Density functional theory study of new azo dyes with different π-spacers for dye-sensitized solar cells

Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 143 (2015) 20–34

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Density functional theory study of new azo dyes with different p-spacers for dye-sensitized solar cells Samaneh Bagheri Novir, Seyed Majid Hashemianzadeh ⇑ Molecular Simulation Research Laboratory, Department of Chemistry, Iran University of Science & Technology, Tehran, Iran

h i g h l i g h t s

g r a p h i c a l a b s t r a c t

p-spacers on the performance of DSSCs were investigated.  Some of key parameters affecting the Jsc and Voc of DSSCs have been discussed.  The higher Jsc and Voc were estimated for carbazol and flouren-based azo dyes.  Electron lifetime is discussed through different charge recombinations.  The effects of various

a r t i c l e

i n f o

Article history: Received 8 November 2014 Received in revised form 2 February 2015 Accepted 4 February 2015 Available online 16 February 2015 Keywords: Dye sensitized solar cells Charge recombination TDDFT Lifetime Absorption spectra Electron injection

a b s t r a c t Some of new azo-based metal-free dyes with different p-conjugation spacers, such as carbazole, fluorene, pyrrole, thiophene, furan and thiazole, have been investigated with density functional theory (DFT) and time-dependent DFT (TDDFT) calculations. Theoretical calculations allow us to quantify factors such as light harvesting efficiency (LHE), electron injection driving force (DGinject) and the weight of the LUMO orbital on the carboxylic group (QLUMO) related to the short-circuit photocurrent density (Jsc), and to evaluate both charge recombination between the semiconductor conduction band electrons and the oxidized dyes and/or electrolyte, and also the shift of the conduction band of the semiconductor as a result of the adsorption of the dyes onto the semiconductor surface, associated with the open-circuit photovoltage (Voc). According to the results, we could predict that how the p-conjugation spacers influence the Jsc as well as the Voc of DSSCs. Among these dyes, the carbazole and fluorene-based dyes (dyes 1 and 2) show the highest LHE, DGinject, QLUMO, and the slowest recombination rate. Consequently, the obtained results show that the carbazole and fluorene-based dyes could have the better Jsc and Voc compared to the other dyes. Ó 2015 Elsevier B.V. All rights reserved.

Introduction The nanocrystalline dye-sensitized solar cells (DSSCs), which were reported by O’Regan and Grätzel in 1991, have attracted much attention due to their low fabrication costs as compared to conventional silicon-based semiconductor, environmentally friendly ⇑ Corresponding author. Tel.: +98 21 77240287; fax: +98 21 77491204. E-mail addresses: [email protected], (S.M. Hashemianzadeh). http://dx.doi.org/10.1016/j.saa.2015.02.026 1386-1425/Ó 2015 Elsevier B.V. All rights reserved.

[email protected]

components, relatively high conversion efficiencies and flexibility in their manufacture and employment [1–5]. In these devices, light is absorbed by the dye adsorbed on the nanocrystalline semiconductor surface (typically TiO2) and then excited electrons from the excited dye inject into the conduction band (CB) of the TiO2 semiconductor, generating an electric current. The oxidized dye is then reduced by electron transfer from the electrolyte, commonly based on the redox couple I/I 3 in an organic solvent [5–8]. Up to now, two kinds of dyes have been widely studied as sensitizers, metal–organic and metal-free organic dyes. Metal–organic dyes,

S. Bagheri Novir, S.M. Hashemianzadeh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 143 (2015) 20–34

mainly the noble metal ruthenium polypyridyl complexes, have provided the highest performances with solar energy to electrical energy conversion efficiencies beyond 11% [6,8,9]. Recently, more attention has been directed to the use of metal-free organic dyes in DSSCs because of no noble metal resource restriction, high molar absorption coefficient, relatively easy synthetic procedure, several structures, tunable absorption spectral response from the visible to the near infrared area and economical production techniques [10–12]. The structure and physical properties of sensitizers are obviously important for the evaluation of the efficiencies of organic dye-based DSSCs. Organic dyes with good performance in DSSCs generally consist of an electron donor, an electron acceptor, a pconjugated bridge between the donor and acceptor, and/or an anchoring group to maximize the efficiency of the photoinduced intramolecular charge transfer (ICT) [10,13–15]. Organic dyes used in DSSCs must have suitable levels for the HOMO and the LUMO of the sensitizer matching the iodine redox potential and the conduction band edge level of the TiO2. The energy level of the LUMO of the dye must be higher than the conduction band of the TiO2 (4.1 eV). On the other hand, the energy level of the HOMO of the dye must be lower than the I/I 3 redox potential (4.80 eV) [10,14–18]. By changing the electron donor, acceptor, and/or p-spacer group of organic dyes, the HOMO and LUMO energy levels and also absorptivities and electronic excitation energies of the dyes can be altered [16]. Good electronic coupling between the LUMO of the dye and the conduction band of TiO2 is useful for high electron injection from the dye into the semiconductor conduction band [14,15,19]. In addition, strong absorption of visible to near-infrared light with high molar absorption coefficients or high light harvesting ability of the dye, and a large enough driving force for efficient electron injection, are effective on the efficiency of DSSCs. The limitation in the efficiency of organic dyes has been ascribed to both charge recombination of the conduction band electrons of the surface with the oxidized dye or electrolyte and the formation of dye aggregates on the semiconductor surface [14–16,19,20]. Many studies via theoretical calculations have been performed to investigate and improve the performance of DSSCs by modifying the dye, exploring the electron injection and recombination [20–26]. The performances of organic dye-sensitized in DSSCs are various by chemical modification of the dyes [23,26], so it is necessary to design new organic sensitizers to provide insight into the physical origin underlying the relationship of structure and performance by using the quantum chemical calculations [26]. In this work, the effect of various p-conjugated spacers in azo dyes have been studied by computational methods. Azo dyes are a well-known class of compounds containing a N@N double bond, that have been extensively used in organic photoactive materials due to their ability to absorb visible light, their excellent optical switching properties, high solution process ability and good chemical stability. The p-conjugated structures are generally added to extend the p-spacer. In this respect, several electron-rich heteroaromatic rings (e.g. thiophene, furan, thiazole, pyrrole, fluorene, and carbazole) have been used to construct low band gap dyes and extend the absorption band of these dyes into the near-IR region [10,27,28]. In this paper, six candidates organic azo dyes 1–6 with different p-spacers (based on Ref. [10]), shown in Fig. 1, were investigated with density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations. Theoretical calculations on important parameters controlling the short-circuit current density (Jsc) and the open-circuit photovoltage (Voc) were performed to shed light on how and why the p-spacers affect the performance of the dyes. Some of the parameters influencing the short-circuit current density (Jsc), which were evaluated here are: light harvesting efficiency (LHE), energy changes of electron injection (injection driving force DGinject) and the LUMO orbital weight of the dye on the atoms of anchoring group (QLUMO). The evaluated parameters

Dye

21

X= 1

Carbazol 2 Fluorene

3 Pyrrole 4 Thiophen 5 Furan 6 Thiazole

Fig. 1. Molecular structures of studied organic dyes 1–6.

affecting the open-circuit photovoltage (Voc) are: the shift of the conduction band of TiO2 as a result of the adsorption of these dyes onto the TiO2, and the number of electrons in the conduction band of the semiconductor (nc) which is influenced by the charge recombination between the injected electrons in the conduction band of the semiconductor and the oxidized dyes and/or electrolyte. In order to calculate the adsorption energies of different dyes onto the TiO2, and also investigating TiO2 conduction band energy shift due to the dye adsorption, theoretical calculations have been performed on the adsorbed dyes onto the TiO2 anatase (1 0 1) surface. The smallest possible TiO2 anatase (1 0 1), the (TiO2)24, has been used in the present work, because of the limitation of present computational capacity. The lifetime of the excited state (s) and also charge transfer analysis have been studied to consider the efficiency of charge transfer of these dyes. These concepts will be described in details in the following sections. Computational methods The geometries of the free dyes in their neutral, cationic, and anionic states in the gas phase were fully optimized at the DFT level of theory with the B3LYP hybrid functional [29] by using 6311+G⁄⁄ basis set. Reorganization energy k of all dyes were obtained by single point calculations at the same level in their cationic and anionic state calculated with the optimized structure of neutral molecule and single point calculations in their neutral and cationic (anionic) state calculated with the optimized cationic (anionic) structure [26]. Population analysis has been performed on the optimized structures in the ground state to compute the LUMO and HOMO orbital weight of the dye on the atoms of the anchoring (carboxylic) group. Optical absorption spectra at the ground state optimized geometries for the 30 lowest singlet–singlet transitions were investigated using the TDDFT calculations with the hybrid functionals B3LYP, and range-separated functional, coulomb-attenuating method CAM-B3LYP [15,30] with 6-311+G⁄⁄

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basis sets to calculate the excitation energies and oscillator strengths of these dyes. The lifetime of the excited state (s), and the free energy change of electron injection from the excited dyes to the TiO2 surface (DGinject), can be calculated from the results of the DFT and TDDFT calculations. The solvent effects of tetrahydrofuran (THF) were evaluated using the conductor polarizable continuum model (CPCM) [31–33], for both DFT and TD-DFT calculations. THF is chosen because these dyes were soluble and stable in nonprotic solvents such as THF and the results of the experimental work (the designed dyes are based on C1 dye in Ref. [10]) were reported in THF solvent [10,34]. Charge transfer analysis and electron density differences (densities for both the ground and the excited states) were performed with Multiwfn 3.2.1 [26,35–37]. In order to investigate the charge recombination, the interaction between these dyes and I2 in the electrolyte have been simulated. Dye  I2 complexes have been optimized at the B3LYP/6-311+G⁄⁄ (LANL2DZ basis set for I atom) level in the gas phase. Basis set superposition error (BSSE) to the binding energies were carried out by using the counterpoise (CP) method [38,39], and the natural bond orbital (NBO) analysis was done at the optimized dye  I2 structures to explain the electron recombination losses. All the calculations in the ground state were performed with the Gaussian 03 program package [40] and TD-DFT calculations were carried out using the Gamess package [41]. In order to determine the dye adsorption effects on the shift of the conduction band of the semiconductor, we produced a (TiO2)24 with the anatase (1 0 1) surface. Among the three natural forms of TiO2: rutile, anatase and brookite, anatase is the preferred structure in DSSCs because of its larger band gap (3.2 vs 3.0 eV for rutile), easier synthesis at the nanoscale and higher conduction band energy. Anatase (1 0 1) has more application in DSSCs, because TiO2 nanocluster is most thermodynamically stable with the (1 0 1) surface [8,42]. The anatase TiO2 (1 0 1) in this work, consists of a periodically repeated slab of 3  1  2 slabs containing altogether 24 Ti and 48 O atoms, and a vacuum space of 30 Å above the slab. All structures of dye–TiO2, were optimized at the level of DFT/BLYP with a plane wave basis set (cutoff energy = 40 Ry) and Vanderbilt ultra-soft pseudopotentials [42–44] with the CPMD code [45].

Results and discussion Energy levels and Electronic absorption spectra The ground state geometries of the six dyes were optimized at the B3LYP/6-311+G⁄⁄ level in the gas phase and the solvent. The optimized geometries of these dyes in THF, are shown in Fig. 2. The EHOMO, ELUMO and HLG (ELUMO  EHOMO) of these dyes are reported in Table 1. The EHOMO and the ELUMO for these dyes in the two phases are in increasing order: gas < THF, while the HLG is in the opposite order. Calculated results show that the LUMO energy levels of all the six dyes are higher than the TiO2 conduction band edge (4.1 eV), which means that the molecules in the excited states have suitable energy levels for the electron injection into the conduction band of the TiO2. The HOMO energy levels of these dyes are lower than reduction potential energy of the I/I 3 electrolyte (4.8 eV), therefore, these dyes that lose electrons could be restored by getting electrons from the electrolyte. Since the energy gap between the LUMO level and the conduction band of the TiO2 is different for all these dyes, the electron injection efficiency is different for the dyes in DSSCs [10]. TD-DFT excited state calculations with the hybrid functional B3LYP and 6-311+G⁄⁄ basis set, based on the optimized geometries of B3LYP/6-311+G⁄⁄, were carried out on the 30 lowest spinallowed singlet–singlet transitions for the dyes in the gas phase

and the solvent. The calculated maximum wavelengths (kmax) and the UV–Vis spectra of these dyes in the gas phase and THF solvent, are shown in Table 1 and Fig. 3, respectively. The results show that inclusion of solvent shifts the absorption bands of these dyes toward the longer wavelength and larger oscillator strength. The HLG of these dyes in THF at B3LYP/6-311+G⁄⁄ level (Table 1) is smaller than that in vacuum, which it induces a red-shift of the absorption as compared with that in vacuum. Solvent, specially polar solvent such as THF, could affect the geometry, electronic structure and the properties of molecules via the long-range interaction between solute and solvent molecules, thus solvent effects cause the lower energy of the solute molecules, and induce significant red-shift for absorption bands [9]. Experimental measurements of electronic absorption spectra are usually carried out in solution, and the discrepancy between TDDFT and experimental results may be resulted from DFT exchange and correlation function and the computational model of solvent effects. So it is difficult to get the accurate quantitative results from the TDDFT calculations, but they are capable of describing the spectral features of dyes, qualitatively [5,9,46]. TDDFT calculation with the long-range-corrected CAM-B3LYP/6-311+G⁄⁄ were also carried out on the 30 lowest spin-allowed singlet–singlet transitions for the dyes in THF. This method has been used to describe the intramolecular charge-transfer of the organic dyes [23,47]. The simulated absorption spectra by B3LYP and CAM-B3LYP in THF for all the six dyes are shown in Fig. 4. The calculated HLG in THF and maximum wavelengths of dyes 1–6 (Table 1 and Fig. 4), show that the dyes with lower HLG have larger kmax. The kmaxs calculated with the CAM-B3LYP indicate that the order of kmaxs in the six dyes is similar to the order of those calculated with the B3LYP hybrid functional, but the kmaxs obtained at the CAM-B3LYP level are shifted toward the shorter wavelengths (blue-shift) with respect to the B3LYP. The other parameters resulted from TDDFT calculations will be discussed in details in the next sections. Evaluating the factors influencing short-circuit current density (Jsc) The solar-to-electricity conversion efficiency (g) of the DSSCs is calculated from the following definition:

g¼

J sc V oc FF Pin

ð1Þ

where Jsc is the short-circuit photocurrent density, Voc is the opencircuit photovoltage, FF is the fill factor and Pin is the intensity of the incident light [8,15,26]. According to Eq. (1), it is clear that Jsc, Voc and FF are important factors influencing the efficiency of dye sensitized solar cells. However, it is still difficult to quantitatively characterize the parameters affecting the FF, while key factors influencing Jsc and Voc have been widely discussed. Improving the Jsc and Voc are effective resources to enhance the efficiency of DSSCs [15,22,48]. We aimed to see the sensitizer p-conjugated spacer effects on the Jsc and Voc of the DSSCs through discussing the key parameters affecting the Jsc and Voc. The Jsc in DSSCs can be determined by the following equation [15]:

J sc ¼

Z

LHEðkÞUinject  gcollect  dk

ð2Þ

k

where LHE(k) is the light harvesting efficiency, which can be calculated from this equation [26]:

LHE ¼ 1  10A ¼ 1  10f

ð3Þ

where A(f) is the absorption (oscillator strength) of the dye corresponding to the kmax. Usually, the higher LHE value, due to the larger f, increases the light capturing. Uinject defines the electron

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1

2

3

4

5

6 Fig. 2. Optimized geometries of dyes 1–6 in THF with B3LYP/6-311+G⁄⁄.

Table 1 EHOMO (eV), ELUMO (eV), HLG (eV) and maximum wavelengths (kmax) of dyes 1–6. EHOMO

ELUMO

HLG

kmaxa

kmaxb

1

Gas THF

6.54 6.26

3.28 3.33

3.26 2.93

446.09 480.39

398.36

2

Gas THF

6.50 6.29

3.43 3.34

3.07 2.95

405.41 438.62

396.21

3

Gas THF

6.48 6.24

3.70 3.50

2.78 2.74

477.93 515.37

446.18

4

Gas THF

6.72 6.51

3.88 3.69

2.84 2.82

467.27 495.76

437.01

5

Gas THF

6.68 6.48

3.82 3.66

2.86 2.82

462.28 491.46

431.79

Gas THF

6.75 6.60

3.89 3.77

2.86 2.83

463.95 487.78

423.34

Dye

6 a b

B3LYP. CAM-B3LYP (in THF).

injection efficiency, and gcollect is the charge collection efficiency. For the same DSSCs with only different dyes, it is sensible to presume that the gcollect is a constant. Consequently, LHE and Uinject are the two key factors affecting the Jsc. Improving the LHE and Uinject could enhance the Jsc [15,22,26], which the electron injection efficiency Uinject is closely related to the driving force (DGinject) of the electron injection from the excited states of organic dyes to the conduction band of the TiO2. In general, as DGinject gets larger, Uinject increases [15,23]. The rate of electron injection from a dye

to a semiconductor, can be derived from the general classical Marcus theory [47,49,50]:

p kinject ¼ 2 h vkB T

!0:5 jV RP j2 e½ðDGinject =þvÞ

2

=4vkB T

ð4Þ

where in Eq. (4), kinject is the rate constant of the electron injection h is related to Planck’s form the dye excited state to the TiO2 CB,  h= h/2p), kBT is the Boltzmann thermal energy, VRP is constant (

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Fig. 3. Electronic absorption spectra of the dyes 1–6 in the gas phase and solvent (THF) at B3LYP/6-311+G⁄⁄ level.

defined as the coupling constant between the reagents and the products potential curves, v is the reorganization energy of the system and DGinject is the free energy of electron injection from dye to semiconductor. Troisi and his co-workers in their study [51] show that the dyes with the same adsorption chemistry have the similar coupling and the coupling between the semiconductor and dye is estimated by the anchoring group [22,24–26]. Since the dyes under study in this work have the same anchoring group, we assume that they have comparable coupling constant VRP. On the basis of the Marcus theory, the electron injection rate constants can be affected by the free energy change of electron

injection (electron injection driving force). A larger driving force is favorable for more rapid electron injection rate and then higher efficiency of DSSCs [23,47,52]. The free energy change (in eV) of electron injection from excited dyes to TiO2 surface, (driving force of electron injection (DGinject)), can be calculated from Rehm Weller equation: TiO2 DGinject ¼ Edye OX  ECB

ð5Þ

where Edye is the oxidation potential energy of the dyes in the OX 2 excited state and ETiO is the reduction potential of the conduction CB

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Table 2 Calculated kmax (nm), oscillator strengths (f), light harvesting efficiency (LHE) and free energy change of electron injection (DGinject) of dyes 1–6 with CAM-B3LYP/6-311+G⁄⁄ in THF with the B3LYP/6-311+G⁄⁄ geometries.

Fig. 4. Electronic absorption spectra of the dyes 1–6 in the solvent (THF) with (a) B3LYP/6-311+G⁄⁄ (b) CAM-B3LYP/6-311+G⁄⁄.

2 band of the TiO2 [18,52,53]. The ETiO CB ¼ 4:1 eV adopted in this

work obtained from experiment [10]. Edye OX can be expressed as: dye Edye OX ¼ EOX  kmax

ð6Þ

In this definition, Edye OX is the oxidation potential energy of the dyes in the ground state that can be estimated as negative EHOMO [18,26], and kmax is vertical transition energy [15,23]. The free energy change of the dyes is a factor for the evaluation of spontaneous electron injection from dye to TiO2. When the DGinject is negative, the electron injection from the dye to semiconductor is spontaneous [18,22]. In order to give a description of how the p-spacer affect the parameters influencing Jsc, maximum absorption wavelengths (kmax), oscillator strengths (f), light harvesting efficiency (LHE) and free energy change of electron injection (DGinject) calculated with TD-CPCM-CAM-B3LYP using 6-311+G⁄⁄ basis set in THF with the B3LYP/6-311+G⁄⁄ geometries are summarized in Table 2. Also, in order to investigate the effects of different p-spacers on LHE, the UV/Vis absorption spectra of the six dyes in THF, have been considered in Fig. 4. Combining Table 2 with Fig. 4, we could find that different p-spacers in the molecular structures could influence the maximum absorption wavelength (kmax) and oscillator strength (f). As can be seen in Table 2, the kmax of dyes 1–6 is in the order: 3 > 4 > 5 > 6 > 1 > 2, and LHE is 2 P 1 > 5 P 3 P 4 > 6. As follows from Fig. 3, dyes 1 and 2 have almost similar oscillator strengths (f) and larger than that of the other dyes, and have achieved an improved LHE. The oscillator strengths of dyes 3–5 are also almost similar and larger than that of dye 6, and consequently increases

Dyes

kmax (nm)

f

LHE

DGinject

1 2 3 4 5 6

398.36 396.21 446.18 437.01 431.79 423.34

2.0225 2.1471 1.6002 1.5144 1.6336 1.3539

0.9905 0.9928 0.975 0.969 0.976 0.955

0.94 0.93 0.64 0.45 0.49 0.27

the LHE to some extent. Compared with dyes 3–6, the larger f of dyes 1 and 2, leading to the higher LHE (0.9905 for 1 and 0.9928 for 2), compensates well for their blue-shift adsorption spectrum. Comparing the LHE of these dyes indicates that the LHE of the dyes based on carbazole and fluorene p-spacers is higher than that of dyes based on pyrrole, thiophene, furan and thiazole p-spacers. This means that the carbazole and fluorene-based dyes that have longer p-spacers, generate the larger oscillator strength, the higher LHE and have more efficient light harvesting capability than the other dyes. The calculated free energy changes of electron injection (Table 2) show that the DGinject of the dyes are negative, which indicates that the dye excited state lies above the TiO2 conduction band edge, implying that the electron injection from the dye to the semiconductor, is spontaneous. The absolute value of DGinject of the six designed dyes is in the order: 1 P 2 > 3 > 5 P 4 > 6. The DGinject decreases from 0.94 eV to 0.27 eV for 1 to 6, which indicates that the driving force of the electron injection decreases in this order. The results show that dyes 1 and 2, and also dyes 4 and 5 have almost similar driving force. The larger DGinject of the carbazole and fluorene-based dyes, suggests that introducing the longer p-conjugated spacers increase the DGinject, and then increase the driving force of electron injection. Dye 6 with thiazole p-spacer has the smallest driving force of electron injection compared with the other dyes. Thus combined with the discussion of the electron injection driving force and light harvesting efficiency, we could predict that the improving LHE and DGinject could enhance the Jsc of the DSSCs. Therefore, we could expect that dyes 1 and 2 with the carbazole and fluorene p-spacer, respectively, that have the higher LHE and driving force than the other dyes, should have the larger Jsc than the other dyes. The Jsc of dye 3 with pyrrole p-spacer, may be higher than that of dyes 4–6 due to its higher LHE and driving force compared with the dyes 4–6. We could find that dyes 4 and 5 with thiophene and furan p-spacer, respectively, should have similar Jsc due to their similar LHE and injection driving force, and dye 6 with thiazole p-spacer group has the smallest Jsc due to its smaller LHE and driving force than the other dyes. On the other hand, the kinetics of the electron injection into the conduction band of the semiconductor (and the recombination from the semiconductor to the oxidized dyes that will be discussed in the next section) can be estimated based on the studies of Troisi et al. [24–26]. To predict charge injection and recombination based on the nonadiabatic electron transfer theory, the dye adsorbed system is divided into the sensitizer molecule, the semiconductor surface, and the interface between the two. The dye–semiconductor coupling C(E) can be expressed as [26]:

Css ðEÞ ¼

X

Cmn ðEÞcm cn

ð7Þ

m;n

Cmn ðEÞ ¼

2p X ðESmk  V mk ÞðESnk0  V nk0 Þqkk0 ðEÞ h 0 kk

ð8Þ

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S. Bagheri Novir, S.M. Hashemianzadeh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 143 (2015) 20–34

X qkk0 ðEÞ ¼ C kl C k0 l dðE  El Þ

ð9Þ

l

where qkk’ (E) is the local density of states dependent on the electrode and a computation on the electrode is used to obtain it, Vmk is the dye–electrode coupling dependent on the dye–electrode interaction and a computation on the interface gives the coupling Vmk, and cm is the molecular orbital coefficients of LUMO or HOMO that a computation on the isolated dye gives the molecular orbital coefficients [24–26]. Since these dyes have the same anchoring group and adsorb onto the same semiconductor, we assume that the Vmk and qkk’(E) of our systems are identical. A dye with a fast charge injection has a strong coupling between its anchoring group and the semiconductor, that this coupling is specified by the LUMO orbital weight of the dye on the atoms of the anchoring (carboxylic) group (QLUMO) [21,24,26]. The calculated QLUMO of the six dyes (Table 3) show that the QLUMO of dyes 1–3 is almost similar and larger than that of dyes 4–6, which indicates stronger coupling with the semiconductor and faster charge injection. The QLUMO of dye 4 is larger than that of dyes 5 and 6 which shows that dyes 5 and 6 have the slower charge injection. These quantities are in line with the LHE, driving force and consequently Jsc. In the following, we offer a sensible description for another factor affecting the energy conversion efficiency: open-circuit photovoltage Voc. Evaluating the factors influencing open-circuit photovoltage (Voc) As for Voc in DSSCs, it could be expressed as [22,23]:

the conduction band of the semiconductor and the oxidized dyes, and the charge recombination between the injected electrons in the conduction band of the semiconductor and the redox couple in the electrolyte which the latter one is the main way of photovoltage losses. In general, the shorter (longer) electron lifetime, the higher (slower) recombination rates, therefore the lower (larger) Voc [20,22,23]. To investigate the charge recombination from semiconductor (TiO2) conduction band to oxidized dyes based on the nonadiabatic electron transfer theory, the recombination rate constant could be evaluated through the following expression [25,26]:

kCR ¼

Z

CðEÞf ðE  EF ÞFðE; DG; kÞdE

where C(E) is the dye–semiconductor coupling, f(E  EF) is the Fermi–Dirac distribution which depends on the quasi-Fermi level of the system, and F(E, DG, k) is the Franck–Condon term, that can be treated classically and evaluated analytically [25,26]:

" # 1 ðE þ DG þ kÞ2 FðE; DG; kÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp  4kkB T 4pkkB T

ð12Þ

where T is the absolute temperature of the system, kB is the Boltzmann constant, DG is the free energy difference between the cation (initial) and neutral (final) forms for the molecular adsorbate, and k is the reorganization energy, which can be calculated with the following formula [26]:

ki ¼ ½E0  E  þ ½E0  E0 

  ECB kT nc Eredox  ¼ þ þ ln q q NCB q

ð11Þ

CB

ð13Þ

ð10Þ

where in this equation, E0 is the energy of the neutral molecule at ground state geometry, E 0 is the energy of the cation (or anion) cal-

where in this equation, kT, q, Eredox and NCB are assumed as constants, represent the thermal energy, the unit charge, the oxidation potential of the electrolyte and the accessible density of conduction band states, respectively. ECB is the conduction band edge of the semiconductor and nc is the number of electrons in the conduction band. The nc is mainly determined by the electron injection rate (kinject) and electron lifetime (s) that can be affected by electron photoinjection and electron recombination, respectively. Apparently, nc is a key factor affecting the Voc [22–26]. In the following we will investigate different p-spacers effects on these two parameters affecting nc. As discussed in Section ‘‘Evaluating the factors influencing short-circuit current density (Jsc)’’, we could predict that kinject of the six dyes is almost in the order: 1 P 2 > 3 > 5 P 4 > 6, which indicate that the electron injection rate can be affected by the electron injection driving force and the weight of the LUMO on the carboxylic group (QLUMO). The electron lifetime in dye-sensitized solar cells (DSSCs) is an important factor that corresponds to the charge recombination process [22,54]. There are two main charge recombination after injection of electrons into the conduction band of the semiconductor: the charge recombination between the injected electrons in

culated with the optimized geometry of the neutral molecule, E0 is the energy of the neutral molecule calculated at the cationic (or anionic) state and E  is defined as the energy of the cation (or anion) calculated by the optimized cation (or anion) structure [26,55]. Here, for evaluating C(E) in the charge recombination, as in the previous section (Section ‘‘Evaluating the factors influencing shortcircuit current density (Jsc)’’), we assume that the qkk’ and Vmk in our systems are almost similar in every dye–semiconductor system, but the molecular orbital coefficients of HOMO, cm, which give the weight of the HOMO on the anchoring (carboxylic) group (QHOMO), will differ depending on the isolated dyes structures. Hence, C(E) would be proportional to the QHOMO of the dyes [26]. Therefore, the important parameters that determine the recombination rate from the semiconductor (TiO2) to the oxidized dyes are the reorganization energy k and free energy change DG, which belong to the Fermi–Dirac term, as well as QHOMO which is correlated with the C(E). These calculated parameters are listed in Table 3. As is seen from Table 3, the QHOMO of the dyes is in the order: 6 > 5 > 4 > 3 > 2 1, therefore, C(E) decreased in the order 6 > 5 > 4 > 3 > 2 1. On the other hand, the reorganization energy k and the free energy changes DG could influence the Fermi–Dirac term. The order of total k is 6 > 5 > 4 > 3 > 2 > 1; the smaller k helps the separation of hole-charge and thus reduce the recombination rate [26]. The change of free energy DG decreased in the order of 1, 2, 3, 4, 5 and 6 dyes. So, on the basis of k and DG, we conclude that the order of F(E, DG, k) is 6 > 5 > 4 > 3 > 2 > 1. Thus combined with the C(E) and F(E, DG, k), based on Eq. (11), we could predict that the charge recombination rate from semiconductor (TiO2) to the oxidized dyes decreased in the order 6 > 5 > 4 > 3 > 2 > 1. It means that dye 6 has the highest recombination rate and dyes 1 and 2 have the lowest recombination rate from the semiconductor CB to the oxidized dyes.

V OC

Table 3 Free energy differences DG, reorganization energies k, the hole reorganization energy kh, the electron reorganization energy ke, the weight of the HOMO on the anchoring group (carboxylic) QHOMO and the weight of the LUMO on the anchoring group (carboxylic) QLUMO of all dyes. Dyes

DG

k

kh

ke

QHOMO (%)

QLUMO (%)

1 2 3 4 5 6

7.72 7.34 6.88 6.43 6.34 5.88

0.72 0.75 0.82 0.88 0.93 0.95

0.36 0.37 0.28 0.35 0.38 0.41

0.36 0.38 0.54 0.53 0.55 0.54

0.59 0.59 0.70 0.93 0.98 1.29

2.26 2.10 2.01 1.80 1.70 1.69

S. Bagheri Novir, S.M. Hashemianzadeh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 143 (2015) 20–34

In order to investigate the charge recombination between the injected electrons in the conduction band of the semiconductor and the redox couple (I/I 3 ) in the electrolyte, we also investigated the interaction between the organic dyes and electron acceptor (I2) in the electrolyte. Usually, between I2 and I 3 as electron acceptors in the electrolyte, the rate of electron recombination with I2 is faster than with I 3 [23,56], so, in this study, we consider I2 as the chief electron acceptor in the electrolyte and evaluate the intermolecular interaction of dye–I2, which could affect the concentration of the iodine near the TiO2 nanocrystal surface. It is usually accepted that, the higher iodine concentration in the proximity of the TiO2 surface, the shorter electron lifetime in the conduction band of the TiO2 semiconductor and thus the more charge recombination rate and the lower Voc [22,23,26]. It is known that iodine (as an electron-deficient halogen atom) can form the halogen bonding through a noncovalent interaction with other electron-rich atoms such as nitrogen, oxygen and sulfur atoms in the organic dyes [23,57]. The optimized geometries of the various adducts of 1, 2, 3, 4, 5 and 6 with I2 are displayed in Figs 5–7. The binding energies of I2 with different sites of the dyes after BSSE correction as well as the corresponding I–X (with X = N, O and S) distances are reported in Table 4. Our calculated binding energies indicate that although the p-spacer changed, the most preferred binding site for each dye is the CN group except dye 6. This means that for dyes 1–5, dye-CN-I2 has the largest binding energy compared to the other sites, and for dye 6, dye-N-I2 has the largest binding energy. The obtained distances show that the intramolecular I–I bond distances in all structures (that is averagely 2.98 Å) are larger than the covalent radii 2.86 Å showing that the I2 bond is destabilized. Meanwhile, the distances of the preferred binding site at CN group (CN  I2) are larger than the net covalent radii 2.03 Å of the binding atoms and smaller than the net van der Waals radii 3.53 Å. Also, similar results are found in the distances of O  I2 and S  I2, which these distances are smaller than the net van der Waals radii (3.50 Å for O  I2 and 3.78 Å for S  I2) and larger than the net covalent radii (2.06 Å for O  I2 and 2.35 Å for S  I2) [26,58,59]. It means that all the I–X distances are noncovalent and the distances (interaction) of S  I2 are larger (weaker) than that of O  I2 or N  I2 and thus the binding energies of SI2 is smaller than that of the other sites. Here we compare the binding energies of dye–I2 structures for dyes 1–6 in different interaction sites. Our results show that dye 6 has more interaction sites (5 interaction sites) than dyes 4 and 5 (with 4 interaction sites) and dyes 1–3 (with 3 interaction sites). A dye with more interaction sites favoring the formation of dye–I2 complexes, therefore in this case, we could expect that the iodine concentration near the TiO2 surface increases that leads to increase of charge recombination and thus decrease of Voc [57]. For dyes 1, 2 and 3 with fewer interaction sites compared to the other dyes, we could find that the binding energy of dye-CN-I2 (that is the preferred binding site) is larger than that of the other sites and these values are 4.10, 4.06 and 4.03 kcal/mol for dye1-CN-I2, dye2-CN-I2 and dye3-CN-I2, respectively. These results suggest that the intermolecular interaction in dye1-CN-I2 is a little stronger than that of dye2-CN-I2 and dye3-CN-I2, and, as a result, decreases the iodine concentration close to the TiO2 surface, increases the electron lifetime in the CB of the TiO2 and decreases the charge recombination rate. Consequently, we could expect that the order of the iodine concentration and the recombination rate in dyes 1–3 is 3 > 2 P 1, and an opposite order can be observed for the electron lifetime and the Voc. The binding energies of dye4CN-I2 and dye5-CN-I2 with four interaction sites are 3.86 and 3.88 kcal/mol, respectively, hence, we could expect that dye 5 should have a bit smaller iodine concentration near the surface than that of dye 4. Therefore, the electron lifetime in the CB of the TiO2 is almost in the order of dye 5 P dye 4. Dye 6 has the highest iodine concentration in the vicinity of TiO2 surface because

27

of more interaction sites compared to the other dyes and has the shortest electron lifetime in the CB of the TiO2. On the other hand, the distance between the preferred binding site and the semiconductor surface could influence the I2 concentration in the vicinity of the TiO2 surface and thus the electron lifetime in the CB of the TiO2. Based on De Angelis and his co-workers paper [20], we think it is sensible to only study the isolate dye–I2 interaction to qualitatively investigate the distance between the preferred binding sites and the TiO2 surface [20,22]. The distance between the preferred binding site in dye 6 (with binding energy 5.67 kcal/mol) from the semiconductor surface is shorter than that of the other dyes, leading to a shorter electron lifetime due to the higher iodine concentration and a more charge recombination rate. On the other hand, the NBO analysis on dye–I2 complexes is also performed to explain the reason of charge recombination. Our computed results (Table 4) show that for dyes 1, 2 and 3 the negative atomic charges of I2 in the dye-CN-I2 complexes are almost similar and smaller than that of dyes 4, 5 and 6, suggesting that the intermolecular interaction between I2 and CN group in dyes 1, 2 and 3 is stronger than the other dyes, which reduces the iodine concentration and increases the electron lifetime in the conduction band of the semiconductor. In conclusion, on the basis of the binding energies of the preferred binding sites, the number of interaction sites and NBO results, we conclude that the order of iodine concentration (and thereby the recombination rate) among these six dyes is 6 > 4 P 5 > 3 > 2 P 1, and the lifetime of electron in the CB (and thereby Voc) is in the order of 1 P 2 > 3 > 5 P 4 > 6. This means that the dyes with the carbazole and fluorene units could have a longer electron lifetime in the CB and a slower charge recombination rate in comparison with the other dyes. Dyes 4 and 5 with thiophene and furan units could have similar features, and dye 6 with thiazole unit has the shortest electron lifetime in the CB and the highest recombination rate. Based on Eq. (10), another factor that can affect the Voc, is ECB that is sensitive to condition. When a dye is adsorbed on the semiconductor surface, the shift of ECB can be estimated as [60]:

DCB ¼ 

qlnormal c

e0 e

ð14Þ

where in this equation, e0 and e are the permittivity of the vacuum and the dielectric constant of the organic monolayer, q is the electron charge, lnormal is the component of dipole moment of the single molecule perpendicular to the surface of semiconductor, and c is the dye’s surface concentration [22,23]. According to Eqs. (10) and (14), lnormal is an important factor that can induce a shift in the conduction band edge of the semiconductor and thus will induce a change of Voc. In general accepted that the larger lnormal of the adsorbed dyes pointing outward the semiconductor surface, leads to the larger Voc [15,22,23,26]. However, some studies showed that there is no correlation between lnormal and the shift of ECB in liquide DSSCs [61], because the adsorbed dye could interact with the ions of electrolyte and could hinder or vary the role of interface dipoles. In fact, the correlation between the lnormal and the shift of ECB is actually difficult to be observed in liquid DSSCs [22,61]. Therefore, it is more applicable to study the shift of ECB from the point of dye adsorption. In this study, in order to determine the dye adsorption effects on DECB, dyes-TiO2 structures with bidentate bridging (BB) adsorption mode, that the two O atoms of the carboxylic group are bound to two 5c-Ti atoms, have been studied. The optimized structures of the various dyes adsorbed onto the (TiO2)24 with BB mode, are shown in Fig. 8. The adsorption energies (Eads) of dyes on the TiO2 are calculated by the equation [42,62]:

Eads ¼ Edye þ ETiO2  EdyeþTiO2

ð15Þ

where Edye is the total energy of isolated dye, ETiO2 represents the total energy of (TiO2)24, and Edye+TiO2 is the total energy of

28

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-2.09 kcal.mol

-4.10 kcal.mol

-2.92 kcal.mol

1-CN-I2

1-N-I2

-4.06 kcal.mol

1-O-I2

-2.03 kcal.mol

-2.75 kcal.mol

2-CN-I2

2-N-I2

2-O-I2

-2.06 kcal.mol

-4.03 kcal.mol

-2.97 kcal.mol

3-CN-I2

3-N-I2

3-O-I2 ⁄⁄

Fig. 5. Optimized molecular structures of the dyes 1, 2 and 3 with I2 at the B3LYP/6-311+G

dye–(TiO2)24. The positive value of Eads displays a stable adsorption of dye on (TiO2)24 surface. The conduction band energy of the TiO2 could be shifted by the adsorbed dyes. The LUMO of the dye–TiO2 should be located above the conduction band edge of the TiO2 [12,42]. The calculated LUMO energy level of TiO2 is: 4.30 eV which is close to the experimental conduction band of TiO2

(LANL2DZ basis set for I atom).

(-4.1 eV) [10]. The calculated LUMO energy levels of the various dyes–TiO2, the adsorption energies (Eads) of these configurations and DECB of these dyes in BB structures are shown in Table 5. From the results, it is found that the dyes 1 and 2 have higher adsorption energy than the other dyes, which indicates they are

S. Bagheri Novir, S.M. Hashemianzadeh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 143 (2015) 20–34

29

Table 4 Calculated binding energies of I2-dyes after BSSE correction (kcal/mol), the corresponding I–X (with X = N, O and S) distances (Å) and iodide atomic charge (au). Dyes

Site

Binding energies (kcal/mol)

1

I2-CN I2-N I2-O

4.1 2.92 2.09

2.73 2.76 2.74

0.0892 0.195 0.107

2

I2-CN I2-N I2-O

4.06 2.75 2.03

2.73 2.77 2.74

0.0896 0.189 0.105

3

I2-CN I2-N I2-O

4.03 2.97 2.06

2.73 2.7 2.75

0.0888 0.209 0.101

4

I2-CN I2-N I2-O I2-S

3.86 1.96 1.77 1.09

2.74 2.73 2.77 3.25

0.084 0.174 0.098 0.098

5

I2-CN I2-N I2-O I2-O(furan)

3.88 3.43 1.89 0.91

2.74 2.76 2.77 3.26

0.083 0.178 0.098 0.177

6

I2-CN I2-N I2-N(thiazol) I2-O I2-S

3.65 1.17 5.67 1.75 0.83

2.75 2.86 2.61 2.77 3.27

0.08 0.133 0.162 0.098 0.089

-3.86 kcal.mol

I–X distance (Å)

Iodide atomic charge (au)

-1.77 kcal.mol

-1.09 kcal.mol

-1.96 kcal.mol

4-CN-I2

4-N-I2

4-O-I2

4-S-I2

-1.89 kcal.mol -3.87 kcal.mol -0.91 kcal.mol -3.43 kcal.mol

5-CN-I2

5-N-I2

5-O-I2

5-O(furan)-I2

Fig. 6. Optimized molecular structures of the dyes 4 and 5 with I2 at the B3LYP/6-311+G⁄⁄ (LANL2DZ basis set for I atom).

more stable compared with dyes 3–6 and have stronger interactions with the TiO2 surface and thereby stronger electronic coupling. The calculated LUMO energies of all dye–TiO2 structures

are higher than the calculated conduction band of TiO2 (4.30 eV), and the order of the negative shift of the conduction band of TiO2 as a result of the adsorption of these dyes onto the TiO2 (DECB) is:

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S. Bagheri Novir, S.M. Hashemianzadeh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 143 (2015) 20–34

-3.65 kcal.mol

-1.75 kcal.mol

-1.17 kcal.mol

6-CN-I2

6-N-I2

6-O-I2

-0.83 kcal.mol

-5.67 kcal.mol

6-N(thiazole)-I2

6-S-I2 ⁄⁄

Fig. 7. Optimized molecular structures of the dye 6 with I2 at the B3LYP/6-311+G

1 > 2 > 3 > 4 > 5 > 6, suggesting that the shift of ECB of dye 1 is higher than that of dye 2 and so on. The lifetime of the excited state (s) is a main parameter for considering the efficiency of charge transfer. A dye with a longer lifetime in the excited state is estimated to be more favorable for charge transfer and have the higher efficiency in electron injection from the sensitizer to the semiconductor. In this work, the lifetime of an excited state was estimated by the following formula [63,64]:

s¼

4e2 DE3k0 ;k 1 ; Ak;k0 ¼ jr k;k0 j2 4 Ak;k0 3 h c3

ð16Þ

 is the where Ak,k’ is Einstein coefficient for spontaneous emission, h reduced Planck’ s constant, c is the speed of light in vacuum, e is the elementary charge, DEk,k’ and rk,k’ are the transition energy and transition dipole moment from states k to k’, respectively [26,63,65,66]. The calculated maximum wavelengths (k), the excited state lifetime of the dyes (s) and the corresponding transition dipole moments rk,k’, calculated with the TD-CPCM-B3LYP/6-311+G⁄⁄//B3LYP/6-311+G⁄⁄ in THF solution are listed in Table 6. It can be found that the carbazole and fluorene-based dyes show the longest lifetimes (4.39 and 4.29 ns for dye 1 and dye 2, respectively), while dyes 4, 5 and 6 have the shortest lifetimes (2.78, 2.74 and 2.82 ns for dye 4, dye 5 and dye 6, respectively), which their lifetimes are almost identical. The pyrrole-based dye (dye 3) has a shorter lifetime than dyes 1 and 2, and a longer lifetime than dyes 4–6. This trend is inversely related to the transition dipole moment based on Eq. (16), since the

(LANL2DZ basis set for I atom).

excitation energies do not change very much. These results reveal that the p-spacer in dyes 1 and 2 can be a more efficient structure in electron injection relative to the one in the other dyes, i.e. these dyes with the slower immediate charge recombination may have the higher efficiency in electron injection from the dyes to the semiconductor, while the thiophene, furan and thiazole-based dyes with the shorter excited state lifetimes, increase the immediate charge recombination and thus decrease the efficiency of electron injection from the dyes to the semiconductor. Thus combining the parameters affecting Voc, i.e. nc and the shift of ECB, and according to the key factors affecting nc, i.e., lifetime and kinject, considering the order of kinject, charge recombination rate from the semiconductor to the oxidized dyes and/or electrolyte and the order of excited state lifetime, we can conclude that the Voc of the six dyes with different p-spacers, may be in the order of 1 P 2 > 3 > 4 P 5 > 6. This means that dyes 1 and 2 with the carbazole and fluorene units (longer p-spacers) should have the larger Voc due to their slower electron recombination rate and their larger DECB; also we could expect that the thiophene and furan-based dyes should have almost the similar features, the larger Voc than the thiazole-based dye and the smaller Voc than the pyrrole-based dye. Charge-transfer Intramolecular charge transfer (CT) in organic dyes plays a key role in the light-to-electricity conversion in dye sensitized solar cells (DSSCs). In DSSCs, the absorption of light by a dye adsorbed

31

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1

2

4

3

5

6

Fig. 8. Optimized geometrical structures of dyes 1–6 adsorbed on (TiO2)24.

Table 5 Calculated adsorption energies (kcal/mol), ELUMO (eV) dye–TiO2 and CB shift DECB (eV) of dyes1–6. (Calculated ELUMO (TiO2) = 4.30 eV).

Table 6 Calculated maximum wavelengths (k), the relative lifetime (s), and the transition dipole momentares (rk,k0 ) of dyes 1–6 with TD-CPCM-B3LYP/6-311+G⁄⁄//B3LYP/6311+G⁄⁄.

Dyes

Eads

ELUMO (dye–TiO2)

DECB

Dyes

k (nm)

s (ns)

rk,k0

1 2 3 4 5 6

41.50 40.61 35.16 26.38 27.57 24.11

3.92 3.95 4.06 4.19 4.15 4.24

0.38 0.35 0.24 0.11 0.15 0.06

1 2 3 4 5 6

480.39 438.62 515.37 495.76 491.46 487.78

4.39 4.29 3.72 2.78 2.74 2.82

12.45 9.71 18.14 21.58 21.35 20.23

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Table 7 Computed kmax (nm), transferred charge (qCT in the e), charge transfer length (dCT in Å), H and t (in Å) at the TD-CPCM-CAM-B3LYP/6-311+G⁄⁄//B3LYP/6-311+G⁄⁄ level. Dyes

kmax (nm)

qCT

dCT

H

t

1 2 3 4 5 6

398.36 396.21 446.18 437.01 431.79 423.34

0.87 0.87 0.49 0.84 0.83 0.83

0.21 0.18 0.56 0.46 0.51 0.32

4.86 4.88 4.39 3.83 3.78 3.76

4.65 4.70 3.83 3.37 3.27 3.44

helpful. The electronic densities related to the ground and excited states are defined as qGS(r) and qES(r) and the difference between them is expressed by [35,67]:

DqðrÞ ¼ qES ðrÞ  qGS ðrÞ

The regions in space where an increase or a decrease of the density resulting from the photon absorption is produced, can be defined as:

qþ ðrÞ ¼ on a semiconductor makes a holeelectron separation, that the distance between positive and negative charges should be enough to allow a favorable charge transfer. Generally, a strong through-space charge transfer is highly appropriate to maximize the efficiency of DSSCs. In order to maximize CT, a dye molecule should be designed as push–pull rod-like compounds, that donor (D) and acceptor (A) groups separated by a p-conjugated segment and a photon absorption qualitatively induces that a D–A ground state (GS) goes to a D+–A excited state (ES). To evaluate the efficiency of rod-like structures, a simple approach to quantify CT is reported that this model is wholly general and requires only GS and ES total electronic densities. In that framework, DFT calculations to obtain GS density and TD-DFT calculations to get ES density are surely

ð17Þ



DqðrÞ if DqðrÞ > 0 0 if DqðrÞ < 0

ð18Þ

And a similar equation for q(r). The amount of transferred charge, qCT, can be obtained by:

qCT ¼

Z

qþ ðrÞdr

ð19Þ

The barycenters of the q+(r) and q(r) functions, can be computed from:

Z

rþ ¼ ðxþ ; yþ ; zþ Þ ¼

1 qCT

r ¼ ðx ; y ; z Þ ¼

1 qCT

Z

1

2

3

4

5

r qþ ðrÞdr

ð20Þ

r q ðrÞdr

ð21Þ

6 EX

Fig. 9. Plot of the density difference between the GS and the ES (Dq(r) = q

GS

(r)  q (r), isovalue 0.001 au).

S. Bagheri Novir, S.M. Hashemianzadeh / Spectrochimica Acta Part A: Molecular and Biomolecular Spectroscopy 143 (2015) 20–34

The charge transfer distance, dCT can be determined by the following equations: CT

d

¼ jr þ  r  j

ð22Þ

The root-mean-square deviation (rms), for the positive part along the x axis, can be used to quantify the spread of the charge on the A and D groups:

r

þx

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi Z 1 2 þ þ ¼ q ðrÞðX  x Þ dr qCT

ð23Þ

Subsequently, for the rod-like systems, half of the sum of the centroids axis along x axis, H, is defined as:

H¼

rþx þ rx 2

ð24Þ

In order to investigate if there is a considerable overlap between the electron-accepting and electron-donating regions, H can be compared to dCT. If H P dCT, an overlap between the centroids along x axis can be expected, that the t represents the difference between dCT and H (t = dCT  H) [35,67–70]. To this end, the ground state geometries of the dyes were optimized at the B3LYP/6-311+G⁄⁄ level and the excited state calculations were performed with the TD-DFT approach at the CAMB3LYP/6-311+G⁄⁄ level on the optimized ground state geometries, and qCT, dCT, H and t, are computed with the Multiwfn 3.2.1 program that is summarized in Table 7, and the density difference plots (Dq(r) = qES(r)  qGS(r)) for these dyes, are shown in Fig 9. For all these structures the density variations are closer to the carboxylic acid group (Fig. 9), and consequently the electron transfer from the bridge to the electron-withdrawing group. The computed transferred charge (qCT) is approximately the same for the carbazole and fluorene-based dyes (dyes 1 and 2) while slightly larger for the other dyes, allowing us to conclude that the strength of the charge transfer (measured by qCT) is sensitive to the different p-spacer groups. Indeed, replacing the central rings by various p-conjugated groups, can affect the dCT, H and t, too. The order of charge transfer length (dCT) in these dyes is 3 P 5 > 4 > 6 > 1 > 2, which the higher dCT is due to the higher delocalization of the transferred charge. For dyes 1–6, we obtain transition wavelengths of 398.36, 396.2, 446.18, 437.01, 431.79 and 423.34 nm, respectively. The corresponding qCT are 0.87, 0.87, 0.49, 0.84, 0.83 and 0.83 e, whereas the dCT reach 0.21, 0.18, 0.56, 0.46, 0.51, and 0.32 Å. Then, in this study, the order of qCT is almost in the opposite order of kmax. The overlap between the centroids could be evaluated with H (and thus t). The order of maximal spread, H, is 2 P 1 > 3 > 4 P 5 P 6 which is explicable by the longer p-conjugated path [68], and thus, the computed t values (the through-space CT character of a transition) [35,69] confirm the amount of the transferred charge in these dyes. Regarding to that dCT measures the spacing between the centroid of r+ and r, and H is a measure of diffusion of r+ and r, so a small value of t suggests that the center of r + is not too far away from that of r, and r+ and r have relatively large degree of diffusion. Hence, in this case the distribution of r+ could easily overlap with r, and when they overlap, r+ and r cancel each other, consequently the larger the t, the less cancelation, and thus the higher the qCT. But this correlation is not true at all times, because the distribution of r+ (or r) is not identical to the two centroids C+ (or C) (Ref. [35]), and the large overlap of C+ and C (and thereby small t) doesn’t necessarily lead to large cancellation of r+ and r. Therefore, we can conclude that the amount of the transferred charge of dyes 1 and 2, with the carbazole and fluorene units, is larger than that of the other dyes, which is consistent with the excited state lifetime of dyes 1 and 2 and this lifetime is correlated with the charge transfer.

33

It is worth noting that for DSSCs, there are many other parameters affecting Voc and Jsc, for example, electrolyte component, semiconductor morphology, the dye sensitizer adsorption amount and so on [22,71]. Here we estimate the order of Voc and Jsc based on different dyes by keeping other features the same. The comparison and variation trends of Jsc and Voc are important to evaluate the relationships between the dye structure and the performance of DSSC and give instructions for the experiment synthesis. Conclusions In summary, six azo-based organic dyes with different p-spacers have been investigated by DFT and TDDFT methods to see the various p-spacers effects on the important parameters affecting the performance of the DSSCs. The factors affecting the short-circuit current density (Jsc) and open-circuit photovoltage (Voc), allow us to estimate the performance of the dyes. The Jsc could be enhanced by the increase of the light harvesting efficiency (LHE), the absolute value of electron injection driving force (DGinject) and the weight of the LUMO on the carboxylic group (QLUMO) which among these dyes, the carbazole and fluorene-based dyes (dyes 1 and 2) have the highest LHE, DGinject, QLUMO and therefore the highest Jsc. The Voc could be enhanced by the increase of DECB and decrease of the charge recombination rate, which dyes 1 and 2 show the highest DECB and the slowest recombination rate. On the basis of the results of the other dyes, dye 3 with the pyrrole spacer shows the higher Jsc and Voc than the dyes with the thiophene, furan and thiazole spacers (dyes 4–6). Dyes 4 and 5 with thiophene and furan groups have almost the similar Jsc and Voc (because of the almost similar features of thiophene and furan units) and lower than dyes 1–3, and dye 6 with thiazole group has the lowest Jsc and Voc. Also, excited state lifetime (s) and charge transfer analysis show that dyes 1 and 2 have the higher efficiency in electron injection from these dyes to the semiconductor and the amount of transferred charge (qCT) of both dyes 1 and 2 is larger than that of the other dyes. The results of this study demonstrate that the different p-spacers influence the factors affecting the Jsc and Voc and these factors confirm each other and it is reasonable to expect that dye 1 and 2 with the carbazole and fluorene units (with longer p-conjugation spacers), should have the larger Jsc and Voc because of their higher electron injection efficiency and less electron recombination. We expect this study will be useful for the design of organic dyes with target properties to improve the efficiency of dye sensitized solar cells. Acknowledgements We would like to thank Dr. Sabzyan for providing us with hardware and software facilities, and prof. Tian Lu for the discussion on charge transfer and Multiwfn program, and Ms. Sepideh Bagheri for her help in grammatical correction. References [1] [2] [3] [4] [5] [6] [7] [8] [9]

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