Rational Design of Dithienopicenocarbazole-Based Dyes and a

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Rational Design of Dithienopicenocarbazole-based Dyes and a Prediction of their Energy-Conversion Efficiency Characteristics for Dye-Sensitized Solar Cells Zhenqing Yang, Chunmeng Liu, Kuan Li, Jacqueline Manina Cole, Changjin Shao, and Dapeng Cao ACS Appl. Energy Mater., Just Accepted Manuscript • DOI: 10.1021/acsaem.7b00154 • Publication Date (Web): 13 Mar 2018 Downloaded from http://pubs.acs.org on March 13, 2018

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ACS Applied Energy Materials

Rational Design of Dithienopicenocarbazole-based Dyes and a Prediction of their Energy-Conversion Efficiency Characteristics for Dye-Sensitized Solar Cells Zhenqing Yang§,a,b, Chunmeng Liu§,a , Kuan Li§,a, Jacqueline M. Coleb,c,d,e*,Changjin Shaoa* and Dapeng Caof* a

State Key Laboratory of Heavy Oil Processing, Beijing Key Laboratory of Optical

Detection Technology for Oil and Gas, and College of Science, China University of Petroleum, Beijing 102249, P. R. China b

Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge

CB3 0HE, United Kingdom c

ISIS Neutron and Muon Source, Rutherford Appleton Laboratory, Harwell Science

and Innovation Campus, Didcot, Oxfordshire, OX11 0QX, UK d

Department of Chemical Engineering and Biotechnology, University of Cambridge,

Philippa Fawcett Drive, Cambridge, CB3 0AS, UK. e

f

Argonne National Laboratory, 9700 S. Cass Avenue, Argonne, IL 60439, USA

State Key Laboratory of Organic-Inorganic Composites, Beijing University of

Chemical Technology, Beijing 100029, China § These authors contributed equally * Authors for correspondence

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Email:

Zhenqing Yang:

[email protected]

Chunmeng Liu:

[email protected]

Kuan Li:

[email protected]

Jacqueline M. Cole:* [email protected] Changjin Shao:* Dapeng Cao:*

[email protected] [email protected]


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ABSTRACT A series of metal-free organic donor-acceptor (D-A) derivatives (ME01-ME06) of the known dye C281 were designed using first principles calculations in order to evaluate their potential for applications in dye-sensitized solar cells (DSSCs). Their physical and electronic properties were calculated using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). These include molecular properties that are required to assess the feasibility of a dye to function in DSSCs: UV/vis absorption spectra, light-harvesting efficiency (LHE), and driving forces of electron injection (∆Ginj). ME01, ME02, and ME04 are predicted to exhibit broad absorption optical spectra that cover the entire visible range, rendering these three dyes promising DSSC prospects. Device-relevant calculations on these three short-listed dyes and the parent dye C281 were then performed, whereupon the dye molecules were adsorbed onto anatase TiO2 surfaces to form the DSSC working electrode. Associated DSSC device characteristics of this dye…TiO2 interfacial structure were determined. These include the light-harvesting efficiency, the number of injected electrons, the electron-injection lifetime, and the quantum energy alignment of the adsorbed dye molecule to that of its device components. In turn, these calculated parameters enabled the derivation of the DSSC device performance parameters: short-circuit current density, JSC, incident photon-to-electron conversion efficiency, IPCE, and open-circuit voltage, VOC. Thus, we demonstrate a systematic ab initio approach to screen rationally designed D-A dyes with respect to their potential applicability in high-performance DSSC devices.



Keywords: metal-free organic dyes, donor-acceptor (D-A), dye-sensitized solar cells, DFT/TD-DFT, absorption spectrum

1. Introduction Dye-sensitized solar cells (DSSCs) have garnered considerable attention over the last 20 years in the area of renewable energy sources, mostly owing to their low cost and good power-conversion efficiencies (PCEs).1-3 One of the most important components in DSSCs, is the sensitizer (dye), which serves two principal functions: i) absorption of light and ii) injection of electrons into the semiconductor surface. Traditionally, organometallic dyes have been used predominantly as dyes in DSSCs; but recently, metal-free organic dyes have emerged as viable alternatives by virtue of their ample availability, their versatile molecular design, and their relatively low environmental impact.4-15 Wang and coworkers have recently synthesized the first polycyclic 9,14-dihydro4H-dithieno[2’ ,3’:2,3;3’’,2’’:10,11]piceno[1,14,13,12-bcdefgh] carbazole (DTPC) via ′

a palladium-catalyzed direct arylation, and an intramolecular Friedel–Crafts cyclization. Conjugating a DTPC-containing moiety with an electron-withdrawing 4(benzo[c][1,2,5]thiadiazol-4-ylethynyl)benzoic acid (BTEBA) segment (Figure 1) has resulted in the formation of C281, which is an organic dye with a low energy gap whose associated DSSC PCE reaches an excellent 13% under AM1.5G illumination.16 Despite this promising result, it remains difficult to examine the impact of different electron acceptors on the DSSC efficiency, without synthesizing and characterizing all possible options experimentally. Therefore, the rational in silico design and analysis of each functional component (including the donor and the acceptor group) of the


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parent organic D-A dye, C281, should be desirable toward the development of more efficient organic DSSC dyes. To this end, we herein present a systematic investigation on the influence of the electron acceptor group of C281 dye derivatives on their electronic and optical properties. This influence is expected to be significant since the electron acceptor group in these dyes has a dual function: it not only aids intramolecular charge transfer, it also contains the anchoring substituent that enables the dye molecules to adsorb onto the surface of TiO2, to form the dye…TiO2 interface that comprises the DSSC working electrode. The electron acceptor group thus has a critical role on optical absorption and electron-transfer processes that relate to DSSC device characteristics. Accordingly, dyes are first modeled as isolated molecules to determine their intrinsic molecular properties. Those whose optical and electronic properties show promise are short-listed for additional calculations, whereupon the parent dye, C281, and three of its derivatives are modeled as a dye…TiO2 interface to represent a DSSC working electrode. Associated DSSC device efficiency characteristics are determined as part of these property calculations. Results demonstrate the merit of in silico calculations in screening for new DSSC dyes.



Figure 1. Molecular structures of the parent dye, C281, and its in silico designed derivatives, ME01-ME06.

2. Computational methods 2.1. Molecular design of D-A Models. Considering computational cost, the molecular structure model for experimentally obtained C281 (Figure 1) was simplified for this work, by replacing its long alkyl chains with methyl groups. Similar simplifications have previously shown that such modifications are able to capture the essential character of organic dyes, while leaving the relative trends of the obtained results unaffected.17 In order to identify donoracceptor dyes that are more efficient than C281, chemical moieties of different electronegativity, size, and shape, have been attached at different positions in this model. To this end, we designed a series of dyes (ME01-ME06) by examining the variation of the electron-withdrawing acceptor group on the structure of C281 (Figure 1). Heterocycles partly replace primary atoms of the BTEBA segments in


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C281, in an attempt to lower the band gap effectively and thus control the absorption spectra. Different heteroatoms in these heterocycles were selected according to their atomic size and electronegativity, in order to modify the properties of the electronwithdrawing acceptor and, hence, the opto-electronic properties of the dyes. In all cases, the electron acceptor group featured a para-substituted carboxylic acid was attached to act as the anchoring group, since these have been shown to provide strong dye…TiO2 adsorption.18, 19 2.2 Electronic structure calculations on the dye molecules The geometric and electronic structures of the ground and excited states, absorption spectra, electronic properties, and energy gaps for ME01-ME06 and C281 were predicted by means of density functional theory (DFT) and time-dependent density functional theory (TDDFT) methods. DFT20 calculations on the isolated dyes were performed using the Gaussian09 program package.21 Full geometry optimizations and electronic structure calculations were calculated at the B3LYP/6-311G(d, p) level of theory in tetrahydrofuran (THF).22 Frequency calculations were carried out at the same level of theory to ensure that the geometries correspond to a minimum point on the potential energy surface (no imaginary frequencies). To obtain relatively accurate optical absorption calculations comparable to the experimental results, the UV−Vis spectra of C281 were obtained by TD-DFT methods. The calculated maximum absorption wavelength (λmax = 596 ± 13 nm) for C281 agreed well with the experimental data (609 nm).16 The result calculated using the MPW1K functional is also in good agreement with the experimentally obtained value. Therefore, we used the TD-MPW1K/6-311G(d,p) level of theory for all dyes, applying the conductor-like polarizable continuum model (CPCM) in THF to predict the optical properties of the new dyes. Associated property calculations on these isolated dyes are summarized in §3, where relevant, while further details are given in the Supporting Information §S1-S11. 2.3. Electronic structure calculations on the dye…TiO2 interfaces



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The adsorption of dye molecules onto TiO2 surfaces was simulated using vacuum slab models. As a periodic slab system, the anatase TiO2 (101) surface, consisting of 64 Ti and 128 O atoms, was constructed using a two-layer 2 × 4 super cell along the [101̅] and [010] directions. A vacuum region of 50 Å above the anatase TiO2 (101) slabs was used in order to guarantee decoupling between neighboring systems. DFT calculations were carried out on this starting model using the Vienna ab initio simulation package (VASP)23,

24

with the frozen-core all electron projector-augment-wave (PAW)25,

26

method. The generalized gradient approximation (GGA) with the Perdew-BurkeErnzerh (PBE)27 functional was used for the exchange-correction potential in all calculations.28 The PAW method was applied to describe the electron−ion interactions, and the cutoff energy for the plane-wave basis set was set to 500 eV. Extensive tests were carried out to ensure the convergence with respect to the number of k-point mesh29 for all systems. Here, every atomic position was optimized by the conjugated gradient method, except for the underlying atoms of TiO2, until the forces on each ion were reduced to < 0.01 eV/Å, and the resulting structures were subsequently used to calculate the electronic structures. For the geometry optimizations, atoms in the bottom layer of the TiO2 (101) slab were fixed to their bulk positions, while those in the top layer were allowed to relax. Such vacuum slab models30, 31 have previously been used for theoretical calculations on DSSCs using the HSE06 hybrid functional.32 Considering that calculations employing HSE06 run on such a large slab model would be very time-consuming, the DFT+U33 method was adopted for the geometry optimization and subsequent electronic structure calculations. Initially, the following onsite parameters were applied to the Ti-3d electrons: U = 6.28 eV and J = 0.5 eV.34 Associated property calculations on these dye…TiO2 interfacial structures are summarized in §3, where relevant, while further details are given in the Supporting Information §1.


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3. Results and Discussion 3.1. Electronic Structure and Photo-absorption characteristics of ME01-ME06. The optimized dye geometries of ME01-ME06 are shown in Figure S1. The calculated energy levels of ME01-ME06 and C281 are shown in Figure S2. The results indicate that the LUMO levels of photo-excited ME01-ME06 match well with those of the TiO2 conduction band edge (CBE). Interestingly, the HOMO energy levels of these C281 derivatives generally match those of their electron-donors DTPC, while the decreasing energy gap values are predominantly due to the decrease of the LUMO energy levels. This result confirms that partly substituting the primary atoms with electron-withdrawing segments can lead to a change of the LUMO energy levels of the dyes. The contribution of the frontier molecular orbitals (FMO) strongly affects the charge-separated states of the dyes.35 In real processes, the electron transition is generally dominated by a transition between the HOMOs and the LUMOs. The FMO isodensity plots of C281 and ME01-ME06, which were built using the B3LYP level of theory, are shown in Figure S3. In order to efficiently create charge-separated states, the main electron transitions occur from the HOMO and HOMO-1 to the LUMO and LUMO+1 orbitals, respectively, while contributions from other orbitals amount to less than 20% (see Table 1). Chemical modifications of the electron-withdrawing groups should allow tuning the photo absorption of the dyes. In order to obtain a basic idea of how the heteroatoms in the acceptor groups affect the light-harvesting efficiency, TD-DFT was used to simulate the UV/Vis absorption spectra of ME01-ME06 and C281, which revealed broad absorption spectra (Figure 2). The origins of the absorptions can be determined by calculating the singlet electronic transition (see Supporting Information). ME01, ME02, and ME03were designed by introducing the heteroatoms N, F, and Se into benzothiadiozine (BTD), respectively. ME01 and ME02 were designed by introducing a heterocycle with only one N and two F atoms to replace the



S and H atoms of BTD, respectively. The molar extinction coefficient of ME01 and ME02 improved by ca. 18.6% and -8.1%, respectively, while the maximum absorption peaks experienced a red-shift by 12 and 19 nm compared to C281. The introduction of N and F heteroatoms into BTD greatly enhances the light-absorption properties of the dye. Therefore, a Se heterocyclic atom was introduced to replace the S atom of BTD (ME03), in order to identify highly efficient DSSC dyes. Unexpectedly, ME03 showed not only a 3 nm blue-shift, but also a slightly decreased (~8.1%) molar extinction coefficient relative to C281. One possible explanation for this unexpected result could be the poor electron-withdrawing ability of the coacceptor, considering that the electronegativity of Se (2.55) is lower than that of S (2.58), and it may prevent intramolecular electron transfer from the donor to the acceptor and thus reduce the light-harvesting ability of the dye. To the best of our knowledge, if the electron-withdrawing ability of the co-acceptor is too strong, electrons will not be able to transfer to the real acceptor through the conjugate bridge. In contrast, if it is too weak, it will not be able to serve as an electron transfer sink, that is, the driving force for withdrawing electrons from the donor is inadequate, which is also not conducive to intramolecular electron transfer. In ME04 and ME05, an 3,4-ethyl-dioxythiophene (EDOT) group has been added between the BTD group

and phenyl ring of C281. The maximum absorption peak of ME04 (603 nm) exhibits slight (7 nm) red-shift compared to that of C281 and the molar extinction coefficient is improved significantly by ~12.4%. Although the molar extinction coefficient of ME05 is improved, the maximum absorption peak shows a small blue-shift (6 nm). ME06 was designed by replacing the phenyl ring of C281 with thiophene. Interesting, both the molar extinction coefficient and the maximum absorption peak were comparable to those of C281. In summary, changing the electron-withdrawing acceptor group by the introduction of heterocyclic atoms thus led to small changes in the maximum absorption peaks and the molar extinction coefficients relative to C281.


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12.0

C281 ME01 ME02 ME03 ME04 ME05 ME06

10.0 8.0

4

-1

-1

ε (10 M .cm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


6.0 4.0 2.0 0.0 200

400

600

800

1000

wavelength(nm)

Figure 2. Simulated UV/Vis absorption spectra for ME01-ME06 and C281.

Table 1. Simulated maximum absorption wavelengths (λmax/nm), corresponding to the vertical excitation energies Eex (eV), oscillator strengths (f), light harvesting efficiency (LHE) and the composition of the

corresponding electronic transitions (H = HOMO; L = LUMO), calculated at the TD-MPW1K/6-311+G(d,p) level of theory. ԑ Dyes

λmax

Eex

f

C281

596

2.08

2.2775

ME01

608

2.04

ME02

615

ME03

LHE

Main composition (%)

9.480

0.995

H-1→L (5%), H→L (79%), H→L+1 (12%)

2.7597

11.245

0.998

H-1→L (4%), H→L (83%), H→L+1 (9%)

2.02

2.072

8.716

0.992

H-1→L (4%), H→L (83%), H→L+1 (9%)

593

2.09

2.0625

8.725

0.991

H-1→L (7%), H→L (80%), H→L+1 (9%)

ME04

603

2.60

2.6025

10.654

0.998

H-1→L (6%), H→L (81%), H→L+1 (9%)

ME05

590

2.10

2.6189

10.781

0.998

H-1→L (6%), H→L (81%), H→L+1 (9%)

ME06

596

2.06

2.2842

9.575

0.995

H-1→L (7%), H→L (79%), H→L+1 (11%)

（104）

As described in the Supporting Information, §S3, the short-circuit current density, JSC, can be defined as:



J SC = ∫∫

SI LHE × φinjη coll d λ dx hc / eλ

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(1)

While JSC is calculated later (see §3.7), this equation is helpful to present at this stage to demonstrate that JSC is closely dependent on the light-harvesting efficiency (LHE), the electron-injection efficiency, φinj, and the collection efficiency, ηcoll. Considering the role of dyes in DSSCs, the LHE is a very important factor for organic dyes. The LHE values of ME01, ME02, and ME04 fall in a narrow range 0.992–0.998 (Table 1), which means that all sensitizers afford a similar photocurrent. Another way to enhance JSC is to improve the electron injection free energy, ∆Ginj. Calculation details for the determination of ∆Ginj are described in the Supporting Information, cf. Equation S6. Based on the Koopman theorem, the energy of the ground-state oxidation potential (Edye) is related to the ionization potential energy. Edye can be estimated as the negative EHOMO,36 while Edye* is the oxidation potential of the photoexcited dye (Table 2). All dyes exhibit negative ∆Ginj values (Table 2), implying that the electron-injection process is spontaneous. ME04 shows the largest absolute value of ∆Ginj, indicating the fastest electron-injection process, which best matches the shortest electron-injection time, τinj. The reorganization energy is another factor that influences the efficiency of DSSCs. Considering the geometrical structures, energy levels, absorption spectra, and calculated electronic properties of ME01-ME06, better Jsc values are expected for ME01, ME02, and ME04, given the observed slight red-shift in combination with the 12.4%-18.6% increase of the molar extinction coefficient for ME01 and ME04 compared to C281. Moreover, LHE of ME01 and ME04 is large compared to C281. Considering the Jsc of ME01, ME02, and ME04 in combination with their high molar extinction coefficients, and the bathochromically shifted absorption, these dyes represent promising prospects for the adsorption onto TiO2 surfaces, which should lead to increased Jsc value, and thus improve the PCE of DSSCs.


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Table 2. Calculated electronic properties of C281 and ME01-ME06: the redox potential of the ground state of the dyes (Edye), vertical transition energy (E0-0), driving force of injection (∆Ginj), and the excited state lifetimes of the dyes (τe) Dye

Edye (eV)

E0-0 (eV)

∆Ginj (eV)

τe (ns)

C281

4.83

2.08

-1.25

2.848362

ME01

4.82

2.04

-1.22

2.259591

ME02

4.85

2.02

-1.16

2.944102

ME03

5.00

2.09

-1.09

3.179849

ME04

4.82

2.06

-1.79

3.901148

ME05

4.82

2.10

-1.28

2.525628

ME06

4.83

2.06

-1.22

2.791614

3.2. Electronic Structures of the dye…TiO2 interface and associated Dye Adsorption characteristics The energy alignment of the dye…TiO2 interfacial structure, relative to other device components of a DSSC, is an important parameter to consider when determining how the nature of the DSSC working electrode affects the photovoltaic performance of DSSC devices. Accordingly, DFT and TD-DFT was employed in order to model this interfacial structure and energy alignment. The (101) face of anatase TiO2 was selected as the dye substrate for this interface model, since this TiO2 surface is considered to provide the most efficient dye binding for the adsorption process.30 C281, ME01, ME02, or ME04 was chosen as the photosensitizer for each of the four dye…TiO2 models constructed, owing to the high prospects in performance conversion efficiency for DSSCs containing such dyes. The optimized geometry of ME01, ME02, and ME04 adsorbed on TiO2is displayed in Figure S4. The most stable dye…TiO2 binding mode for these sensitizers was discovered to be bidentate bridging,



a result that is consistent with previous calculations on other organic dyes adsorbed onto TiO2 surfaces.37 The relative alignment of electronic levels of the dye…TiO2 interface was then calculated against that of other DSSC material components. Figure 3 shows the density of states (DOS) and projected density of states (PDOS) for the dye adsorption configurations of each dye…TiO2 interface. All dye…TiO2 models met the mandatory requirement in energy alignment for a functioning DSSC device, that is, the LUMO of the dye must be located above, and overlap with, the conduction band minimum (CBM) edge of the TiO2 substrate, which leads to efficient electron injection from the excited dye to the conduction band (CB) of TiO2. The electronic structures of these interfaces were then examined for bare and dyeadsorbed regions of the TiO2 surface. Compared with the bare (101) surface, the band gap of the TiO2 surface is decreased following the dye adsorption, with a concomitant lowering of the TiO2 CB. This can be explained in terms of the generation of a favorable dipolar field at the interface to tune the band energy levels of the surface TiO2, which is due to charge transfer between TiO2 and the dye molecules.38 This band gap reduction for the TiO2 surface should facilitate electron transport, as well as afford an increased gap between the LUMO of the dyes and the CBM of TiO2 which leads to an increased driving force for charge injection at the interface. However, lowering the CB of the TiO2 surface should also lead to a reduced Voc value. Furthermore, the DOS of the dye molecules shifts to higher energy after adsorption, indicating significant charge transfer from the dye molecules onto the TiO2 surface. The HOMOs of the dye molecules thus shift into the band gap region of TiO2, and the LUMOs increase to 0.4-0.6 eV above the CBM of the TiO2 surface, providing sufficient driving force for charge injection, which is crucial for DSSC applications. The band gaps of isolated C281, ME01, ME02, and ME04 are 1.75, 2.03, 1.69, and 1.88 eV. Interestingly, the band gaps decrease to 0.45, 0.91, 0.41, and 0.43 eV after adsorption onto the TiO2 surface (Figure 3), indicating that the absorption range for the dyes is increased and that the band gap difference for these molecules is ACS Paragon Plus Environment

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reduced. Where narrowed band gaps and small band gap differences exist for such dye molecules, this is likely a manifestation of comparable intramolecular charge transfer. These results show that the band gap differences for these molecules are reduced when the electrons are transferred to TiO2. These findings thus suggest that changing the heteroatoms of the electron-withdrawing acceptor groups or introducing additional electron-withdrawing units affect the alignment of the electronic levels at the dye…TiO2 interface.

Figure 3. Calculated total density of states (DOS) and projected density of states (PDOS) for (a) bare TiO2 (101) surface; and dye…TiO2 interfaces with the dye being (b) C281, (c) ME01, (d) ME02, and (e) ME04.



3.3. Photo-induced Electron Injection Characteristics To elucidate the mechanism underlying electron injection in these dye…TiO2 interfaces, the molecular orbitals of isolated C281, ME01, ME02, and ME04 were also calculated using the Gaussian09 package.21

Figure 4. Isodensity plots for the HOMO and LUMO levels and calculated energy levels of ME01, ME02, ME04, and C281. The red horizontal solid line indicates the level of CBM of the anatase (101) TiO2 surface (-4.0 eV).

The molecular orbitals of C281, ME01, ME02, and ME04 were calculated at the B3LYP/6-311G(d,p) level of theory. The thus obtained HOMOs and LUMOs are shown in Figure 4. The LUMOs are predominantly located at the BTEBA acceptor groups, while the HOMOs are mainly situated at the DTPC segments of the donor units. The calculated electronic transfer in the dye…TiO2 interfaces (Figure 5) illustrates how electrons are transferred from C281, ME01, ME02, and ME04 to the


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semiconductor. The calculations clearly show that, when adsorbed onto the TiO2 surface, the HOMOs of the dye…TiO2 interfaces are exclusively localized on the donor moieties of the dyes. Meanwhile, the LUMOs of dye…TiO2 interfaces are delocalized over the TiO2 slabs in energy levels, which should allow efficient electrons to transfer from the dyes to the semiconductor. Considering solvent effects, electrons should thus be injected into the semiconductor CB indirectly upon photoinduced excitation of the dyes, which is induced by intramolecular charge transfer (ICT). The favorable electron injection mechanism was confirmed by electron transfer rate calculations. The News-Anderson approach (Equation S10 in the Supporting Information) was applied, leading to ultra-fast injection time (τ) estimates of 5.48, 5.28, 3.85, and 3.23 fs for C281, ME01, ME02, and ME04, respectively, which should be sufficient for efficient electron injection.

Figure 5. Illustration of the orbitals involved in the photo-induced electron injection mechanism for C281, ME01, ME02, and ME04 adsorbed on TiO2. The energy level increases from the bottom to the top, and the Fermi energy level (EF, red dashed line) of each system is aligned for



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clarity. Blue arrows indicate the electron transfer mechanism: electrons are excited from the ground state to the excited state and then injected into the semiconductor conduction band. The ultra-fast electron injection times τ estimated by the News-Anderson model are also presented. The isovalue of the electron density is set to |0.05 au|.

3.4. Excited State Lifetimes (τe) The lifetime of the excited state (τe) has a major impact on the efficiency of the charge transfer. A dye with a stable cationic form and a longer excited state lifetime is more likely to exhibit long-term stability, which should favor charge transfer. The τe values of the dyes can be evaluated using the equation

τe =1.499/f E2,

(2)

where E is the excitation energy of the different electronic states and f is the oscillator strength of the electronic state.35 The first excited lifetime values, corresponding to the lowest excitation energies of all dyes, are listed in Table 2. For C281, ME01, ME02, and ME04, τe values of 2.85, 2.26, 2.94, and 3.90 ns, respectively were calculated. The longer electron lifetimes for ME02 and ME04 should ensure their efficient charge transfer and electron injection into the CB of TiO2.The introduction of heteroatoms in the electron-withdrawing acceptor should thus be considered as an effective approach to increase τe, which may be related to the nature of the heteroatom (e.g. electronegativity and size), and may retard charge recombination, thereby enhancing the DSSC power conversion efficiency. 3.5. Empirical Models to Estimate Reorganization Energies and Charge Transfer Distances The previously described procedure for estimating the ultra-fast electron injection lifetimes from first principles electron dynamics is both very time-consuming and costly, limiting large-scale applications of this theoretical approach. It would thus be desirable, if the injection lifetime (τinj) and recombination lifetime (τrec) could be calculated in a simpler fashion.


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Marcus theory39 could offer an effective solution to this problem. The chargetransport in organic thin films can be considered as a self-exchange hopping process,40, 41 commensurate with an electron or a hole transfer between neighboring molecules. This process can be quantified by Marcus theory, which delivers the rate of the non-adiabatic intermolecular charge transfer (kET)42-44 between two centers, held at a fixed distance and orientation, via: గ

݇ா் = ‫ܣ‬ටℏమ ఒ௞

ಳ

݁ ሺିఉ௥ሻ ݁ ்

൭

ష൫౴ಸబ శഊ೟೚೟ೌ೗൯ రഊೖಳ ೅

మ

൱

(3)

wherein ∆G0 refers to the driving force for the reaction, r to the electron transfer distance, λtotal to the reorganization energy, while β represents an attenuation factor, kB the Boltzmann constant, and A a constant. One important factor to mention in the determination of kET is λtotal, which is derived from DFT calculations on molecules in solution, whereby the exponential factor largely dominates the transfer rates.37, 45 The rate of charge transport increases with decreasing λtotal. Therefore, the calculated λtotal is also important for the analysis of the relationship between the electronic structure and Jsc. Our discussion focuses accordingly predominantly on the reorganization energy, i.e., only the internal reorganization energy is determined in this study, while the impact of the external environment is neglected. As mentioned in the Supporting Information, §S7, the Jsc should be enhanced by small values of λtotal, which comprises the hole and electron reorganization energy. The calculated λtotal of all dyes increase in the order C281

Rational Design of Dithienopicenocarbazole-Based Dyes and a

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