to the mechanical energy required to disassemble the complex into the oxidized dye and iodine ions, and the dissociate energy of the complex, which corresponds to disassembling the complex into the centralized dye and iodine ions. This definition B



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corresponds to a positive binding energy. The larger the binding energy, the more stable the complex. In the regeneration processes of the oxidized dye by the I−/I3− redox couple, the oxidized dye can react with I− or I2− to form a series of complexes such as [dye·I], [dye·I2]−, and [dye·I2] (see section III.D). Once the complexes are formed, subsequently they are required to dissociate into the centralized dye and iodine ions for the regeneration processes to proceed. If a complex cannot be easily dissociated, the corresponding regeneration mechanism of the dye will not be efficient. Meanwhile, we conduct a natural bond orbital (NBO) analysis51,52 on the complexes with the NBO 3.1 program53 in the Gaussian program package. The interactions between the “filled” (donor) Lewis-type NBOs and the “empty” (acceptor) non-Lewis NBOs are calculated by second-order perturbation theory. This interaction is used to describe the noncovalent delocalization effects and can be considered as a measure of the relative stability of donor−acceptor systems as Habibi and coworkers indicated.54,55 This stabilization energy E(2), associated with i → j delocalization, is estimated by the following equation: E(2) = ΔEij = qi

F 2(i , j) εj − εi

Figure 1. Calculated absorption spectra of isolated YDoc in THF solution by TD-DFT coupled with PCM. To have a close comparison with the experimental result, the calculated spectra generated by TDcam-B3LYP and TD-ωB97X-D red shift 50 nm.

spectrum, which was measured in THF solvent,8 exhibits three major absorption bands: an intense B (Soret) band around 450 nm and two weaker Q bands (Q(0,1) and Q(0,0)) around 580 and 640 nm.8 A shoulder near 490 nm is also observed in the experimental spectrum. The calculated spectra were obtained by the TD-DFT method coupled with the PCM model. The different DFT XC functionals are employed. To compare with the experimental spectrum, the whole simulated spectra yielded by LRC-DFT XC functionals, cam-B3LYP43 and ωB97X-D,44 are red shifted 50 nm in Figure 1. It is noted that the influence of DFT XC functionals on the vertical excitation energies is significant. The LRC-DFT XC functionals overestimate the excitation energies, but give more reasonable descriptions on the relative intensities and energy level spacings of absorption bands than B3LYP. B3LYP underestimates the excitation energy of the lowest-energy band and gives incorrect relative intensities and energy level spacings of absorption bands. Here the vibronic structures are not taken into account. Therefore, the Q(0,1) band is not yielded in the theoretical spectra. To characterize the natures of excited states, we plot the hole/particle NTO pairs for the low-lying dipole-allowed singlet excited states of YDoc. The results come from TDcam-B3LYP calculation. Figure 2 visualizes three excited states by the “hole” and “particle” NTO pairs with a larger excitation amplitude of λ. The three excited states correspond to the first, fourth, and fifth dipole-allowed singlet excited states (simply noted as S1, S4, S5) with the excitation energies 2.08, 3.07, and 3.11 eV and the corresponding oscillator strengths 0.35, 1.15 and 1.96, respectively (see Table 1). Obviously, the photon absorptions of YDoc are arisen from the π−π* electronic transitions. The electron densities in all the “hole” NTOs, are mainly centralized on the porphyrin core and the N-phenyl groups, while in “particle” NTOs they are located on the porphyrin core and π-conjugated bridge. Obvious orbital mixing of the porphyrin core with the π-conjugated bridge is observed in all three excited states. The role of N-phenyl groups is obvious, which act as electronic donors and significantly enhance the photoabsorption. From the electronic density distributions of the typical hole/particle NTOs of excited states, we observe evident intramolecular charge-transfer characteristics. The electronic donor groups are the N-phenyl groups, and the acceptor groups are the porphyrin core and πconjugated bridge. The obvious intramolecular charge-transfer

(3)

where qi is the ith donor orbital occupancy, εi and εj are the diagonal elements (orbital energies), and F(i,j) is the offdiagonal element associated with the NBO Fock matrix.51,52 Periodic calculations in section III.C were carried out with DMol3 program package56,57 from Materials studio 6.0 at the theoretical level of PBE/DNP. We apply a large supercell with dimensions of 15.1 Å and 27.2 Å in the periodic [010] and [0.5 0.5 0] directions and 34.3 Å in the nonperiodic [101] direction. Sampling of the irreducible Brillouin zone was done with (2 × 2 × 1) k-points. Due to the limitation of the computational resource, only three atomic layers are involved in the model. This supercell can mimics the TiO2 (anatase) substrate by our calculation in principle. During the dye adsorption, all the adsorbed molecules were allowed to fully relax with the one outermost atomic plane.

III. RESULTS AND DISCUSSION III.A. Electronic Excitation of YDoc Dye. In this work, all the calculations are conducted for zinc porphyrin complex (named YDoc; see the inset of Figure1) sensitized TiO2 DSSC systems.8 YDoc has a typical donor−porphyrin−π-conjugated bridge structure. It has been functionalized with COOH anchoring groups, to allow upright adsorption on the TiO2 surfaces. First, we check the nature of the electronic excitation of the isolated YDoc molecule. To decrease the computational burden, we simplify the molecule by removing the big hydrocarbyls, which are used to inhibit the close intermolecular π−π stacking aggregation. The geometries were optimized in vacuo, in tetrahydofuran (THF), and in acetonitrile without any constraints. In Table 1 in the Supporting Information, the main optimal structure parameters of YDoc in the three solvents are listed. The differences between the bond angles in vacuo, in THF, and in acetonitrile are small, which indicates that the solvent effect has a modest influence on the geometry of YDoc. TD-DFT has been used to calculate the vertical excitation energies of low-lying singlet excited states. The calculated absorption spectra together with the experimental results of free YDoc dye are shown in Figure 1. The experimental C



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Figure 3. Optimized geometry of YDoc/(TiO2)38 and calculated absorption spectrum of the YDoc/(TiO2)38 complex by TD-camB3LYP (red line). The spectrum of the isolated YDoc (black line) is shown for the comparison.

DNP. The dye adsorbs almost uprightly on the TiO2 surface. A short binding distance of 2.2 Å (the distance between carboxylate oxygen and surface titanium atom) indicates that YDoc is firmly attached to the surface of the semiconductor by virtue of the anchoring groups which ensures a better donor− acceptor interaction between dye molecules and the semiconductor substrate, increasing the electron-transfer efficiency. The optical absorption of YDoc is affected by the interaction of TiO2 nanoparticle, leading to the overall spectral line shape of YDoc/(TiO2)38 complex being different from that of the isolated YDoc. Two main absorption bands red shift about 30 nm, and their relative oscillator strengths change in comparison with those of free dye. The absorption in the high-frequency range is reduced and that in the low-energy range is enhanced. To obtain a better clarification of the electron-transfer mechanisms from photoexcited dye to the conduction band of the semiconductor, we conduct an additional analysis on the electronic excitations of the corresponding states. Figure 4 shows the pairs of “hole” and “particle” NTOs of the three bright excited states. Since states 36 and 37 have similar characteristics, only the particle/hole NTOs of state 36 are shown in Figure 4. The nature of the first singlet excited state of the complex is analogous to that of the free dye. However, this photoexcitation pumps more particles to the π-conjugated bridge group, the anchoring ligand. The lowest excited state displays that initially photoexcitation takes place within the dye, but photoexcitation pushes the electrons toward the ligand actually anchoring the dye to the semiconductor surface, which guarantees the efficient electronic injection from the excited dye to the semiconductor.60−63 The two high-energy excited states show the evident charge-transfer properties. The electron densities in “hole” and “particle” NTOs are separately located on the dye and TiO2 nanoparticle. Two higher-energy excited states favor a direct electronic injection from the dye to (TiO2)38 upon the photoexcitation.

Figure 2. Electronic densities of “hole” and “particle” NTO pairs with largest values of λ for the dipole-allowed singlet excited states of YDoc dye.

characteristics explains the failure of B3LYP on the description of electronic excitations of YDoc since TD-DFT with a conventional XC functional has been found to give a poor description of the large delocalization excitation and long-range charge-transfer excitation due to the nonlocality and incorrect asymptotic behavior of the XC potential. The LRC-DFT XC functionals overcome the drawback of the traditional XC functionals and yield results which agree better with the experiments. III.B. YDoc/(TiO2)38 Complex. III.B.1. Electronic Excitation. TiO2 nanoparticles are sensitized with light-harvesting dyes. First, we model the TiO2 nanoparticles by a nanocluster with a size as large as (TiO2)38, which was cut from anatase bulk structure and adopted by many other works (e.g., refs 58 and 59). Figure 3 shows the binding structure of the sensitizer anchored on a TiO2 nanoparticle. The geometry of the YDoc/ (TiO2)38 system was optimized in DMols program with PBE/

Table 1. Vertical Excitation Energies of Low-Lying Dipole-Allowed Singlet Excited States with Oscillator Strength f > 0.2 for Isolated YDoc and YDoc/(TiO2)38 Complex (in eV)

YDoc YDoc/(TiO2)38

S1

S4

S5

2.08 (0.35) 1.98 (0.78)

3.07 (1.15)

3.11 (1.96)

D

S36

S37

S48

2.90 (0.40)

2.91 (0.31)

2.99 (0.23)



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(HOMO) and the LUMO of (TiO2)38, which is set to 0 eV in Figure 5.

Figure 5. DOS and PDOS of YDoc/(TiO2)38 for a bridging adsorption mode on a nanoparticle.

The main features of DOS can be found as follows. 1. (TiO2)38 nanoparticle has a HOMO−LUMO gap of 6.1 eV, which is larger than the band gap of 3.2 eV in the bulk TiO2 due to the quantum confinement effect of nanoparticles and the overestimation of the gap by the cam-B3LYP DFT functional. 2. The YDoc/(TiO2)38 complex has a smaller HOMO− LUMO gap of 2.05 eV. The YDoc dye inserts the occupied orbitals within the HOMO−LUMO gap of the TiO 2 nanoparticle, which decreases the computed HOMO−LUMO gap from 6.1 eV for the free nanoparticle to 2.05 eV for the YDoc/(TiO2)38 system. This type of DOS can create new optical excited states that are lower in energy than the TiO2 nanoparticle band gap absorption. 3. For the complex, the orbitals near the HOMO and LUMO are free of the combining states and have no mixing MO characters. The higher-lying occupied orbitals of the complex nearly have the characteristics of dye molecules, while the lowlying virtual orbitals of the complex nearly have the same characteristics of the TiO2 nanoparticle, which is manifested by the charge densities of frontier MOs shown in Figure 6. 4. The total DOS of the YDoc/(TiO2)38 complex has been projected to the individual components of the complex. From the PDOS, we note that the high-energy states of the valence band are contributed to by the N-phenyl group and porphyrin core while the bottom of the conduction band is only contributed to by (TiO2)38, the electronic acceptor. To achieve a high efficiency of excited-state electron injection, the LUMO energy level of the electron donor is usually required to be

Figure 4. Electronic densities of “hole” and “particle” NTO pairs of low-lying dipole-allowed singlet excited states of YDoc/(TiO2)38 with largest values of λ.

III.B.2. Density of States. To have a clearer picture of the mechanism of charge injection, we then perform a calculation on the density of states (DOS) of the coupled dye−TiO2 complexes along with their projection onto the individual constituents of the dye. The Fermi energy is defined as the middle point of the highest occupied molecular orbital E



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Figure 7. Suggested pathways of the electron injection from YDoc to TiO2 nanoparticle.

charge separation should occur within a few femtoseconds and the nuclear motion will not play a crucial role.50 The second injection pathway is from the excited dye to the semiconductor. When the dye is excited, part of excited particles are pumped to the anchoring ligand. Electrons then transfer from the ligand actually anchoring the dye to the semiconductor surface. This is the most effective and fast injection channel.64 The electron injection from the excited dye to the semiconductor should be a nonadiabatic radiationless process.65 The injection rate depends on two factors: the squared electronic coupling matrix element between the donor and the acceptor and the Franck−Condon weighted density of states.65 Due to the close contact of the anchoring ligand with the TiO2 surface, the electronic coupling between the initial state (the photoexcited dye) and the final state (the conduction bands of TiO2) should be strong, which guarantees an ultrafast and efficient excited-state injection into the semiconductor. The third pathway with the longer time scale is also from the excited dye to the semiconductor, but the electron transfer takes place from the excited porphyrin to the semiconductor. The direct through-space electronic transfer from porphyrin to the semiconductor may not be effective due to the 8 Å separation (between the center of porphyrin and the surface of the cluster in the YDoc/(TiO2)38 system). The electronic transfer may take place by a stepwise mechanism. For a donor− bridge−acceptor system, the attenuation factor β in the donor− acceptor coupling varies from ∼1 Å−1 when donor and acceptor are separated by an alkane bridge (high HOMO−LUMO gap) to values as low as ∼0.2 Å−1 for a connection made by a πconjugated fragment (small HOMO−LUMO gap).66 For low β, charge separation over distances of many tens of angstroms has been observed in a generic bulk heterojunction solar cell.66 Therefore, with a distance of 8 Å in the YDoc/(TiO2)38 interface, π-conjugated bridging chromophore promotes electron transfer of the strongly bound hole−electron pairs located within the porphyrin and easily generates partially separated electrons and holes which can easily overcome their

Figure 6. Calculated LUMOs and HOMOs for the YDoc/(TiO2)38 complex.

higher than that of the electron acceptor (at least 0.3 eV) in order to have sufficient driving force for electron transfer from the donor to acceptor. From DOS and PDOS spectra of the YDoc/(TiO2)38 complex, we clearly observe that the energy levels of the electron donor and acceptor satisfy this feature. The N-phenyl group, which acts as the electron donor, inserts its unoccupied MOs deeply into the conduction band of TiO2 and generates enough driving force for the electron injection from excited dye to TiO2. It is interesting to know that aromatic porphyrin contributes both the top of the valence band and the low-energy states of the conduction band. The π−π* electronic excitation within the porphyrin can take place by UV−vis irradiation. III.B.3. Suggested Pathways of Charge Separation in YDoc/(TiO2)38 Interface. By following the different initial charge separations or different types of electronic distributions in the initial and final states, and the different degrees of orbital mixing between the virtual orbitals of the dye and those of the TiO2 nanoparticle, we suggest three different types of injection mechanisms in the YDoc/TiO2 interface. One is the direct onestep injection by photoexcitation, and the other two are from the excited YDoc to the semiconductor. Figure 7 plots the suggested injection mechanisms. The fastest injection mechanism is the direct one-step photoexcitation. As shown in Figure 4, two dipole-allowed higher-energy excited states demonstrate the evident photoinduced intermolecular charge-transfer character. A direct electronic injection from the dye to (TiO2)38 is induced by the photoexcitation. In this case, the F



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Figure 8. Optimized structures of the (YDoc)/(TiO2), (YDoc)/(TiO2 + H2O), (YDoc + MP)/(TiO2 + H2O), and (YDoc + Li+)/(TiO2 + H2O) systems and their DOS spectra.

III.C. Effects of Electrolyte Interactions. The choice of electrolyte is a greatly adjustable parameter to optimize the efficiency of DSSC devices because the electrolyte component is usually made of several tunable types of molecules.70−73 Indeed, it contains solvent, I−/I3−, and various additives. Both the solvent and additives can affect the CB edge by adsorbing on the oxide surface and modify the DSSC’s efficiency.70,74 For example, 4-tert-butylpyridine (TBP) is found to increase the energy of the CB bottom edge. Conversely, lithium ion (Li+) is commonly used to decrease the energy of the CB bottom edge.71,72

Coulombic attraction and form free charges. Our prediction of the injection time scale based on the electron population of the initial state and the electronic coupling should be reasonable. Previous theoretical works have also pointed out that the electron injection from the high-energy states is faster than the electron injection from low-energy states67,68 and that the electron injection includes the adiabatic mechanism and nonadiabatic mechanism and the adiabatic mechanism is faster than the nonadiabatic mechanism.69 However, the injection from the excited dye is more efficient than the one-step photoinduced intermolecular electron transfer considering the absorption intensity of excited states. G



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Figure 9. Optimized geometries of [YDoc]+, [YDoc−I]0, [YDoc−I2]0, and [YDoc−I2]−. Blue = N, red = O, gray = C, white = H, brown = I, and purple = Zn.

strong chemisorption of the dye. As expected, the water adsorbs an oxygen atom of the TiO2 surface with an intermolecular Ti− O bond distance of 2.33 Å, the Li+ cation interacts with an oxygen atom of the surface with a Li−O distance of 1.91 Å, and the MP molecule preferably adsorbs on a Ti atom with a N−Ti distance of 2.35 Å. The DOS patterns of the YDoc/(TiO2), YDoc/(TiO2 + H2O), (YDoc + Li+)/(TiO2 + H2O), and (YDoc + MP)/(TiO2 + H2O) systems are presented in Figure 8. Comparing the DOS pattern of the YDoc/(TiO2) with that of YDoc/(TiO2 + H2O), a significant variation is observed when waters are coadsorbed on the TiO2. The CB edge of YDoc/(TiO2 + H2O) is located 0.4 eV above that of the YDoc/(TiO2), and the energy offset between the YDoc LUMO and the TiO2 conduction band edge decreases from 1.26 to 1.12 eV (see Figure 8). With MP additive, the CB edge is shifted to 0.1 eV above that of YDoc/(TiO2 + H2O) and the MP molecule continues to decrease the energy difference from 1.12 to 1.01 eV. Contrary to MP, Li+ decreases the CB edge to locate 0.4 eV below that of YDoc/(TiO2 + H2O) and increases the energy offset from 1.12 to 1.25 eV. A similar trend is also observed in experiments71,72 and other theoretical works.70,73 These changes in DOS confirm the capabilities of the solvent, Li+, and MP (by analogy with TBP) to modify the energy of the critical CB edge of oxides and further change the energy difference between the TiO2 CB edge and the dye LUMO. Hence, we can clearly predict that the solvent and these additive molecules should substantially influence the electron injection in the case of the YDoc/TiO2 system. The increase/reduction of the YDoc LUMO level relative to the acceptor TiO2 CB edge suggests that Li+/MP increases/ reduces the energetic driving force for the interfacial charge

Here we perform an atomistic investigation of the effects of the electrolyte interactions by using DFT-based methods with periodic boundary conditions. The surface studied is the 101 surface of the anatase structure of TiO2. Here YDoc is modeled by a porphyrin bridge (see Figure 2 in the Supporting Information) in order to decrease the computational burden. The dye was adsorbed via its carboxylate group in a bridgedunidentate manner, which is the most stable adsorption mode. TiO2 nanoparticles are sensitized with light-harvesting dyes, which are typically surrounded by a liquid-phase electrolyte containing the I−/I3− redox pair and acetonitrile (CH3CN) as solvent. DSSCs are generally fabricated under normal atmospheric conditions. In this environment, humidity is always present. Thus DSSCs always contain a certain amount of water in their constituting materials. Here we focus on the influences of solvent and two different additives, Li+ and TBP, which have opposite impacts on the CB edge of the oxide-based semiconductor. In our work, solvent is modeled by water and TBP is modeled by 4-methylpyridine (denoted MP) to reduce the computational burden. This simplification has been shown to be successfully validated in previous works.70,73 The optimized geometries of the dye with different modified TiO2 interfaces are presented in Figure 8. The optimal intermolecular bond lengths of Ti−O are 2.15, 2.14, and 2.12 Å in YDoc/ (TiO2 + H2O), (YDoc + MP)/(TiO2 + H2O), and (YDoc + Li+)/(TiO2 + H2O) systems, and the binding energies are 1.05, 1.13, and 1.31 eV, respectively. All are somewhat longer and lower than the intermolecular Ti−O distance of 2.07 Å and the binding energy of 1.21 eV in the geometry of YDoc/TiO2. The different modifications on the TiO2 surface have slightly different influences on the geometries of the DSSC system. The optimized intermolecular bond lengths of Ti−O confirm the H



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Table 2. Selected Occupancy Numbers of “Filled” NBOs, Stabilization Energies E(2) Associated with Orbital Pairs of Bonding and Antibonding NBOs, and Binding Energies E of the Complexes (in kcal·mol−1) parameter occupancy

E(2)

LP(1)I6 LP(2)I6 LP(3)I6 LP(4)I6 LP(1)I6 LP(1)I6 LP(2)I6 LP(3)I6 LP(3)I6 LP(3)I6 LP(3)I6 LP(4)I6 LP(4)I6

→ → → → → → → → →

LP*(6)Zn LP*(7)Zn LP*(7)Zn LP*(6)Zn LP*(7)Zn LP*(8)Zn LP*(9)Zn LP*(6)Zn LP*(7)Zn

[YDoc−I2]−

[YDoc−I2]0

0.9833 0.9807 0.9789 0.8160 2.25 2.77 2.98 3.19

0.9968 0.9919 0.9337

1.9948 1.9923 1.9456

2.63 9.56 6.05 2.36

43.42 7.68 62.30 74.90

sum of E(2) E E(second I−) a

[YDoc−I]0

17.97 74.90a 37.84b

5.47 4.84 7.78

20.70 36.10

Corresponds to the binding energy of YDoc+ + I− → [YDoc−I]. bCorresponds to the binding energy of [YDoc−I] + I− → [YDoc−I2]−.

However, there has not been any experimental and theoretical report on the regeneration mechanism of oxidized porphyrin dye. Herein, we focus on the intermolecular interaction of the zinc porphyrin complex (YDoc) with iodide ions and elucidate the regeneration mechanism of the YDoc theoretically. Our study begins with the oxidized species, [YDoc]+, in the doublet electronic spin state with a total charge of +1 (see Figure 9). Its geometry is optimized at the theoretical level of B3LYP/LanL2DZ and the corresponding geometric parameters are shown in Table 2 in the Supporting Information. Taking into consideration the steric effect and chemical affinity between Zn and I, the interaction of I− with the oxidized dye via the Zn atom seems plausible. In fact, other optimal geometries of the [YDoc−I]0 complex are not observed by our calculations. The optimized geometry is shown in Figure 9 with a total charge of 0 and multiplicity of 2. Table 2 in the Supporting Information lists geometric parameters. The intermolecular distance between Zn and I6 is about 2.79 Å, which is shorter than the net van der Waals radius of the binding atoms. The Zn atom is slightly out of the plane surface of the porphyrin, which increases the distance between Zn and N. To confirm whether regeneration mechanism A (eqs A1−A3) is applicable to YDoc, the complex [YDoc−I2]−1 is optimized with a total charge of −1. The distance of Zn−I6 in [YDoc−I2]− becomes 3.24 Å and the bond length of I6−I7 is 3.44 Å, which is shorter than that for isolated I2−, 3.46 Å. (More details are shown in Table S2 in the Supporting Information.) Meanwhile, [YDoc−I2]0 is optimized to explain the regeneration mechanism B (eqs B1 and B2) for YDoc. The distance of Zn−I6 in [YDoc−I2]0 is 3.36 Å, which is slightly longer than that of Zn−I6 in [YDoc−I2]−. The length of I6−I7 in [YDoc− I2]0 is 2.99 Å, which is longer than that of isolated I2, 2.86 Å. The conformational stability of the three complexes, [YDoc− I]0, [YDoc−I2]−, and [YDoc−I2]0, indicates that regeneration mechanisms A (eqs A1−A3), B (eqs B1 and B2), and C (eqs C1 and C2) are applicable to YDoc. The different geometric parameters of the complexes suggest different stiffnesses of coupling of molecules, which may give rise to the different reaction rates of the regeneration of dye via the different mechanisms.

injection. Once the charge transfer is complete, the carriers will move away from the interface with a driving force provided by the energy difference between the dye LUMO and the CB edge of the acceptor. Since the energy offset is greater in the Li+ modified interface than in the TBP modified interface, so is the driving force for the charge separation. Meanwhile, the solvent has an important influence on the electronic structure of the system. In order to improve the performance of the DSSC system, we should appropriately adjust the solvent. III.D. Molecular Mechanism of the Regeneration Process of the Dye. To further improve the authorized maximum solar energy conversion efficiency, the regeneration mechanism of oxidized dye by an I−/I3− redox couple has been investigated.2 A variety of regeneration mechanisms have been proposed for the regeneration reaction in DSSCs,3,75,76 for example, mechanisms A−C. mechanism A: [dye]+ + I− → [dye+·I−]

(A1)

[dye+·I−] + I− → dye ·I 2− → dye 0 + I 2−

(A2)

2I 2− → I− + I3−

(A3)

mechanism B: dye+ + I 2− → [dye+·I 2−] → dye 0 + I 2

(B1)

I 2 + I− → I3−

(B2)

mechanism C: [dye]+ + I− → [dye+·I−] → dye 0 + I

(C1)

I + I− → I 2−

(C2)

O’Regan and co-workers have also noted that there is not a “one and only” mechanism for regeneration.4 For instance, mechanism C (eqs C1 and C2) is similar to mechanism A (eqs A1−A3), except [dye+·I−] dissociates without the subsequent reaction of a second I−. The regeneration mechanism of the polypyridyl-Ru dye has been investigated experimentally3 and theoretically,55,77,78 confirming the notions of O’Regan that more than one mechanism exists in the regeneration of dye. I



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iodide ions with the oxidized dye becomes weaker than that without MP, and the sum of all E(2) terms corresponding to the delocalization of LPI6 in the three species are 7.5 kcal/mol for [MP−YDoc−I2]0 and 11.3 kcal/mol for [MP−YDoc−I]0, respectively, by NBO analysis (more details are shown in Table 4 in the Supporting Information).

In order to understand the nature and magnitude of the intermolecular interaction between the Zn atom of the dye and the iodide ions, NBO analyses were conducted on [YDoc−I]0, [YDoc−I2]−, and [YDoc−I2]0. The I atom interacts with Zn atom in [YDoc−I]0 with four valence lone pairs, LP(1)I6, LP(2)I6, LP(3)I6, and LP(4)I6, while the atom I6 in [YDoc− I2]− and [YDoc−I2]0 possesses three valence lone pairs, LP(1)I6, LP(2)I6, and LP(3)I6 (Table 2). For [YDoc−I]0, LP(4)I6 is more stabilized than the other valence lone pairs. The stabilization energy, E(2), of the LP(4)I6 → LP*(6)Zn orbital pair, where LP(4)I6 is a donor and LP*(6)Zn is an acceptor in a intermolecular charge-transfer interaction, is 43.42 kcal·mol−1. This value is larger than those for other LPI6 → LP*Zn orbital pairs. This finding indicates that there is a σ lone pair which binds iodide in [YDoc−I]0. As Habibi and coworkers indicated, the interaction of LP → LP* can be considered as a measure of the relative stability of dye−I complexes;54,55 we therefore sum all the interaction energies of LPI6 → LP*Zn. The results are 62.3, 17.97, and 20.7 kcal·mol−1, respectively, with an ascending order of E[YDoc−I2]− < E[YDoc−I2]0 < E[YDoc−I]0. It is explicit that [YDoc−I]0 is the most stable. Moreover, we calculate the intermolecular interaction energies, E, which are determined as the energy differences between the reactants (the iodide ions and the oxidized dye or the intermediate) and the complexes. With the definition, a more positive interaction energy corresponds to a stronger interaction. As shown in Table 2, a mechanical energy of 74.90 kcal/mol is required to disassemble the complex [YDoc−I]0 into YDoc+ and I−, which is larger than that to disassemble [YDoc−I2]− into [YDoc−I]0 and I− (37.84 kcal/mol) as well as that to disassemble [YDoc−I2]0 into YDoc+ and I2− (36.10 kcal/mol). Consistent with the NBO analysis, the interaction between I− and [YDoc]+ in [YDoc−I]0 is strongest. [YDoc−I]0 is the most stable and can be easily formed. Meanwhile, we calculate the dissociation energies of the three complexes. To dissociate the complexes into the corresponding iodide ions and the neutralized dye, energies of −94.05, 18.38, and 13.50 kcal/mol are required, respectively, with a descending order of E[YDoc−I2]0 < E[YDoc−I2]− < E[YDoc−I]0. It is explicit that [YDoc−I2]0 can be easily dissociated into YDoc and I2. Dissociating [YDoc−I]0 (into YDoc and I) and [YDoc−I2]− (into YDoc and I2−) requires the system to provide energies of about 18.38 and 13.50 kcal/mol, respectively. The formation of [dye+·I−] has been confirmed to be kinetically fast. However, the difficult dissociation of [YDoc−I]0 and the easier formation of [YDoc− I2]− suggest that mechanism C (eqs C1 and C2) has a lower efficiency for the regeneration of dye. In mechanism A (eqs A1−A3), a subsequent reaction of the intermediate, [dye+·I−], with a second iodide species is required, which has been predicted to be slower than the formation of [dye+·I−].3,75 However, the formation of [YDoc−I2]0 may deplete I2− which comes from the dissociation of [YDoc−I2]− and thereby speeds up the dissociation and improves the performance of regeneration of dye although [YDoc−I2]− requires a relatively large dissociation energy. [YDoc−I2]0 can be easily dissociated, which indicates that mechanism B (eqs B1 and B2) effectively competes with mechanisms A (eqs A1−A3) and C (eqs C1 and C2)in the regeneration reaction of the oxidized dye. When TBP (modeled by MP) coexists, the geometries are optimized at the same conditions (see Figure 5 in the Supporting Information). We find that the interaction of the

IV. CONCLUDING REMARKS To summarize, first-principles simulations are carried out to investigate the working principle of zinc porphyrin dyesensitized TiO2 solar cells. The geometric structure, electronic structure, and energy alignment of the interface have been studied for both the nanoparticle and bulk TiO2 surface. Both bare and modified TiO2 surfaces have been adopted, which allows a critical judgment of the role of the electrolyte compositions. The favored regeneration mechanism of oxidized dye has also been suggested. Our works correctly describe both the isolated dye and the dye−TiO2 interface and get insights into their key electronic features including UV−vis spectra and the charge-transfer character of their lower-lying electronic transitions. Meanwhile, the electron injection mechanism in different environments is analyzed in the calculations, which is useful for the design and the optimization of new DSSC systems. A significant charge-transfer nature has been visualized in dipole-allowed excited states of isolated YDoc. It is found that the photoexcitation pushes the electrons toward the ligand actually anchoring the dye to the semiconductor surface, which guarantees the efficient electronic injection from the excited dye to the semiconductor. To improve light absorption, we suggest increasing the donor groups (for example, the N-phenyl groups) of the dye. With the LRC functionals adopted, the theoretical spectra reach a satisfactory result consistent with the experimental measurements. With a detailed investigation of the interaction between YDoc and (TiO2)38, together with the analysis of hole/particle NTOs and PDOS, we reveal the possibility of a favorable electron transfer from the excited dye to the semiconductor CB due to the larger energy difference between the dye LUMO and the CB edge of TiO2. In addition, a one-step electronic injection by photoexcitation is also possible. Finally, we suggest three possible paths for the electron injection from the dye to the nanoparticle (TiO2)38, which is in agreement with the experimental evidence that electron injection dynamics is multiexponential and the time scales are from femtoseconds to picoseconds.79−81 The influence of the electrolyte composition on the geometric and electronic features of the dye/TiO2 system has been studied. Calculations of the dye/TiO2 system with the solvent and additives of the electrolyte confirm the role of the additives to modify the geometric and electronic features of the system. It is found that with the additive of the lithium ion, the energy gap between the LUMO of dye and the TiO2 CB edge increases, which subsequently increases the driving force of the electron injection, while the TBP additive brings the opposite effect. Therefore, we elucidate the efficiency of the electronic injection by performing calculations with the different additive molecules and solvent of the electrolyte. It is essential to improve the performance of the DSSC system by adjusting the composition of the electrolyte. Our theoretical study suggests that there is not only one mechanism for regeneration of oxidized dye, as O’Regan and co-workers have pointed out. The computational results of the J



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oxidized dye interacting with I− and I2− reveal that mechanisms B (eqs B1 and B2) and C (eqs C1 and C2) are applicable to the YDoc dye, and the formation of [YDoc−I2]− demonstrates that the two-step regeneration mechanism A (eqs A1−A3) is also applicable to the YDoc dye. However, mechanisms A and B may have higher reaction rates than mechanism C. Moreover, our computations suggest that TBP has an important influence on the regeneration reaction of YDoc and the quantity of TBP additive to DSSC must be considered to improve the performance of the DSSC.

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ASSOCIATED CONTENT

S Supporting Information *

Major geometric structures of YDoc and those with TBP (modeled by MP), DFT results of the interactions of the iodide ions with the oxidized dye, optimized geometry and DOS of (TiO2 + H2O). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the National Science Foundation of China (Grants 21073168 and 21290193) and the National Basic Research Program of China (Grant 2011CB808501) is acknowledged. The partial numerical calculations have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.

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