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Spacer Effects of Donor‑π Spacer-Acceptor Sensitizers on Photophysical Properties in Dye-Sensitized Solar Cells Chun-Jui Tan,† Chin-Sheng Yang,† Yung-Ching Sheng,† Helda Wika Amini,†,‡ and Hui-Hsu Gavin Tsai*,† †

Department of Chemistry, National Central University, No. 300, Zhongda Rd., Zhongli District, Taoyuan City 32001, Taiwan Department of Chemistry, Brawijaya University, Jl. Veteran, Malang 65145, Indonesia

‡

S Supporting Information *

ABSTRACT: The donor (D)-π spacer-acceptor (A) framework with electronic push−pull effects provides suitable molecular architectures for molecular design used as efficient light-harvesting sensitizers in dye-sensitized solar cells (DSSCs). Efficiencies of light harvesting and electron injection to the semiconductor of sensitizers play critical roles in DSSC performance. Here, we employed density functional theory to systematically and comparatively investigate the effects of π-spacers of D-π spacerA types of dyes in solution and adsorbed on a (TiO2)38 anatase cluster on various photophysical properties. The absorption spectra, electron transfer probability, and related photophysical properties of D-π spacer-A types of dyes were investigated as functions of different types (thiophene (Th)- and phenyl (Ph)based), lengths, and planarity (bridging two neighboring rings; dithieno-thiophene (DTT) and fluorene (FL)-based) of πspacers, while the D (diphenylamine) and A (cyano-acrylic acid) moieties remained the same. Spacers could significantly influence the λmax values and electron transfer probability. The spacer length has a red-shifted effect in λmax for the Th-, DTT-, and FL-based sensitizers due to their planar conjugated structures; nevertheless, the λmax values are saturated by ring number three. In contrast, the Ph-based spacers induce a blue-shift in λmax with spacer length due to their nonplanar structures. Interestingly, the Th- and DTT-based spacers with lower LUMO energy levels trap more electron density and thus reduce the probability of electron density transfer to TiO2 φET(λmax, TiO2) upon photoexcitation; moreover, the φET(λmax, TiO2) values decrease significantly with ring number. On the other hand, the φET(λmax, TiO2) values for the Ph- and FL-based sensitizers are less sensitive to the spacer length. Interestingly, the orders of theoretical maximum short-circuit current density of four studied families of molecules are correlated with their λmax values. Our study shows the Th−Th motif used as a π-spacer balances the spectral match with solar radiation and φET(λmax, TiO2) suitable for DSSC applications. Our results based on molecular and electronic structures could be used for rational sensitizer design of organic dyes for DSSC applications.

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INTRODUCTION As a result of global warming and the rapid depletion of fossil fuels, there is mounting interest in renewable energy especially solar energy and solar cells. In particular, dyesensitized solar cells (DSSCs) have attracted a great deal of scientific, technical, and industrial interest1−7 because of low manufacturing cost and high efficiency. Research on DSSCs has been very active since they were first developed by O’Regan and Grätzel.8 Over the past 10 years, there have been substantial improvements in the efficiency of DSSCs. In 1993, Grät zel 9 developed the well-known N3 dye, a ruthenium-based complex, which shows 10.0% performance under AM1.5 sunlight. Also, in 2005, the N719 dye showed 11.18% power conversion efficiency (η),10 currently usually used as the benchmark of DSSC performance.11−13 Later, Wu and her co-workers developed a polypyridyl ruthenium complex that showed η = 11.5%,14 which was the best efficiency obtained by 2009.15 More recently, Yeh and his coworkers achieved a photoelectric conversion efficiency of 12.3% © 2016 American Chemical Society

with porphyrin dye supplemented with an organic cosensitizer by utilizing the cobalt-based electrolyte.16 Soon after, Mathew et al. reported a porphyrin-based DSSC with a D-A-π-A framework having an efficiency up to 13%.17 DSSCs work on the principle of light-harvesting processes similar to those of the photosynthetic system in nature. A typical DSSC device comprises three major components:8 (i) a photosensitized dye-coated photoanode (e.g., TiO2), (ii) an electrolyte solution, usually containing iodide/triiodide (I−/ I3−), and (iii) a counter electrode. The working process of DSSCs begins with photoexcitation of the dye sensitizers under irradiation. After the sensitizer absorbs the light and converts photons to electrons, one of the most important processes is to transfer the electron from the dye sensitizers to the semiconductor. This process is called “charge transfer” or Received: July 13, 2016 Revised: August 28, 2016 Published: August 29, 2016 21272

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through a π-conjugated spacer to the electron-acceptor group (A), an electron-poor moiety directly anchoring to the semiconductor surface. On the basis of different design strategies, organic dyes with other types of structures have been proposed, such as D-D-π-A,19 (D)2-π-A,20 D-π-(A)2,21 double D-π-A,22 and D-A-π-A,23 where the (D)2 structure has two D moieties connected to a π-spacer and D-D structure introduces an additional donor moiety to the donor moiety of a D-π-A structure. However, organic dyes with D-π spacer-A structure provide us with simple model systems to understand the roles of donors, spacers, and acceptors in DSSC applications. Modification of donors, spacers, and anchors of dyes is expected to tune their optical and electrochemical properties and further influence their performance in DSSCs. From the point of view of molecular design, the π-conjugated spacer of dye can be more flexibly engineered, which is one of the key factors to obtain the panchromatic absorption. There are three strategies commonly utilized in engineering spacers. The first strategy is to vary the spacer length. Variation of the spacer lengths can change the π-conjugation length of dyes. When the length of π-conjugated spacer is extended in the D-πA type dyes, the HOMO−LUMO gap is expected to be narrower shifting the absorption spectrum to a longer wavelength and vice versa. Ehara, Promarak, and their coworkers have demonstrated that, as the number of thiophene units utilized as spacers in the D-D-π-A type molecules increases, the absorption bands show a red-shift (6−9 nm/per additional thiophene) and increased absorbance.19 The second strategy is the alternation of the spacer types: Types of πconjugated spacer units of dyes play a critical role in absorption spectra. Thiophene has been widely used as a conjugated moiety in solar cells.24 A previous study by Lin, Ko, and coworkers has shown that the thiophene conjugated in a spacer has a stronger ability to shift the absorption spectra of the molecule more to the bathochromic side than that of the phenyl moiety.25 Theoretical investigations have shown that utilization of thiophene units as spacers significantly decreased the LUMO energy level in comparison with that of the phenyl ring.26 The thiophene unity has been found to remain a more planar structure with its neighboring rings than that of the phenyl ring,26,27 increasing the effective conjugation length and thus having more red-shifted absorption spectra. The third strategy is the modification of the planarity of spacers: A spacer is commonly composed of several chemically connected aromatic rings, which can be nonplanar depending on the types of aromatic rings. It is known that the nonplanarity of connected aromatic rings can partially decrease its degree of πconjugation. Thus, increasing of the planarity of spacers is one method through which to extend the effective π-conjugation length. One of the strategies used to maximize the planarity of π-conjugated spacers is to bridge the two neighboring rings. Kang, Ko, and co-workers have shown that incorporation of a planar and cyclic indeno[1,2-b]thiophene unit as a spacer into a dye led to a strong molar absorption coefficient as well as a redshifted absorption compared to its analogue using a nonplanar phenyl-thiophene unit as a spacer.28 For example, replacement of the biphenyl ring by a fluorene moiety can result in a 14−19 nm red-shift in absorption spectra. On this basis, some planar units such as fluorene,27,29 cyclopentadithiophene,30 dithieno[3,2-b;2′,3′-d]thienyl,31 indenofluorene,32 and so on have been used as spacers in dyes. The “external quantum efficiency”, known as “incident photon to converted electron (IPCE)”, is defined as the ratio

“electron injection”.18 The electrons should be transferred to the semiconductor diffusing in the substrate and then producing electric power. The oxidized dye is reduced by the I−/I3− redox couple in the electrolyte solution. The electron injected in the semiconductor electrode flows through an external circuit to the counter electrode, where the I− ion is restored through reduction of I3−, completing the circuit. Therefore, the absorption of sunlight by the dye sensitizer is the first necessary and significant step in the operation of a DSSC. The electron injection process plays a critical role in DSSC performance. As one of the essential parts of a DSSC, for high performance, the photosensitizing dye should fulfill some crucial features.7 For efficient high-harvesting, the dye should have its absorption spectra well matched with sunlight spectra as well as have a high extinction coefficient. In addition, it is necessary that a large amount of dye loads on the semiconductor electrode, and the dye should have anchoring groups to strongly bind the dye onto the semiconductor surface. To achieve efficient electron injection into the semiconductor electrode, the dye should have its electronically excited state higher in energy than that of the conduction band edge of the semiconductor, providing a driving energy for fast electron injection. Moreover, it is necessary to avoid unnecessary dye aggregation on the semiconductor surface to reduce selfquenching through optimization of the molecular structure of the dye. After electron injection, the dye is in its oxidized state and has to be reduced by an electrolyte for regeneration. The energy level of the oxidized dye has to be lower than the electrolyte potential (e.g., I−/I3− redox potential) for efficient oxidation and regeneration of the dye. For durability, the longterm stability of the dye is required in all of its working processes. On the basis of these requirements, several different types of dyes such as metal complexes, porphyrins, and metalfree organic dyes have been developed as photosensitizers and applied to DSSCs over the past decades. Although there has been remarkable progress in the development of dye sensitizers for DSSC applications, the required molecular properties of dyes as sensitizers in high-performance DSSC applications seem to be dependent on and occasionally conflict with each other; therefore, delicate molecular design strategies are essential to optimize the required molecular properties for further improvement of their performance. Dye sensitizers used in DSSCs are generally classified into two broad categories: (i) metal complexes and (ii) metal-free organic dyes. In the former, the most well-known is the ruthenium (Ru) complex, N3, which has been shown to have a light-to-electricity energy conversion efficiency of over 10%.9 Although the Ru-based sensitizers usually have broad absorption spectra in the range 400−700 nm, the absorbance of Ru-complexes in the near IR region is usually lower than that of most organic dyes. Moreover, the metal contained in Rusensitizers is expensive and the synthesis and purification of Ru dyes are tricky. On the other hand, the metal-free organic dyes can be prepared inexpensively by following well-established synthesis methods. Furthermore, the structure, absorption spectra, and electrochemical properties of metal-free organic dyes can be systemically tuned using molecular design strategies. Among published organic dyes for DSSC applications, the D-π spacer-A framework is probably the most popular molecular architecture; D-π-A structure has a dipolar character based on the push−pull architecture. The electron donating group (D) is designed to be an electron-rich moiety, linked 21273

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Figure 1. Chemical structures of studied molecules with the framework of DPA-π spacer-CAA. Four different types of spacers with various lengths were studied: (a) DPA-Phn-CAA, (b) DPA-[Ph′]n-CAA, (c) DPA-Thn-CAA, and (d) DPA-[Th′]n-CAA families.

spacers in D-π-A type organic dyes on photophysical properties. On the basis of the D-π-A framework of organic dyes, we employed density functional theory (DFT) and timedependent DFT (TD-DFT) to systematically investigate the influences of the type (phenyl and thiophene rings), length (ring number up to 12), and coplanarity (fluorene and dithieno-thiophene) of π-spacers of the D-π-A framework with diphenylamine as the electron-donating moiety and cyanoacrylic acid as the electron-acceptor moiety (Figure 1) on the light harvesting efficiency, electron transfer, and dye regeneration properties. In addition, the effects of TiO2 are also taken into calculations. The results could be used for predicting the intrinsic properties of organic dyes suitable for fast development of organic dyes in DSSC applications.

of the number of carried electrons to the number of photons of a given wavelength. In the AM1.5 solar spectrum, the highest spectral irradiance is observed at about 530 nm. The decrease in spectral irradiance after 530 nm is slower than that at shorter wavelengths. Also, the absorption wavelength of metal-free organic dyes was about 100 nm, much shorter than that of standard ruthenium dye N3 (λmax = 534 nm). Hence, researchers design dye sensitizers that can absorb more redshifted wavelength or even have a wide absorption spectrum to increase the spectral coverage with the solar spectrum for lightharvesting. Lin and co-workers introduced a cyanovinyl unit into a conjugated spacer based on a D-π-A framework to increase the absorption wavelength for better light harvesting. The absorption bands of all the compounds lay in the visible region from 450 to 580 nm, which were attributed by inserting a cyanovinyl unit into the π-bridge. Furthermore, the extinction coefficient became higher with increasing length of conjugated spacer.33 However, the improvement of the red-shifted absorption spectrum and higher extinction coefficient are not enough to increase efficiency significantly. Besides, dye molecules should have effective charge transfer upon photoexcitation. Probably due to the complexity and time-consuming synthesis process, there has been no systematic report on the principles of how the length,34,35 type, and planarity of spacers in D-π-A dye sensitizers govern the photophysical properties such as absorption spectra and electron transfer properties. Therefore, it is necessary to derive the principles for effective development of the dye sensitizers suitable for DSSC applications. Increasingly, first-principles computational approaches are being developed as design strategies for DSSCs based on the fast development of software and hardware techniques.10,27,36,37 The aim of the present computational work on D-π-A type organic dyes is to provide a systematic and comparative study of the effects of length, type, and planarity of

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THEORETICAL METHODS Studied Molecular Systems and Nomenclature. Four families of spacer motifs (Figure 1; 46 molecules) were studied for the analysis of their photophysical properties based on the D-π-A framework, where the donor is diphenylamine (DPA) and the acceptor is cyano-acrylic acid (CAA). We calculated four types of π-spacers, thiophene- (Th), dithieno-thiophene(DTT), phenyl- (Ph), and fluorene- (FL) based aromatic rings, based on the DPA-π spacer-CAA framework. The molecular and electronic properties of selected spacers include the three strategies of spacer design mentioned in the Introduction and cover a wide range of spacers used in previous studied sensitizers, making them suitable for the systemically analysis. Th and Ph rings are the most common compositions used for the backbone of the π-spacer in dye sensitizers.38 DTT and FL are the analogues of Th and Ph, respectively; instead, their neighboring rings are constrained as planar by covalent bonds. In addition, we also studied the length effects of these four types of spacers. 21274

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dye−(TiO2)38 complexes were partially optimized at the B3LYP/6-31G(d,p) level in the gas phase; the dye molecule and several Ti and O atoms near the binding sites were relaxed (Figure 2), and other atoms on TiO2 were fixed. This model system was chosen as a compromise between computational cost and the stated purpose of predicting the properties of dyes on TiO2 thin film. Finally, the optimized structures of all the studied dye−(TiO2)38 complexes were used to calculate the UV−vis spectra, using the CAM-B3LYP/6-31G(d,p) method with Gaussian 0939 in the acetonitrile. Electron density difference maps (EDDMs) derived from the transition electron density of dyes before and after excitation were generated using GaussSum (v. 2.2.6).44 Theoretical Maximum Short-Circuit Current Density. The solar power conversion efficiency (η) is proportional to the product of the short-circuit current density (JSC), the opencircuit photovoltage (VOC), and the fill factor (FF). Obviously, the way to improve η is to increase JSC, VOC, and/or FF. In this study, we focus on understanding the spacer effects on JSC. For a given dye and solar cell design, the JSC factor can be determined by integrating the incident photon to current efficiency (IPCE) over the solar spectral density (Is(λ)) on the wavelength length of incident light

For convenience, the studied molecules were named by their sequence combination of the abbreviations by their donor, πspacer, and acceptor, as well as the ring numbers of the πspacer. For examples, the DPA-Th2-CAA in the DPA-Thn-CAA family of molecules (Figure 1a) is the one using DPA as the donor, two Th rings as the π-spacer, and CAA as the acceptor; the DPA-[Th′]2-CAA in the DPA-[Th′]n-CAA family of molecules (Figure 1b) is the one using one DTT unit (composed of two “thiophene” rings) as the π-spacer, and for the DPA-[Ph′]n-CAA family of molecules (Figure 1d), the DPA-[Ph′]2-CAA is the one using one FL unit (composed of two “phenyl” rings) as the π-spacer. Computational Methods. The ground-state molecular geometries of all studied molecules were optimized by the Becke, three-parameter, Lee−Yang−Parr (B3LYP) functional and 6-31G(d,p) basis set, as implemented in the Gaussian 09 program.39 The conductor-like polarizable continuum model (C-PCM)40 was used to account for the solvation effect. The solvent used in this study is dichloromethane. The calculated stable structures of free molecules were further examined by vibrational frequency calculations with all positive vibrational frequencies. The time-dependent DFT (TD-DFT) calculations were performed to calculate the UV−vis spectra. To account for the charge transfer excitations, the coulomb-attenuating method (CAM)41 was applied (at TD-CAM-B3LYP/6-31G(d,p) level) to calculate the UV−vis spectra of the dye sensitizers based on their corresponding optimized geometries calculated at the B3LYP/6-31G(d,p) level. To model the photophysical properties of sensitizers adsorbed on TiO2 thin films, we calculated dyes adsorbed on (TiO2)38 clusters with an anatase (101) surface. The (TiO2)38 cluster was first optimized at the B3LYP/6-31G(d,p) level. Dye in its deprotonated state is adsorbed on the anatase (101) surface of the (TiO2)38 supercluster42 in a bidentate manner with one proton transferred to a nearby surface oxygen atom (O2c); the two O atoms of the carboxylate are bound to the two neighboring five-coordinated Ti atoms (Ti5c) on the TiO2 surface43 (Figure 2). The ground-state molecular geometries of

JSC = e

∫0

∞

IPCE(λ)Is(λ) dλ

(1)

where e is the charge of an electron. The IPCE can be calculated by45 IPCE(λ) = LHE(λ)φinj(λ)ηcoll ηreg = APCIE(λ)ηcoll ηreg (2)

where LHE(λ) is light-harvesting efficiency at a given wavelength, λ, φinj(λ) is the electron injection efficiency, ηcoll is the charge collection efficiency, and ηreg is the dye regeneration efficiency. LHE(λ) corresponds to the fraction of photons absorbed at a specific λ by LHE(λ) = (1 − 10−A(λ))

(3)

where A(λ) is the absorbance. LHE(λ) can be quantified by the Beer−Lamber law (ref 46) A(λ) = 1000 × ε(λ)Γ

(4)

where ε(λ) is the wavelength-dependent molar extinction coefficient in M−1 cm−1 and Γ in mol/cm2 is a macroscopic surface coverage. The APCIE(λ) is the product of LHE(λ) and φinj(λ) corresponding to the absorbed photon to charge injection efficiency at a given wavelength. Equation 1 shows that JSC is calculated by integrating the IPCE on the wavelength length of incident light. Therefore, JSC is the product of ηcoll, ηreg, and the integral of APCIE(λ) on the wavelength. To further evaluate the spacer effects on the JSC value, we integrated the overlap of the LHE spectrum derived from the calculated absorption spectrum with the AM1.5G solar spectrum to give a theoretical maximum JSC value (J′SC) of a specific molecule by ′ =e JSC

∫0

∞

LHE(λ)Is(λ) dλ

(5)

The reference solar spectral irradiance is downloaded from a renewable resource data center.47 To calculate the J′SC value of a given dye, the absorption spectra were simulated through Gaussian convolution with a full width at half-maximum

Figure 2. Top view of a (TiO2)38 cluster with an anatase (101) surface highlighting the relaxed Ti (white) and O (red) atoms during geometry optimization. 21275

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The Journal of Physical Chemistry C Table 1. Available Experimental Absorption Spectra and Calculated Absorption Spectra experiment dyes DPA-Ph1-CAA DPA-Ph2-CAA DPA-Ph3-CAA DPA-[Ph′]2-CAA DPA-[Ph′]3-CAA DPA-Th3-CAA a

λmax (nm) 54

391 40555 38056 a 42455 40857 a 47658 b

calculation

ε (M−1 cm−1)

λmax (nm)

deviation from EXP.

oscillator strength

23100 20900 30167 25600 37000 21330

384 387 363a 406 403a 507b

−7 −18 −17 −18 −5 +31

1.166 1.358 1.776 1.434 1.871 1.657

In THF. bIn chloroform.

(FWHM) of 0.66 eV and the surface coverage Γ is set to 10−7 mol/cm2 adapted from a previous dye loading study of a lineartype D-π-A dye with a cyano-acrylic acid anchoring group on a TiO2 electrode.48

Table 2. Available Experimental GSOP Values (in eV) of Studied Dyes and the Calculated GSOP Values CAM-B3LYP/6-31G(d,p)

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Exp 54

5.81 DPA-Ph1-CAA DPA-Ph2-CAA 5.4055 DPA-Ph3-CAA 5.3556 DPA-[Ph′]2-CAA 5.3455 DPA-[Ph′]3-CAA 5.5157 DPA-Th3-CAA 5.0258 Mean Absolute Deviation

RESULTS AND DISCUSSION Assessment of Calculation Quality. The development of TD-DFT has made it possible to calculate the UV−vis absorption spectra of dyes at a reasonable level of accuracy. In many previous works,49−53 the long-range corrected CAMB3LYP functional has been reported to be an accurate method for the absorption spectra calculations of typical organic D-π-A dyes. Herein, we first evaluated the quality of calculations by UV−vis spectra. Table 1 lists the six available experimental absorption spectra of our studied dyes as well as our calculated UV−vis spectra. It is shown that the calculated absorption spectra are all blue-shifted relative to their corresponding experimental values except for the DPA-Th3-CAA. The absolute deviations of λ max between experiments and calculations are in the range 5−31 nm, and the average absolute deviation is 16 nm. The calculated λmax values are in good agreement with experimental values. Next, we compared the calculated oscillator strengths with the experimental molar absorption coefficient (ε). The oscillator strength is proportional to ε. The experimental ε values of DPA-[Ph′]n-CAA (n = 2 and 3) in CH2Cl2 are increased with the length of the πspacer (n value); our calculated oscillator strengths of these two molecules are also increased with the spacer length, which is consistent with the tendency of the experimental ε values. For the DPA-Phn-CAA (n = 1, 2, and 3) molecules, our calculated oscillator strengths are increased with the length of the π-spacer (n value), while the experimental results show the DPA-Ph2CAA has the smallest ε values. For the cases of DPA-Ph1-CAA and DPA-[Ph′]2-CAA in CH2Cl2, the calculated oscillator strengths are increased with the spacer length, which is consistent with the tendency in their experimental ε values. The ground-state oxidation potential (GSOP) is generally used in the alignment of the excited-state energy level of dyes.59−61 Table 2 lists the available experimental GSOP values and corresponding calculated GSOP values. The largest absolute deviation of calculated GSOP (ΔE) from experimental values is 0.33 eV, and the mean absolute deviation (MAD) is 0.14 eV. The absolute deviation of calculated GSOP (ΔG) values has a similar quantity to those of calculated GSOP (ΔE) values. The calculated GSOP values using CAM-B3LYP/631G(d,p) based on optimized molecular geometry by B3LYP/ 6-31G(d,p) are in a reasonable agreement with the experimental values. Molecular Geometry. The molecular geometries of the studied molecules shown in Figure 1 were optimized at the

GSOP (ΔG)

GSOP (ΔE)

5.54 5.30 5.23 5.26 5.17 5.03 0.15

5.60 5.33 5.27 5.28 5.19 5.14 0.14

B3LYP/6-31G(d,p) level in dichloromethane. The molecules we studied were mainly constituted by π-conjugated, rigid aromatic units, the geometries of which are affected little by their environment. The largest structural changes in the molecules after incorporating the different spacers were the dihedral angles of the two adjacent rigid aromatic rings. This structural parameter is particularly important because it affects each dye molecule’s degree of π conjugation, which will affect its photophysical properties. For the DPA-Phn-CAA family of molecules (Table S1 in the Supporting Information), we found that their π-spacers (n > 1) are nonplanar between the two neighboring Ph rings with dihedral angles in the range 30−35° (the average value is 34.1°), which is close to the inter-ring dihedral angle of 37.5° in the crystal structure of 3,3′dimethoxybiphenyl determined by X-ray diffraction methods.62 These results indicate the steric repulsion between two neighboring Ph rings. On the other hand, the π-spacers (n > 1) in the DPA-Thn-CAA family of molecules (Table S2 in the Supporting Information) are close to planar with the dihedral angles of two neighboring Th rings in the range 0.0−11° (average value is 3.1°). The two neighboring Th rings are arranged in an anti-configuration. Our calculations (B3LYP/631G(d,p)) show the anti-configuration of dithiophene is 0.61 kcal/mol more stable than its syn-configuration. The X-ray structure of 5,5′-bis(diphenylselenidophosphino)-2,2′-bithiophene has the two Th rings coplanar and is arranged in an anti-configuration.63 These results imply that the Th ring is a better π-conjugated spacer than a benzene ring.42 As expected, the π-spacers in DPA-[Ph′]n-CAA and DPA-[Th′]n-CAA families of molecules are nearly planar. Absorption Properties of Free Molecules. Figure 3a shows the calculated maximum absorption wavelengths (λmax) of free DPA-Thn-CAA, DPA-[Th′]n-CAA, DPA-Phn-CAA, and DPA-[Ph′]n-CAA families of molecules in dichloromethane as a function of their n values. The absorption spectra of these molecules were calculated at the CAM-B3LYP/6-31G(d,p) level on the basis of the geometries optimized at the B3LYP/631G(d,p) level. For a given n value, the λmax of these four 21276

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CAA family of molecules result in longer λmax; in contrast, the larger HOMO−LUMO energy gap of the Ph unit leads the DPA-Phn-CAA family of molecules to have shorter λmax. The λmax values of the DPA-Thn-CAA family of molecules are increased with the number of Th ring (n value). The λmax value is significantly red-shifted by 82 nm when the n value is increased from 1 to 2 and is red-shifted by 19 nm when the n value is increased from 2 to 3. When the n value is larger than 3, the λmax values are slightly red-shifted by ∼3 nm with each additional ring. The red-shifted tendency in λmax with increased number of Th rings is also observed in the experimental work of Sun and colleagues66 (molecules C1−1, C1−2, and C1−3 and C2−1 and C2−2 in the original literature) and of Thomas and colleagues (molecules IF1 and IF2 in the original literature).67 Another feasible strategy to tune the absorption spectra and other photophysical properties of dyes is to introduce substituents onto the backbone/spacer (e.g., polythiophene) of dyes, which was not investigated here. Recently, a systemically and comprehensively DFT and molecular dynamics study of the effects of electron-withdrawing cyano (−CN) and −F groups on poly(3-hexylthiophene) (P3HT) on the critical parameters for the photovoltaic performance of organic solar cells has been reported.68 Yang and co-workers found that CN-substituted P3HT derivatives induce red-shifted absorption spectra, while introduction of F groups onto the backbone (oligo-thiophene) of P3HT induces blue-shifted absorption spectra. Both F− and CN− groups decrease the HOMO and LUMO energy levels of P3HT; the CN groups decrease the energy level of the HOMO less than that of the LUMO, leading to red-shifted absorption spectra, while F groups affect the HOMO and LUMO energy levels in the opposite, resulting in blue-shifted absorption spectra. The work of Yang and co-workers68 gives clues into tuning the photophysical properties of conjugated polymers at the electronic level. The λmax values of the DPA-[Th′]n-CAA family of molecules are also red-shifted with n value. Similar to those of the DPAThn-CAA family of molecules, the λmax value is significantly redshifted with each additional ring when the n value is smaller than 3; the λmax value is significantly red-shifted by 59 nm when the n value is increased from 1 (DPA-Th1-CA) to 2 and is redshifted by 11 nm when the n value is increased from 2 to 3. When the n value is larger than 3, the λmax values are slightly red-shifted by 1−4 nm with each additional ring. For the DPA-Phn-CAA family of molecules, the calculated λmax values are generally blue-shifted or similar to increase in n values except for DPA-Ph1-CAA and DPA-Ph2-CA; the calculated λmax values remain similar when the n value is greater than 6. Our calculations show the spacers of the DPAPhn-CAA family of molecules have significant nonplanarity, which may reduce the degree of conjugation of the entire molecule. For the DPA-[Ph′]n-CAA family of molecules with a planar spacer, the λmax value is red-shifted by 22 nm when n is increased from 1 (DPA-Ph1-CA) to 2, while the λmax value is saturated at ∼405 nm when n is greater than 2. The restrained planar spacer in the DPA-[Ph′]n-CAA family of molecules induces a red-shift in λmax value compared to those of the nonplanar Phn spacer in the DPA-Phn-CAA family of molecules. On the contrary, the unrestrained Thn spacer induces a red-shift in λmax value in comparison to the restrained planar DTT spacer. Figure 3b displays the calculated oscillator strength ( f) of the λmax peak of the molecules. For a given family of molecules, the

Figure 3. (a) Calculated λmax and (b) calculated oscillator strength ( f) of DPA-Phn-CAA, DPA-[Ph′]n-CAA, DPA-Thn-CAA, and DPA[Th′]n-CAA families of molecules as a function of n values.

families of molecules is in the order of DPA-Thn-CAA > DPA[Th′]n-CAA > DPA-[Ph′]n-CAA > DPA-Phn-CAA. The Th ring used as a spacer can induce a more significant red-shift than others. Experiments also show the absorptions of dyes are red-shifted when a Ph ring as spacer is substituted by a Th ring.64,65 One interesting question is why the Th unit can induce a longer λmax than those of DTT, FL, and Ph units. To investigate this phenomenon, we calculated the HOMO and LUMO energy levels and their energy gap of DPA, Ph-Ph, FL, Th−Th, DTT, and CAA units (Figure 4). It is observed that the Th−Th unit has a smaller HOMO−LUMO energy gap than others; their HOMO−LUMO energy gaps are in the order of Ph−Ph > FL > DTT > Th−Th. The Th units with a smaller HOMO−LUMO energy gap incorporating in the DPA-Thn-

Figure 4. Orbital energy level diagram of DPA, Ph−Ph, FL, Th−Th, DTT, and CAA motifs calculated at the B3LYP/6-31G(d,p) level. 21277

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Figure 5. Charge density (φET(λmax)) of DPA-Phn-CAA, DPA-[Ph′]n-CAA, DPA-Thn-CAA, and DPA-[Th′]n-CAA families of molecules redistributed to their acceptor groups (a) and spacer groups (b) upon photoexcitation.

f values increase linearly with n value except for the DPA-PhnCAA family of molecules; the f values of the DPA-Phn-CAA family of molecules with n = 1−5 increase linearly with n, and are saturated at n > 5. We observed that the DPA-Phn-CAA family of molecules with n > 5 own another higher energy peak with significant f values. We fitted the f values into a linear function of n (the f values of DPA-Phn-CAA molecules were fitted with n = 1−5); the R2 values are in the range 0.973− 1.000. Experimentally, the ε values of DPA-Ph1-CA,69 DPAPh2-CA,70 and DPA-Ph3-CA71 increase with n; the ε values of DPA-[Ph′]2-CAA and DPA-[Ph′]3-CAA also increase with n (see Table 1). Our calculated results are consistent with experimental measurements. For a given n, the calculated oscillator strengths of the DPA-[Ph′]n-CAA family of molecules are larger than those of DPA-Phn-CAA molecules, and the calculated oscillator strengths of the DPA-[Th′]n-CAA family of molecules are larger than those of the DPA-Thn-CAA family of molecules. A similar tendency is also observed experimentally: the ε value of DPA-[Ph′]2-CAA is larger than that of DPA-Ph2CAA (see Table 1). Charge-Transfer Properties of Free Molecules. Figure 5 shows the calculated electron density φET(λmax) redistributed to the accepting/anchoring groups (Figure 5a, φET(λmax, CAA)) and to the spacers (Figure 5b, φET(λmax, spacer)) upon photoexcitation. It is observed that all studied molecules have significant electron density redistributed to the CAA moieties upon photoexcitation indicating the calculated absorptions of studied molecules are all intramolecular charge-transfer (CT) bands. For a given n value, the φET(λmax, CAA) values are in the order DPA-Phn-CAA > DPA-[Ph′]n-CAA > DPA-[Th′]n-CAA > DPA-Thn-CAA. Although the Th group induces a large redshift in λmax, it reduces the quantity of φET(λmax, CAA). As seen in Figure 4, the Th−Th unit has a lower-energy LUMO than Ph, FL, and DTT units; its LUMO energy level is close to that of CAA. Therefore, the Th unit not only plays a role as a spacer but also plays a role as an electron acceptor. Indeed, the Th moiety traps more electron density than others and thus has less electron density redistributed to the acceptor upon photoexcitation. On the other hand, the DPA-Phn-CAA family of molecules has more electron density redistributed to the acceptor. The overall D−A electron transfer (ET) rate is given as a sum of a superexchange (SX) and a sequential (SQ) contribution. The SX mechanism of ET proceeds directly

from donor to acceptor, when the energy level of the spacer is relatively high or the system does not have sufficient thermal energy to induce an ET event. On the other hand, in the SQ mechanism, spacer states are populated during the ET processes occurring when the energy gap between the donor and spacer states is relatively low. The analytical kinetics model72 shows that the multiexponential ET kinetics processes can be reduced to a single-exponential form for the SX mechanism, whereas the SQ kinetics can be described by an ndependence power form. Thus, the analytical kinetics model shows a crossover between the SX and SQ mechanisms, when the length of spacer is varied. The analytical kinetics model well reproduces the experimental kinetics data on distant ET through polyproline bridges.73 Recently, a TD-DFT electronic dynamics study of a series of D-polyene-A dyes with varying lengths of polyene showed a crossover between SX and SQ mechanisms;74 the SX mechanism plays a dominant role in the donor to acceptor ET as the polyene spacer length is short, while the SQ mechanism becomes more important when the polyene spacer is lengthened.74 Our static φET(λmax) values as a function of n values, although the dynamical effects were not taken into consideration, show the characteristics of analytical kinetics model72 and dynamical study74 in a qualitative matter. The φET(λmax, CAA) values (Figure, 5a), which present the electron density transferred directly from donor to acceptor upon photoexcitation, have the significant characteristics of the SX mechanism. The DPA-Thn-CAA, DPA-[Th′]n-CAA, and DPA-[Ph′]n-CAA families of molecules have their φET(λmax, CAA) values decreased exponentially with their n values; we fitted their φET(λmax, CAA) values into an exponential function of n values (φET(λmax, CAA) = Ae−βn), and we obtain (A, β, and R2) as (58.71, 0.036, 0.885), (51.22, 0.089, 0.961), and (50.31, 0.059, 0.939) for the DPA-[Ph′]n-CAA, DPA-Thn-CAA, and DPA-[Th′]n-CAA families of molecules, respectively. The DPAThn-CAA family of molecules has the largest decay constant of φET(λmax, CAA) with n. The φET(λmax, spacer) values (Figure, 5b), presenting the electron density transferred from donor to spacer upon photoexcitation, have the characteristics of the SQ mechanism. When the spacer is lengthened, the φET(λmax, spacer) values of DPA-Thn-CAA, DPA-[Th′]n-CAA, and DPA[Ph′]n-CAA families of molecules have a power law with n values. Interestingly, when the spacer is short, the φET(λmax, CAA) values of DPA-Thn-CAA, DPA-[Th′]n-CAA, and DPA[Ph′]n-CAA families of molecules are larger than those of their 21278

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The Journal of Physical Chemistry C corresponding φET(λmax, spacer) values; these cases are n = 1 for DPA-Thn-CAA and DPA-[Th′]n-CAA and n = 3 for DPA[Ph′]n-CAA, implying that the SX mechanism plays a dominant role in donor to acceptor ET. On the other hand, when the spacer is lengthened, the large φET(λmax, spacer) values imply that the SQ mechanism becomes more important. The φET(λmax, CAA) values of the DPA-Phn-CAA family of molecules are decreased when n is increased from 1 to 3, while they remained similar and large when n > 3. More interestingly, the φET(λmax, CAA) values of the DPA-Phn-CAA family are all larger than their corresponding φET(λmax, spacer) values. These results imply the SX mechanism also plays an important role even when the Ph-based spacer is lengthened. Absorption Properties of Molecules Adsorbed on a TiO2 Anatase Cluster. Figure 6a shows the calculated λmax

Figure 6b shows the calculated oscillated strengths of molecules adsorbed on a (TiO2)38 anatase cluster. The calculated oscillated strengths of all families of molecules are increased linearly with their n values, which have a similar tendency as their free states. Figure 6c simulated the theoretical maximum JSC value (J′SC) ′ calculations when dyes are adsorbed on TiO2. The details of JSC are described in the Theoretical Methods section. It is observed ′ values of the DPA-Thn-CAA and DPA-[Th′]n-CAA that the JSC families of molecules adsorbed on a (TiO2)38 anatase cluster are significantly increased when their n values are increased from 1 to 2, whereas the JSC ′ values are slightly increased when their n value is greater than 2. For the DPA-[Ph′]n-CAA family of molecules, the simulated J′SC values remain similar to the n values. In contrast, the J′SC values of the DPA-Phn-CAA family of molecules adsorbed on a (TiO2)38 anatase cluster decreased ′ values are in the with their n values. For a given n value, the JSC order DPA-Thn-CAA > DPA-[Th′]n-CAA ≫ DPA-[Ph′]n-CAA > DPA-Phn-CA. These results are generally correlated with the λmax values, which arise from the fact that the solar spectral density peaks at 530 nm. In general, Th-based spacers induce significantly larger J′SC values than those of Ph-based spacers. Electron Transfer from Molecules to TiO2 Clusters. Figure 7 shows the calculated electron density φET(λmax) redistributed to the (TiO2)38 anatase cluster (Figure 7a) and to spacers (Figure 7b) upon photoexcitation. For a given n value, the order of φET(λmax, TiO2) values is Ph-based (DPA-Phn-CAA and DPA-[Ph′]n-CAA) families of molecules > Th-based (DPA-Thn-CAA and DPA-[Th′]n-CAA) families of molecules. For the DPA-Thn-CAA and DPA-[Th′]n-CAA families, their φET(λmax, TiO2) values dramatically decrease with n value when n ≤ 2, implying that the SX mechanism plays a dominant role in donor to TiO2 ET. On the other hand, when n ≥ 3, their φET(λmax, TiO2) values remain at smaller and similar values (ca. 0.07), while the φET(λmax, spacer) values remain at larger values (ca. 0.50), implying that the SQ mechanism becomes more important. On the other hand, for the DPA-Phn-CAA and DPA-[Ph′]n-CAA families of molecules, their φET(λmax, TiO2) values are large (>0.65) and φET(λmax, spacer) values are small ( 3). One of the possible reasons for these results is that their higher energy LUMOs (blue-shifted absorption) have a greater probability to couple with the higher-energy TiO2 conduction band, which has a larger density of states.75 Moreover, the Ph- and FL-based spacers have higher-energy LUMOs, which are less capable to accept the density of excited electron. Polythiophene spacers with low-lying LUMO and polyphenyl spacers with higher-energy LUMO mediate the donor to TiO2 ET in terms of different mechanisms when the spacer is lengthened. Further dynamical calculations are needed to validate these results. Table 3 lists the alignment of excited-state energy levels of dye−(TiO2)38 systems. The method of excited-state energy alignment was proposed by De Angelis and colleagues.59,60 The driving force for electron injection is calculated by the aligned excited-state energy relative to the energy level of the experimental TiO2 conduction band (TiO2 C.B., −3.94 eV). It is observed that all families of molecules have the driving forces for electron injection. For the Th-based molecules, the driving forces decrease with their corresponding n values, whereas, for the Ph-based molecules, the driving forces increase

Figure 6. (a) Calculated λmax, (b) calculated oscillator strength ( f), and (c) theoretical maximum short-circuit current density (J′SC)) of DPA-Phn-CAA, DPA-[Ph′]n-CAA, DPA-Thn-CAA, and DPA-[Th′]nCAA families of molecules adsorbed on a (TiO2)38 anatase cluster as a function of n values.

values of molecules adsorbed on a (TiO2)38 anatase cluster. The λmax of a given family of molecules changes with n number and generally has a similar tendency to those of their free states. For example, the calculated λmax values of the DPA-Thn-CAA family of molecules adsorbed on a (TiO2)38 anatase cluster are redshifted with their n values, and have a similar tendency as their corresponding free states. For a given n value, the calculated λmax values are in the order DPA-Thn-CAA > DPA-[Th′]n-CAA ≫ DPA-[Ph′]n-CAA > DPA-Phn-CA. Except for the molecules with n = 1, the calculated λmax values on a (TiO2)38 anatase cluster are slightly changed relative to their corresponding free states. For the molecules with n = 1, the λmax values (adsorbed on a (TiO2)38 anatase cluster) are red-shifted by 13 and 9 nm for DPA-Th1-CAA and DPA-Ph1-CAA, respectively. 21279

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Figure 7. Charge density ((φET(λmax)) of DPA-Phn-CAA, DPA-[Ph′]n-CAA, DPA-Thn-CAA, and DPA-[Th′]n-CAA families of molecules adsorbed on a (TiO2)38 anatase cluster redistributed to the TiO2 cluster (a) and spacers (b) upon photoexcitation.

Table 3. Energy Levels of Dye−(TiO2)38 Moleculesa DPA-Th1-CAA DPA-Th2-CAA DPA-Th3-CAA DPA-Th4-CAA DPA-Th5-CAA DPA-[Th′]2-CAA DPA-[Th′]3-CAA DPA-[Th′]4-CAA DPA-[Th′]5-CAA DPA-Ph1-CAA DPA-Ph2-CAA DPA-Ph3-CAA DPA-Ph4-CAA DPA-Ph5-CAA DPA-[Ph′]2-CAA DPA-[Ph′]3-CAA DPA-[Ph′]4-CAA DPA-[Ph′]5-CAA

GSOP

Eabs

−5.41 −5.12 −5.07 −5.05 −5.04 −5.21 −5.16 −5.14 −5.12 −5.44 −5.20 −5.14 −5.13 −5.13 −5.15 −5.06 −5.04 −5.03

2.92 2.51 2.44 2.42 2.39 2.63 2.58 2.56 2.53 3.15 3.19 3.40 3.51 3.54 3.02 3.04 3.05 3.04

aligned

S1b

−2.48 −2.61 −2.62 −2.63 −2.66 −2.58 −2.58 −2.58 −2.59 −2.29 −2.01 −1.74 −1.63 −1.59 −2.13 −2.02 −1.99 −1.99

driving force 1.46 1.33 1.32 1.31 1.28 1.36 1.36 1.36 1.35 1.65 1.93 2.20 2.31 2.35 1.81 1.92 1.95 1.95

c

the alignments of excited-state energy levels of DPA-Phn-CAA(TiO2)38 families of molecules and electron density distribution before and after photoexcitation. Another parameter determines the IPCE is the electron injection efficiency. To consider the intrinsic property of JSC, we combine the J′SC and electron probability transferred to the TiO2 cluster (φET(λmax, TiO2)) to define a new quantity J′ (Figure 10).

ΔEreg 0.56 0.27 0.22 0.20 0.19 0.36 0.31 0.29 0.27 0.59 0.35 0.29 0.28 0.28 0.30 0.21 0.19 0.18

′ × φET(λmax , TiO2 ) J ′ = JSC

For the DPA-Thn-CAA-(TiO2)38 and DPA-[Th′]n-CAA(TiO2)38 families of molecules, their J′SC values increase and, in contrast, their φET(λmax, TiO2) values decrease with the n values. The J′ values of the DPA-Thn-CAA-(TiO2)38 family slightly increase from n = 1 to 2 and then quickly drop with n > 2 (peaked at n = 2), whereas the J′ values of the DPA-[Th′]nCAA-(TiO2)38 family of molecules decrease with spacer length. For the Ph-based (TiO2)38 family of molecules, their JSC ′ and φET(λmax, TiO2) values remain similar to the n value. Thus, the J′ values of DPA-Phn-CAA-(TiO2)38 and DPA-[Ph′]n-CAA(TiO2)38 families of molecules are less sensitive to the spacer length. Among all studied molecules adsorbed on TiO2, the DPA-Th2-CAA has the largest J′ value, indicating the DPA-Th2CAA as a good candidate for DSSC applications. Regeneration Energy of Molecules Adsorbed on a TiO2 Anatase Cluster. After electrons are injected into the TiO2 conduction band, the oxidized dye can be reduced by the electrolyte for efficient regeneration. The energy variation between dye and electrolyte (ΔEreg) can affect the rate of dye regeneration. Generally, the energy level of the oxidized dye should be (at least ∼0.2 eV) lower than the redox potential of the electrolyte. The ΔEreg can be calculated as

GSOP, excitation energy (Eabs), aligned first excited state (S1), driving force for electron injection (in eV), and ΔEreg. All results are calculated by CAM-B3LYP/6-31G(d,p) in acetonitrile. bE(aligned S1) = E(GSOP) + Eabs. cDriving force = E(aligned S1) − E(EXP. TiO2 C.B.); E(EXP. TiO2 C.B.) = −3.94 eV. a

with their corresponding n values. For a given n value, the GSOP values of four families of molecules are similar; therefore, the aligned excited-state energy is mainly determined by the excitation energy. Among four studied families of molecules, the DPA-Thn-CAA-(TiO2)38 family of molecules has the smallest driving force relative to corresponding molecules, which arises from their red-shifted absorptions. Moreover, the driving force is decreased with the n values. Graphic presentations of the alignments of excited-state energy levels of DPA-Thn-CAA-(TiO2)38 families of molecules and electron density distribution before and after photoexcitation are displayed in Figure 8. The driving forces for electron injection of the DPA-[Th′]n-CAA-(TiO2)38 family of molecules remain similar for all n values. On the other hand, the DPA-Phn-CAA(TiO2)38 families of molecules have the largest driving force, which is mainly due to their blue-shifted absorption. Moreover, the driving force is increased with the n values. Figure 9 shows

electrolyte dye ΔEreg = Eredox − EGSOP

where Eelectrolyte is the redox potential of the electrolyte. The redox standard redox potential of the I−/I3− electrolyte is −4.85 eV (0.35 eV versus NHE).76 Table 3 shows the calculated ΔEreg values of molecules on a (TiO2)38 anatase cluster. For the molecules with a shorter spacer (e.g., n = 1 or 2), ΔEreg values are larger than 0.2 eV. On the other hand, the molecules with a longer spacer length (e.g., n = 5) have ΔEreg values slightly smaller than 0.2 eV. These results indicate the increase of 21280

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Figure 8. Energy levels of the DPA-Thn-CAA family of molecules on a (TiO2)38 anatase cluster: the bottom bars are GSOP, and the upper ones are aligned S1 states. The EDDMs show the electron density of the molecule on TiO2 before (the purple represents where the electron density is coming from) and after (the cyan represents where the electron density is going) photoexcitation.

Figure 9. Energy levels of the DPA-Phn-CAA family of molecules on a (TiO2)38 anatase cluster: the bottom bars are GSOP, and the upper ones are aligned S1 states. The EDDMs show the electron density of the molecule on TiO2 before (the purple represents where the electron density is coming from) and after (the cyan represents where the electron density is going) photoexcitation.

based (DPA-Thn-CAA and DPA-[Th′]n-CAA) ones. These results indicate that the donor moieties of Ph-based dyes have a better electron affinity than those of corresponding Th-based dyes, which thus are favorable for dye regeneration.

spacer length decreases the regeneration energy arising from the increased GSOP values (or HOMO energy). In general, the donor groups of the D-π spacer-A dyes adsorbed on TiO2 are more exposed to the electrolyte than their other moieties. If the donor groups of cationic dyes are more electron deficient, an effective regeneration may occur and vice versa. Figure S1 shows the Mülliken charge of donor moieties of cationic dyes adsorbed on a TiO2 anatase cluster. For the DPA-Thn-CAA and DPA-[Th′]n-CAA families of molecules, Mülliken charge values decrease with n values and have a similar tendency. On the other hand, the DPA-Phn-CAA and DPA-[Ph′]n-CAA families of molecules have a similar tendency of the change of Mülliken charge values with n values; their Mülliken charge values slightly decrease with π-spacer length. For a given n value, the Mülliken charge on the donor group of Ph-based (DPA-Phn-CAA and DPA-[Ph′]n-CAA) cationic dyes is more positive than those of corresponding Th-

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CONCLUSION Here we presented a computational study aiming to increase the understanding of the effects of π-spacers of D-π spacer-A dyes in solution and adsorbed on TiO2 on photophysical properties. Within the TPA-π spacer-CAA architecture, we systemically vary the types, lengths, and planarity of spacers and investigate their subsequent roles in absorption, theoretical maximum JSC value (JSC ′ ), electron transfer probability, and other related photophysical properties. Using Th-, DTT-, and FL-based spacers can induce red-shifts in λmax with spacer length; nevertheless, the λmax values are quickly saturated when the ring number reaches three. 21281

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understanding of π-spacer effects for rational sensitizer design at the electronic and molecular levels for DSSC applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.6b07032. Mülliken charge of donor moieties of cationic dyes adsorbed on a (TiO2)38 anatase cluster and dihedral angles (deg) between two neighboring aromatic rings of DPA-Phn-CAA and DPA-Thn-CAA families of molecules (PDF)

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AUTHOR INFORMATION

Corresponding Author

Figure 10. J′ of the DPA-Phn-CAA, DPA-[Ph′]n-CAA, DPA-Thn-CAA, and DPA-[Th′]n-CAA families of molecules adsorbed on a (TiO2)38 anatase cluster redistributed to the TiO2 cluster upon photoexcitation.

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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Moreover, their f values of λmax increase linearly with spacer lengths. In contrast, using Ph rings as spacers induces a blueshift in λmax with spacer length due to the nonplanarity of spacers. The f values of λmax for Ph-based dyes are increased linearly with spacer length; however, they are saturated when the ring number is up to six (in solution). Among four studied families of molecules, Th-based spacers can effectively induce larger red-shifts in λmax compared with those of DTT-, FL-, and Ph-based spacers. Interestingly, the orders of theoretical maximum JSC values (JSC ′ ) of dye−(TiO2)38 molecules are in good correlation with those of absorption wavelengths, due to the spectral match with solar spectra. On the basis of the EDDM analysis, the λmax absorptions of all studied molecules are all validated as CT bands and their CT characters are affected by spacers. The Th- and DTT-based spacers have lower-energy LUMOs trapping more electron density and thus reduce the electron probability φET(λmax) redistributed to the acceptor moiety (in solution) and to the TiO2 upon photoexcitation; moreover, the φET(λmax, TiO2) values decrease significantly with ring number. The J′SC values of the DPA-Thn-CAA-(TiO2)38 family of molecules increase, and in contrast, their φET(λmax, TiO2) values decrease with the spacer length, resulting in a peaked J′ value at n = 2. On the other hand, the J′ values of the DPA-[Th′]n-CAA-(TiO2)38 family of molecules decrease with spacer length. In contrast, the φET(λmax, TiO2) values for the Ph- and FLbased sensitizers are less sensitive to spacer length. These results are due to their higher energy LUMOs, which have a greater probability to couple with the higher-energy TiO2 conduction band with a larger density of states. Moreover, their higher energy LUMOs are less suitable to accept electron density upon photoexcitation. Consequently, the DPA-PhnCAA-(TiO2)38 and DPA-[Ph′]n-CAA-(TiO2)38 families of molecules have J′ values less sensitive to the spacer length. Our study also shows the spacer length can reduce the dye regeneration driving force. Taken together, the Th−Th unit used as a π-spacer balances the spectral matched with solar spectra and electron density transferred to TiO2 has the largest J′ value, suggesting the DPATh2-CAA as a good candidate for DSSC applications. Moreover, the present study of the relationships between the types, lengths, and planarity of π-spacers and related photophysical properties provides a detailed benchmark and a better

ACKNOWLEDGMENTS We thank the Ministry of Science and Technology of Taiwan (Grant No. MOST 104-2113-M-008-005) for financial support and the National Center for High-Performance Computing and the V’ger computer cluster at the National Central University of Taiwan for allowing access to computer time and facilities. We thank three anonymous reviewers for insightful comments.

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