TD-DFT calculations of the electronic and optical properties of bis-N,N-dimethylaniline-based dyes for use in dye-sensitized solar cells

Accepted Manuscript Title: DFT/TD-DFT Calculations of the Electronic and Optical Properties of Bis-N,N-Dimethylaniline-Based Dyes for Use in Dye-Sensitized Solar Cells Authors: Asmaa B. El-Meligy, Nobuaki Koga, Satoru Iuchi, Kumi Yoshida, Kimihiko Hirao, Ahmed H. Mangood, Ahmed M. El-Nahas PII: DOI: Reference:

S1010-6030(18)30407-6 https://doi.org/10.1016/j.jphotochem.2018.08.036 JPC 11450

To appear in:

Journal of Photochemistry and Photobiology A: Chemistry

Received date: Revised date: Accepted date:

31-3-2018 22-8-2018 23-8-2018

Please cite this article as: El-Meligy AB, Koga N, Iuchi S, Yoshida K, Hirao K, Mangood AH, El-Nahas AM, DFT/TD-DFT Calculations of the Electronic and Optical Properties of Bis-N,N-Dimethylaniline-Based Dyes for Use in Dye-Sensitized Solar Cells, Journal of Photochemistry and amp; Photobiology, A: Chemistry (2018), https://doi.org/10.1016/j.jphotochem.2018.08.036 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

DFT/TD-DFT Calculations of the Electronic and Optical Properties of Bis-N,N-Dimethylaniline-Based Dyes for Use in Dye-Sensitized Solar Cells

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Asmaa B. El-Meligy,a,b Nobuaki Koga,b Satoru Iuchi,b Kumi Yoshida,b Kimihiko Hirao,c Ahmed H. Mangood,a and Ahmed M. El-Nahasa,* a

Chemistry Department, Faculty of Science, Menoufia University, Shebin El-Kom, Egypt Graduate School of Informatics, Nagoya University, Chikusa, Nagoya 464-8601, Japan c RIKEN, Advanced Institute for Computational Science, 7-1-26 Minatojima-minami, Chuo, Kobe 650-0047, Japan b

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Graphical Abstract

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Highlights

TD-DFT calculations have been used for studying π-linkers effects in dimethylaniline dyes in DSSCs.

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Some optical and electron transfer parameters are calculated to accomplish the located objectives. Increasing number of ethylene π-linker enhances light harvesting efficiency. Incorporating cyclic conjugated linkers has a positive effect on the efficiency. A comparison with previous studies on NKX-2554 and NKX-2569 dyes is considered.

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Abstract Using density functional theory (DFT) and time-dependent DFT (TD-DFT) methods, the current study reports the role of inserting acyclic and cyclic conjugated π-linkers in bis-N,N-

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dimethylaniline-based dyes as sensitizers in the dye-sensitized solar cells (DSSCs). Some optical and electron transfer parameters are calculated to accomplish our objective. The results show that increasing number of ethylene π-linker (-CH=CH-) enhances light harvesting efficiency but decreases the driving force for electron injection and possibility of

dye regeneration with encouraging dye aggregation on the surface of the electrode. Extending the conjugation length of the linker decreases the efficiency, while incorporating some cyclic

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conjugated linkers has a positive effect on the efficiency through effective coexistence of both direct and indirect mechanisms of electron injection. A comparison with experiment and

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previous theoretical studies on NKX-2554 (P1) and NKX-2569 (P2) is considered.

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Keyword: DSSC; bis-N,N-dimethylaniline-based dyes; π-linkers; DFT/TD-DFT; light

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harvesting; electron injection.

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1. Introduction Due to the advantage of dye-sensitized solar cells (DSSCs) compared to earlier generations of solar cells, quest for designing new highly efficient and low-cost DSSCs is

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still ongoing [1–9]. DSSC is composed of a dye, conductive transparent glass, a film of nanocrystalline semiconductors, electrolyte, and counter electrodes [1]. Molecular structure

of the dye is one of the most effective factors that control the efficiency of the DSSCs [2–6]. Dyes have the responsibility of absorbing solar radiation and mediate the charge transfer (CT) between the semiconductor and the electrolyte. The excited electron is injected into semiconductor electrode while the oxidized dye is restored by the electrolyte which in turn

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captures electrons from the counter electrode to complete the circuit [9,10].

Design of organic dyes in the form of conjugated donor-linker-acceptor (D-π-A) has

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a positive effect on the stability and performance of DSSCs [11–14]. The cyano acrylic

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(CAA) group is widely used as an acceptor and an anchor bound to the electrode. However,

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various linkers have been exploited in enhancing dyes’ efficiency. For example, solar energy conversion efficiency (η) of coumarin (η = 5.6 %) [15] and porphyrin dye (η = 4.35 [16] and 12 % [17]) can be modified to η = 7.4 or 8.1 % [18] and 9.54 [16] or 13% [17], respectively,

[3,15,19–24],

oligothiophenes

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thiophene

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by designing a linker. Several π-conjugated moieties such as ethylene (-CH=CH-),[6,15] [2,18,25,26],

fused

thiophene

[27],

benzothiadiazole [16,17,28], pyrrole [29–31], furan [32] and benzene [24,32,33] have been

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used as linkers between the donor and acceptor. Since 2003 [34], highly conjugated polyene dyes with bright colors have been

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recognized as promising organic dyes for DSSCs. The combination of bis-N,N-dimethylaniline (DMA) electron donor with CAA acceptor and different linkers achieves reasonable performance with a strong absorption in the visible region. Increasing length of

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the linker group by one -CH=CH- group improved the efficiency from 5.4% in NKX-2554 (hereinafter called P1, Figure 1) to 6.8% in NKX-2569 (P2, Figure 1) [34,35]. Furthermore, 5.9% efficiency was obtained by inserting thiophene between DMA and CAA (NKX-2600, AS, Figure 1). Therefore, both acyclic and cyclic structures of π-conjugated linkers enhanced the dye efficiency.

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In contrast to the reported experimental and theoretical investigations of enhanced efficiency of triphenylamine [6,12,36–46] and coumarin-based dyes [15,19–21,47–49], studies on DMA-based dyes are limited [34,35,50]. The significant effects of linkers on the

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optical properties of the dyes and then on their performance in the solar cell are well known. The smaller energy gap in P2 than in P1, which shifts the P2 spectrum bathchromically, and

the availability of direct and indirect CT into metal oxide rationalized superiority of P2 with a longer linker over P1 [50]. Although longer acyclic π-conjugation was reported to increase

light harvesting capacity of the solar cell by getting high molar absorptivity [6,15,34,35,39,48,50], it decreases open-circuit photovoltage (Voc). This was attributed to

enhancement of charge recombination and aggregation processes [39,51–53]. However,

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shorter polyene linkers improved the electron injection process [6] and prevented the

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recombination between injected electrons and I3- ions on the TiO2 surface [19–21,41].

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Thus, our theoretical study attempts to investigate the possibility of improving the efficiency of DMA-based dyes by incorporating different linkers [6,15,29,30,32,35]. We are

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going to get deeper understanding of the effect of extending π-conjugation length compared to P2 with adding more (-CH=CH-)n groups (P3 for n=1 and P4 for n=2). Moreover, the

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influence of inserting π-conjugated cyclic linkers (cyclopentadiene (AC), thiophene (AS),

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furan (AO), pyrrole (AN), and benzene (AB)) on the electronic and optical properties of the DMA-based dyes are examined. Molecular structures of the dyes considered in this study are

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illustrated in Figure 1.

In this paper, we used density functional theory (DFT) and time-dependent DFT (TD-

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DFT) to explore whether the dyes and those bound to the electrode model (TiO2)38 fulfill the criteria for DSSCs. As the electron injection and regeneration processes are affected by the electronic structure of the semiconductor electrode and dye sensitizer [54,55], we evaluated

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the electronic and optical properties of the isolated dyes and those adsorbed on the electrode modeled by (TiO2)38 cluster (dye/(TiO2)38 clusters) as follows. The DSSC efficiency can be determined by η in Eq. 1. 𝜂=

𝑉OC 𝐽SC 𝑃inc

𝐹𝐹

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(1)

where JSC is the short-circuit current density, Voc is the open-circuit photovoltage, FF is the fill factor (constant for a specific system), and Pinc is the incident solar power. Accordingly, Jsc and Voc are key factors for the efficiency of the dyes in DSSCs. The Jsc is expressed by

𝐽𝑆𝐶 = ∫ 𝐿𝐻𝐸(𝜆)𝛷inject 𝜂collect 𝑑𝜆 𝜆

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Eq. 2. (2)

where LHE(λ) is the light harvesting efficiency as a function of a wavelength λ, 𝛷inject is the electron injection efficiency that is related to free energy of electron injection ΔGinject, and 𝜂collect is the charge collection efficiency at a given wavelength. Though Jsc is not evaluated

here, the electronic and optical properties including LHE, ΔGinject , free energy of regeneration

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ΔGregen, strength of coupling and interaction between dye and surface of metal oxides are

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good indicators of Jsc. Furthermore, mechanism of electron injection is clarified, to judge the

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sustainability and efficiency of the investigated dyes.

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2. Computational details

Geometry optimizations of isolated organic dyes and their complexes with (TiO2)38

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cluster have been carried out using DFT with B3LYP functional [56] and the 6-31G(d,p) basis set in gas phase [57]. Electronic absorption spectra for the isolated dyes and dye/(TiO2)38

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were calculated at the structures thus obtained with TD-DFT-B3LYP (TD-B3LYP). The Coulomb-attenuated method (CAM-B3LYP) [58] was also used for calculating electron

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excitations of the isolated dyes. In these TD-DFT calculations, for fair comparison with experimental results, we conducted single point calculations in acetonitrile using the

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conductor-like polarizable continuum model (C-PCM) [59,60]. All the DFT and TD-DFT calculations were performed using the Gaussian 09 software [61]. The GaussSum program [62] was used to simulate the ultraviolet/visible (UV/Vis) spectra. Natural atomic charges

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were calculated based on natural bond orbital analysis (NBO) [63,64] as implemented in the Gaussian program. The LHE was approximately calculated from oscillator strength (f) [65,66], as given in Eq. 3 and ΔGinject was calculated by using Eq. 4. 𝐿𝐻𝐸 = 1 − 10−𝑓

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(3)

dye∗

TiO2

∆𝐺 inject = 𝐸OX − 𝐸CB dye∗

(4)

TiO

where 𝐸OX and 𝐸CB 2 are the unrelaxed excited state oxidation potential [66] and the energy of the conduction band minimum (CBM) of the semiconductor. Because of the difficulty in TiO2

conditions and the pH of the solution, we used 𝐸CB

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accurately determining the energy of the CBM as a result of its sensitivity to the surface dye∗

= 4.0 eV [67]. 𝐸OX can be calculated

from Eq. 5. dye∗

𝐸OX

dye

= 𝐸OX − Δ𝐸SICT

(5)

where Δ𝐸SICT is the vertical excitation energy corresponding to 𝜆max . The ground state dye

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oxidation potential 𝐸OX of the dye can be approximated by Koopmans’ theorem (the negative

of energy of the highest occupied molecular orbital (HOMO)) [68], a method that is simpler

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than calculating the free energy difference between the neutral and the oxidized species. The

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vertical or adiabatic ionization potential (VIP or AIP) that calculate IP ΔSCF are better than Koopmans' theorem. However, reliable previous works [69–72] supported the comparable

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data resulted from Koopmans' theorem and ΔSCF IP. According to these studies, we think that Koopmans' theorem might be reasonable in this study. Especially, and as reported in

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Table 3, the available experimental oxidation potentials for P1, P2, and AS yield errors of

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less than 0.4 eV with the B3LYP HOMO as IP. To emphasize our statement, we have calculated the VIP and εg (Table S1 in the supporting information) and found a reasonable

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support to use Koopmans' theorem in the current study. Although the Kohn−Sham (KS) orbitals obtained from DFT calculations have no physical meaning, the shape and symmetry

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properties of the KS orbitals are very similar to those calculated by Hartree−Fock (HF) and extended Hückel (eH) methods [73–76]. The energy order of HOMO is in most cases in agreement among various methods. Generally, the KS orbitals are a reasonable qualitative

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tool for interpretation of real molecular orbitals. The oxidation potential of the dye also determines the extent of the excited dye

regeneration. ΔGregen can be calculated by subtracting the oxidation potential of the dye from the oxidation potential of electrolyte (Eq. 6). The redox potential of I-/I3- electrolyte equals 4.8 eV [77].

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dye

∆𝐺 regen = 𝐸OX − 4.8

(6)

The Voc can be approximately calculated [72,78–82] from the difference in energy between the lowest unoccupied molecular orbital (LUMO) of the dye as a donor and the

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minimum of the conduction band (CB) as an acceptor (Eq. 7 in eV). e𝑉oc = 𝐸LUMO − 𝐸CB

(7)

Instead of particularly discussing the canonical orbitals responsible for each electron

excitation to analyze the CT property for the dye/(TiO2)38 systems, the natural transition

orbitals (NTOs) [83] were analyzed in this study. The injection mechanism thus clarified gives a qualitative insight into the efficiency of the DSSC. The contributions of the dye

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atomic orbitals (AOs) to the NTOs were calculated using GaussSum program [62]. The frontier orbitals and NTOs were drawn using Chemcraft 1.8 [84].

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The electron injection time from the dyes to TiO2 surface was also evaluated based

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on the Newns-Anderson model [85–87] in which the adsorbate LUMO level splitting upon

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adsorption is represented by the Lorentzian distribution. The center of the distribution, εLUMO (ads), was calculated as weighted average of orbital energies of dye/(TiO2)38 within the selected range; i.e., εLUMO (ads)=Σpi εi, where pi and εi refer to projected density of states

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(PDOS) and orbital energy of the ith orbital of the cluster system, respectively. The injection

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time is estimated from the distribution width (Δ) which is calculated as the mean deviation from εLUMO (ads); i.e., Δ=Σpi |εi−εLUMO (ads) |.

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3. Result and discussion

3.1. Electronic and optical properties of the isolated dyes

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3.1.1. Frontier molecular orbitals The designed D-π-A dye should provide an efficient electron transfer from the donor

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group to the acceptor group and then electron injection into metal oxide electrode upon photoabsorption. Therefore, the HOMO and LUMO of the dye should have spatial distribution over the donor and acceptor (anchor) group, respectively. The frontier orbitals for P1-P4 dyes are displayed in Figure 2. The optimized structures of all the studied dyes and the frontier orbital for AC-AB/(TiO2)38 are shown in Figure S1 and S2,respectively, in the Supporting Information. The HOMO of each dye is delocalized and covers almost the entire

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dye with more localization on the DMA donor group and slightly extends to the CAA acceptor group. By contrast, the LUMO illustrates delocalization over the π-linker and the CAA parts. Moreover, HOMO-1 is mostly delocalized on the DMA unit. Thus, electron push-

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pull through excitation from HOMO and/or HOMO-1 to LUMO is facilitated. The percent contributions from the donor, the π-linker and the acceptor groups in these molecular orbitals (MOs) listed in Table 1 give quantitative information on their spatial

distributions given in Figure 2. An inspection of Table 1 reveals that there is a high contribution from the donor AOs to the HOMO-1 in all dyes, while the HOMOs and LUMOs have contributions from the AOs in the different units depending on the structure of the

linkers. Comparing the percent contributions among dyes with acyclic π-linkers, it is clear

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that the contributions of the donor group to the HOMOs and that of the acceptor group to the

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LUMOs decrease with increasing the length of π-linker. Accordingly, the HOMO and LUMO

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of P1 have the largest composition from the donor (68%) and the acceptor (26%), respectively. In other words, charges are separated more in the dyes with the shorter acyclic

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linker. This is presumably because the longer conjugation in the linker group destabilizes and stabilizes the occupied and unoccupied orbital components in the linker group, respectively,

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so that the contributions of the linker to the HOMO and LUMO increase. Accordingly, long

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conjugation may negatively affect the electron injection to the electrode in DSSCs. The contributions of the donor AOs to the HOMO and of the acceptor AOs to the LUMO are

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higher in the dyes with the aromatic cyclic π-conjugated linkers than those in AC with the non-aromatic cyclic linker as well as in the s-cis form of P3 (P3-cEcEt), which simulates the

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framework of cyclic π-conjugated linker in AC. Therefore, the more efficient charger separation and injection will be expected for the dyes with the aromatic cyclic linker. The order of the contribution of the acceptor AOs to the LUMO is P3-cEcEt ≈ AC (19-20%) <

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AS (23%) < AO ≈ AN (25%) < AB (29%), whereas that of the donor AOs to the HOMO is P3-cEcEt ≈ AC (54-55%) < AS ≈ AO ≈ AN (60-63%) < AB (71%). The stable occupied and unstable unoccupied MOs in the aromatic linker may lead to increase in the weights of the donor group in the HOMO and those of the acceptor group in the LUMO compared with

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those of the dyes with the non-aromatic linkers. The aromatic nature in the linkers positively affects the electronic structures of the dyes to enhance the charge separation. All the dyes achieve the criteria of the electron injection from the LUMO to the CB

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of the TiO2 and regeneration of the oxidized dye by the electrolyte (I−/I3−) (See Figure 3). They have LUMOs in the energy range from -2.74 to -2.31 eV which is higher than -4.0 eV

[67] reported for the CBM of TiO2. Also, their HOMO energy levels from -5.22 to -4.81 eV are lower than the oxidation potential of I-/I3- electrolyte (-4.8 eV) [77], needed for dye regeneration.

The HOMO of AC is less stable than that of P3-cEcEt because of hyperconjugation

between CH2 group and π system, whereas the HOMOs of AS, AO, and AB are more stable

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due to the aromaticity in the linker moieties, especially for AS and AO, favoring the dye

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regeneration as will be discussed in 3.1.3. Although the pyrrole ring is aromatic, the HOMO

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of AN is the least stable among the studied dyes (except for the HOMO of P4). The LUMOs of the dyes with cyclic linkers have a different degree of destabilization and among them the

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LUMO of AN is the least stable. The instability of the HOMO and LUMO of AN follows the characteristics observed in the small cyclic organic molecules of cyclopentadiene, thiophene,

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furan, pyrrole, and benzene (Table S2), showing that the instability of the HOMO and LUMO

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of AN originates from the electronic features of the pyrrole ring. The energy gap between HOMO and LUMO levels (εg) for dyes with acyclic linkers

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(P1-P4) decreases with increasing π-conjugation length and follows the order P1 (2.83 eV) > P2 (2.49 eV) > P3 (2.24 eV) > P4 (2.04 eV) as shown in Figure 3. It is evident in Figure 3

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that the insertion of additional -CH=CH- group(s) destabilizes HOMO and stabilizes LUMO as theoretically expected. The presence of solvent reduces the εg by ca. 0.16 eV. Relative to P3-cEcEt (Eg =2.17 eV), the cyclic linkers, especially the aromatic cyclic linkers, increase

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the Eg by 0.12-0.38 eV. Among the dyes with the cyclic linkers, the εg for AN (2.55 eV) is the largest and is between those of P1 and P2, whereas that for AC is the smallest because of the non-aromatic character. Again, this is similar to the difference in the small cyclic organic molecules in Table S2. The calculated energies of HOMO and LUMO (εHOMO and

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εLUMO) and the εg values of the dyes in vacuum and acetonitrile at the B3LYP and CAMB3LYP levels are given in Table S3 in the Supporting Information. 3.1.2. Optical properties

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The TD-B3LYP calculations underestimate excitation energies (Eexs) of long acyclic πconjugated systems [88]. Increasing the fraction of Hartree-Fock exchange by means of longrange corrected (LC) CAM-B3LYP approximation improves the description of charge

transfer (CT) [88]. The calculated excitation energies for P1 (2.64/2.93 eV) and P2 (2.28/2.63 eV) using B3LYP/CAM-B3LYP functionals (Tables 2 and S2) are compared with the

experimental [35] values of 2.67 and 2.47 eV for the P1 and P2 dyes, respectively. Thus, P1 and P2 dyes illustrate a different response to the exchange-correlation functional. The

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B3LYP functional can reproduce the experimental excitation energy of P1 with a deviation

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of less than 0.03 eV. While the CAM-B3LYP agrees well with the experimental excitation

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energy of P2 with an error of ca. 0.16 eV, B3LYP underestimates the excitation energy of P2 by only less than 0.2 eV. Relative to these two systems, most of our linkers have compact

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structures and we expected TD-B3LYP could predict semiquantitatively or at least qualitatively reasonable behavior of linkers with different structures/lengths. Therefore, we

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decided to use TD-B3LYP to compare and evaluate the difference in their expected

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performance as DSSCs. There is no experimental data for P4 for estimating its performance. Accordingly, we used B3LYP functional for the calculations of the Eex in this study.

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The π-conjugation length is mainly responsible for the strength, broadening, and shift of the absorption peaks [6,44,89]. Table 2 lists the values of Eex and f and transition

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configurations of two lowest singlet excited states for each dye. Dyes with acyclic linkers (P1-P4) have absorption in the region of 400-900 nm (see the calculated UV/Vis spectra in Figure 4a). Additional ethylene groups in the linkers usually increase the peak strength

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(absorption coefficients) and, also, they cause a bathochromic shift, as expected from the decrease in the εg value, P1 (λmax = 470 nm), P2 (λmax = 544 nm), P3 (λmax = 598 nm), and P4 (λmax = 651 nm). The intense peaks of shorter acyclic-linker containing dyes are attributed to the transitions from HOMO-1 to LUMO and from HOMO to LUMO with their different

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contributions. The first band of the longer acyclic-linker containing dyes, that describes the λmax, mainly corresponds to the HOMO-LUMO transition (see Table 2). As shown in Figure 4b, the intense peaks in the UV-Vis spectra of AC, AS, AO, AN,

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and AB spread over in the range of 450-780 nm with maximum absorption bands at 607, 599, 568, 539 and 600 nm, respectively (Table 2 and Figure 4b). The strong electronic absorption

of these cyclic-linker containing dyes is attributed to the HOMO-LUMO transition. The Eex values for the dyes with the aromatic linkers are larger than that for AC with a non-aromatic cyclic linker, which is, in turn, larger than that for P3-cEcEt, reflecting the differences among the εg values discussed above (Table S3). It might be worth noting that the dyes have absorption ranges in visible region, which is effective for utilizing the solar energy.

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As presented in Table 2, the f value of 1.85 for the S0 → S1 excitation of P4 is the

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largest among the excitations calculated and thus the corresponding LHE value of 0.986 is

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the largest. The next largest value is that for the S0 → S1 excitation of P3 and the longer the acyclic conjugation is, the larger the f and LHE values are. The conformation changes giving

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P3-cEcEt reduce them to be 1.0043 (f) and 0.9010 (LHE), to which the values for the S0 → S1 excitation of AC (0.9824 and 0.8959 for f and LHE, respectively) are comparable. The

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LHE values for the dyes with the aromatic linkers are comparable to that of P2 except for

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AB and thus these dyes would be expected to show a good performance in DSSC based on the LHE values. The highest LHE among the dyes with cyclic aromatic linker was recorded

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for AN (0.880).

3.1.3. Electron transfer parameters dye

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Table 3 collects oxidation potential (𝐸OX ), free energy of injection (ΔGinject), free

energy of regeneration (ΔGregen and open-circuit photovoltage (eVoc) as electron transfer dye

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parameters. The calculated 𝐸OX values reproduce the experimental oxidation potential of P1 dye

and P2 and difference in 𝐸OX between P1 and P2 (0.17 eV) matches the experimental difference (0.19 V) [35]. ΔGregen was calculated using Eq. 6. The value of ΔGregen expected for efficient dye regeneration was reported to be around 0.2 eV [43,90], so that the best εHOMO is expected to

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be around –5.0 eV in the case of using I-/I3- electrolyte. Based on the highest εHOMO as well as the lowest εg, P4 is expected to be a good sensitizer in DSSC. However, this is not the case because the difference between εHOMO of the dye and the redox potential of the electrolyte does

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not fulfill the condition for free energy of regeneration. Thus, similar to the discussion in 3.1.1, the dye with long acyclic conjugation is not appropriate for DSSC, whereas εHOMO (–

5.05 eV) for the dye with shorter acyclic conjugation, i.e. P2, is close to 5.0 eV. εHOMO of P1

with the shortest acyclic conjugation (–5.22 eV) is too low. Similar to P2, AS and AO have dye

the appropriate 𝐸OX values around 5.0 eV owing to their εHOMOs (-4.96 and -4.96 eV, respectively). The HOMOs of these three dyes give the perfect value of ΔGregen (ca. 0.2 eV).

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The negative values of ΔGinject imply spontaneous electron injection. ΔGinject negatively decreases with increasing length of acyclic linker mainly because of the lowering

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of εLUMO. Thus, P1 has the negatively largest ΔGinject (-1.42 eV) followed by P2 (-1.23 eV)

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and so on. Among all of the investigated dyes, the AN dye shows the negatively highest

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ΔGinject (-1.44 eV) because of its least stable LUMO. The values of ΔGinject decrease in the order AN < P1 < P2 ≈ AO < AC < P3 < AS ≈ AB < P4. The difference in the ΔGinject for the

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dyes will be considered in 3.2.2 while studying the mechanism of injection upon binding the dye to the metal oxide electrode.

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The eVoc values presented in Table 3 decrease with increasing acyclic π-conjugation length, because of the decrease in the LUMO energy. The order of eVoc reproduces the

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experimental Voc trend [35] of P1 and P2 in which the Voc decreases from P1 to P2 and also agrees with previous calculations [82,91]. AN has the largest eVoc because of the highest

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εLUMO. The eVoc values for dyes studied approximately follow the order of εLUMOs, being AN (1.69 eV) > P1 > AO (1.48 eV) > P2 > AC (1.43 eV) > AB (1.41 eV) > AS (1.37 eV) > P3 > P4. The results for ΔGregen, ΔGinject and eVoc suggest that AO in addition to P2 would have

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electronic features appropriate for the dyes in DSSC. AS would be a next. As discussed in 3.1.2 the dyes having an aromatic linker have larger f and thus larger LHE values. As a matter of fact, P2 and AS have been reported to give an efficiency of 6-7 % and thus AO is expected to give a similar or higher efficiency. Although the AN dye is superior from the point of

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electron injection as shown by ΔGinject as well as eVoc, its HOMO is too high in energy for regeneration of the dye. 3.1.4. Dipole moment, polarizability, and charge distribution

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Aggregation of the dye molecules plays an important role in the photovoltaic performance. Most types of dye aggregation reduce the efficiency of electron injection by

quenching the excited states of the dyes and, also, decrease the possibility of interaction with electrolyte and in turn decrease the electron recombination [41]; hence, suppressing and controlling aggregation process are essential while designing the materials for DSSCs [92,93]. The tendency of dye aggregation either before or after binding to the electrode are

highly affected by the dye dipole moment and polarizability [52,53]. The calculated dipole

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moment and polarizability of the dye molecules are listed in Table 3. The polarizability (α)

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is calculated from analytical derivative of dipole moment in which α = 1⁄3 ∗

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(αxx + αyy + αzz ). Both dipole moment and polarizability increase with increase in the

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length of acyclic π-conjugation linker [41,51,94]. P1 and P2 illustrate reduced possibility for aggregation based on their low polarizabilities of 345.3 and 426.4 Bohr3, respectively,

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whereas the dyes with the longer acyclic linker, i.e. P3 and P4, as well as P3-cEcEt have larger values. AN and AO dyes especially indicate lower probability for aggregation

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compared to AS and AB because of their low values of polarizability (see Table 3). Thus, the higher performance of the dyes with the aromatic cyclic linker especially with furan and

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pyrrole rings is expected.

To explain charge distribution and electron transfer features of the investigated

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aromatic linker dyes, the natural population analysis of the ground state (S0) and the first excited state (S1) has been performed. The calculated natural atomic charges for the donor, π-linker, and acceptor groups are listed in Table S4. The positive charges on the donor and

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π-linker groups and the negative charges on the acceptor group support again the push-pull effect. The results with the more negative charges in the acceptor in the excited state show that the electrons transfer from the donor to the acceptor group upon excitation and then, if in the DSSC, to the CB of the metal oxide. Although the aromaticity of the linker groups affects the charge distributions, the difference in their changes upon excitation among the

13

isolated dyes is not very large. However, one can find that the larger difference in charge on the donor group in AS and AO between the S1 and S0 states indicates the greater electron transfer in AS and AO dyes than in AN and AB dyes. This supports the statement in the last

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subsection that AO is expected to be a dye in DSSC. To investigate the electron injection process in more detail, the calculations of electron excitation in the dye/(TiO2)38 systems were carried out as shown in the next section 3.2. 3.2. Dye/(TiO2)38

To model DSSC systems, dye/(TiO2)38 cluster systems were adopted as a

compromised way to avoid periodic boundary calculations [95]. The studied anatase (TiO2)38

cluster accurately reproduces the main properties of TiO2 nanoparticles. The Cartesian

U

coordinates of (TiO2)38 cluster were taken from previous work [96]. The band gap of (TiO2)38

N

at the level of calculation was found to be 4.31 eV with minimum level of conduction band

A

at -3.93 eV and valance band at -8.24 eV which agree with experiments [67]. Moreover, Liu and coworker [68] reported similar DOS and PDOS from dye/(TiO2)68 and dye/(TiO2)38

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calculations which can support the validity of using dye/(TiO2)38 in the current work. Among various possible binding modes of the dyes with the (TiO2)38 cluster, the two bidentate

D

binding modes were adopted here (see Figure 5). In one of them, two O atoms of the carboxy

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group bind to the respective five-coordinated Ti atoms and a hydrogen atom from carboxy group is transferred to a nearby two-coordinated O atom. This bidentate bridging mode was

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computed to be stable for several dyes that have carboxy anchor group [45,95,97–99] and was previously adopted for P1/(TiO2)38 and P2/(TiO2)38 [50]. Different from this, the recent

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theoretical studies [100,101] show the possibility of other bidentate binding mode in which the cyano N atom binds to the Ti atom in place of the carboxy O atom. We show in Figure S3 the optimized structures for the dye/(TiO2)38 systems in which the dyes are bound through

A

the two Ti−O bonds keeping the same conformations as in Figure S1. This is called binding mode I. The optimized structures for those with the Ti−O and Ti−N bonds and the same conformations of the dyes (binding mode II) are shown in Figure S4. Thus, we are going to discuss and compare the effects of the binding mode I and II on the optical properties. The bond distances between the Ti and carboxy O atoms (1.89-2.05 Å) and between the Ti and

14

cyano N atoms (2.14-2.17 Å) show the strong interaction between the dyes and (TiO2)38 cluster in agreement with the results of previous studies [102,103] . Previously [104], conformational analysis of AS dye has been conducted for different

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conformation, one of the aniline groups is closer to the cyano group, which was found to be more stable than in the conformer in Figure S1. Thus we investigated the effect of

conformational change in the dyes with cyclic linkers (AC, AS, AO, AN and AB) on the electronic properties of the dye/(TiO2)38 systems. The optimized structures of the

conformationally different dyes bound with two Ti-O bonds are shown in Figure S5. This binding mode will be called I′ (Figure 5). We did not investigate the effects of different conformations for P1-P4, because in such conformers the conjugation in polyene linker is

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broken.

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From the small differences in the calculated adsorption energies (Eads) and stabilities

A

of the dye/(TiO2)38 systems between binding modes I, II and I′, it is anticipated that all the binding modes are possible in the solution (see Table S5). All the cluster systems studied

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here are stable as inferred from large negative adsorption energies, -17 ~ -21 kcal/mol, Table S5. The values are sufficiently large to indicate chemical adsorption nature of the dyes. The

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Eadss for the systems with binding mode II are slightly more negative than those with binding

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mode I except for AC/(TiO2)38 and AO/(TiO2)38, whereas the systems with binding mode I′ have nearly the same Eads as those with binding mode I except for AO/(TiO2)38 for which

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binding mode I′ results in 3.1 kcal/mol higher energy that I. Nevertheless, it can be noticed that the values do not change very much upon change in binding modes.

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3.2.1. Electronic and optical properties of the dye/(TiO2)38 cluster systems The HOMO and LUMO of all dye/(TiO2)38 systems are almost composed of the AOs

of the dye and those of (TiO2)38, respectively, and the component of the dye LUMO is

A

distributed in the low-lying unoccupied orbitals of the dye/(TiO2)38. All systems nearly have the same degree of HOMO stabilization compared to the isolated dyes, whereas their LUMOs are slightly less stabilized relative to the LUMO of (TiO2)38 (-3.18 eV). Table 4 collects εHOMO, εLUMO and εg of the dye/(TiO2)38 systems presented in Figures S3-S5. The εg of these systems is generally lower than that of the isolated dyes [13]. The systems with binding mode II have

15

a slightly larger LUMO stabilization than those with binding mode I (-3.14 ~ -3.16 eV for II and -3.10 ~ -3.13eV for I), so that in the former the εgs are slightly lower than in the latter. The simulated UV/Vis absorption spectra for P1/(TiO2)38, P2/(TiO2)38, AC/(TiO2)38,

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and AO/(TiO2)38 with binding mode I, II, and I′ are displayed in Figure 4 (c-f). The maximum absorbance peak located at 2.25 eV (550 nm, f = 0.29) for P1/(TiO2)38 with binding mode I is consistent with previous calculations [50] (P1/(TiO2)38; Eex= 2.20 eV (f = 0.40)) that shows a good agreement with the available experimental incident photon to electron

conversion efficiency (IPCE) [35]. The calculated absorption spectra for binding modes I and II are comparable as illustrated in Figures 4c and 4d, respectively. The bathochromic shift for dye/(TiO2)38 is expected due to decrease in the εg upon binding of dye with the cluster

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system. As a matter of fact, the absorption peaks with non-negligible oscillator strengths for

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dye/(TiO2)38 systems appear at longer wavelength of 550~754 nm compared with those for

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the isolated dyes at 470~650 nm (compare the Eex values in Table 2 with those in Table 5 for binding mode I).

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The computed absorption data (εg and f) for P1-P4/(TiO2)38 with binding modes I and II are listed in Tables 5 and 6, respectively, and those for AC-AB/(TiO2)38 with binding

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mode I and II in Tables S6 and S7, respectively. We can realized that the difference in the

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binding modes I and II does not affect electronic transition very much. Here, we compare the absorption properties for P2/(TiO2)38 between binding modes I and II. As shown in

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Tables 5 and 6, the P2/(TiO2)38 systems with binding modes I and II have the two strongest absorptions, respectively, at 629 nm (f = 0.8186) and 578 nm (f = 0.3827) and at 623 nm (f =

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0.7188) and 563 nm (f = 0.2441). The longer wavelength peaks are assigned to electron transition from HOMO, whereas those of a shorter wavelength are from HOMO-1. These orbitals are similar in binding modes I and II and are mainly composed of the HOMO-1 and

A

HOMO of isolated P2 dye in Figure 2, respectively. The above-mentioned two high-intensity absorptions reflect the characteristics of the absorptions in the case of the isolated P2 dye, which has two similar strong absorptions at lower wavelengths of 544 nm (f=0.8781) and 511 nm (f=0.6041) which are assigned to the transition from the HOMO to the LUMO and

16

from the HOMO-1 to the LUMO (Table 2). This resemblance holds true for the other systems. The bathochromic shift along with hypochromicity of the absorption band of most

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dye/(TiO2)38 systems with cyclic linkers can be observed upon changing the binding mode and becomes significant with changing dye conformation (mode I’,

Figure 4e). The

hypochromicity in mode I’ is not related to TiO2 cluster but can be interpreted by the two peaks observed in the isolated dyes (AC and AO). This is clearly shown in Figure 4f, in

which the absorption spectra of AC and AO dyes are compared with those of AC/(TiO2)38 and AO/(TiO2)38. The isolated AO dye has two dominant absorption peaks at 1.99 eV (623

nm, f=0.3628) and 2.35 eV (527 nm, f=0.4828) due to transition from HOMO to LUMO and

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from HOMO-1 to LUMO, respectively. The AO/(TiO2)38 system has similarly two

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excitations; the first peak is located at 2.03 eV (612 nm, f=0.4273) and the second peak at

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1.69 eV (732 nm, f=0.4409). The same argument holds true for the AC/(TiO2)38, AN/(TiO2)38 and AS/(TiO2)38 systems with binding mode I′. The computed absorption data (εg and f)

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assigned to the conformers of these dyes and their cluster systems are given in Table S6. The extension of absorption bands into near-infrared region together with the stability of the

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dye/(TiO2)38 could be one of the reasons of moderate efficiency of 5.9% for AS [35] and thus

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the other dyes with cyclic linkers studied here are suggested to be candidates in DSSC.

3.2.2. Electron injection mechanism

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Here, from the electronic properties of the isolated dye and dye/(TiO2)38 systems, the electron injection is discussed mainly in terms of direct and indirect mechanisms. The direct mechanism exhibits CT from the dye occupied orbitals to the semiconductor CB in a single

A

step, whereas the indirect mechanism consists of two steps: electronic excitation within the dye, followed by electron injection into the semiconductor CB [48,105–108]. For this purpose, the CT characteristics upon electronic excitation for the dye/(TiO2)38 systems are analyzed using the natural transition orbitals (NTOs). The NTOs generally give a simpler description of excited state than the canonical orbitals. In fact, as shown in Tables 5, 6, and

17

S5-S7, where the canonical orbitals were used, even the dominant configurations for the excitations in the dye/(TiO2)38 systems sometimes have small weights less than 50 %, which makes the analysis of excitations cubersome. By contrast, as illustrated in Tables 7 and 8,

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excited states are characterized by one or a few pairs of the hole and the corresponding particle using the NTOs.

The NTOs for high-intensity excited states of all dye/(TiO2)38 systems with binding modes I and II are shown in Figures 6, S6, 7 and S7, respectively. Those related to the

systems with binding mode I′ are displayed in Figure S8. For all excitations in these Figures, it is found that the holes mostly consist of the dye AOs and that the holes are delocalized

over the whole dyes except P1/(TiO2)38 with binding mode I in which two pairs are

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responsible for the excitation and one of the holes is localized in the donor of P1. Comparison

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of the holes in Figures 6 and 7 with the orbitals for the isolated dyes in Figure 2 suggests that

A

the delocalized holes mainly originate from the dye HOMO, whereas the localized hole in P1/(TiO2)38 from the HOMO-1 of P1. By contrast, the particles are delocalized between the

M

dye and (TiO2)38 and the weights of the dye AOs in the particles seem to depend on the systems. Thus, the electron injection mechanism is analyzed by investigating contributions

D

of the dye AOs to the particles. Tables 7 and 8 summarize the contributions of the dye AOs

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to the holes and particles for the excitations in Tables 5, S7, 6, and S8 for the dye/(TiO2)38 systems with binding mode I and II, respectively. The results for the dye/(TiO2)38 systems

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with binding mode I′ are listed in Table S9. The results for P1/(TiO2)38 and P2/(TiO2)38 are consistent with and support findings

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in a previous study [50]. This also validates the results for others dye/(TiO2)38 systems in the present study. The smaller contributions of the P1 AOs to the particle for the seventh, twelfth, and thirteenth excited states of P1/(TiO2)38 with binding mode I (23, 26 and 31%,

A

respectively, as shown in Table 7) suggests that the direct mechanism is dominant in this system (Table 7). The same holds true for P1/(TiO2)38 with binding mode II (Table 8). For P2/(TiO2)38 with binding mode I (Table 7), the fourth and twelfth excited states are considered, because these states have large oscillator strengths of 0.8186 and 0.3827, respectively (Table 5). As can be noticed from Table 7 and Figure 6, the holes are totally

18

from the P2 dye, whereas the particles are delocalized between P2 and (TiO2)38. The contribution of the P2 AOs to the particle for the highest-intensity fourth excited state is 68% and those contributions to the particles for the first and second pairs of the twelfth excited

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states with the second highest-intensity are 67 and 9%, respectively. These results indicate that the contributions of the dye AOs in P2/(TiO2)38 is larger than those in P1/(TiO2)38, but

there are still significant contributions of (TiO2)38. Thus, as reported previously [50], the indirect mechanism works in P2/(TiO2)38 more than in in P1/(TiO2)38 and the direct and indirect mechanism coexists in P2/(TiO2)38 [50]. The contributions of the P2, P3, and P4

AOs for the highest-intensity excited state with the binding modes I and II are larger than that of P1 AOs. This result reveals the domination of an indirect mechanism with stretching

U

the length of the linker.

N

Among the dye/(TiO2)38 systems having the cyclic linkers with binding mode I,

A

AN/(TiO2)38 is closer to P1/(TiO2)38 than dyes with other cyclic linkers. AN/(TiO2)38 has 19% contribution of the dye AOs to the particle for the highest-intensity excitation (sixth excited

M

state, f =0.3695, Table S7), which indicates that the direct mechanism is more dominant. The small contributions of dye AOs to the particle in the AN/(TiO2)38 and P1/(TiO2)38 systems

D

are ascribed to the higher energies of the dye LUMOs discussed in 3.1.1. Also, the

TE

domination of the direct mechanism in the two systems supports the large negative values of ∆𝐺 inject for these two dyes (Table 3). Unlike AN/(TiO2)38, the highest-intensity electron-

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excitations of AC/(TiO2)38, AS/(TiO2)38, AO/(TiO2)38, and AB/(TiO2)38 have larger dye contributions to the particles (67, 66, 57 and 60%, respectively). Thus, similar to the case of

CC

P2/(TiO2)38, the AC/(TiO2)38, AS/(TiO2)38, AO/(TiO2)38, and AB/(TiO2)38 are expected to have both direct and indirect mechanisms. It is found from Tables 7 and 8 that the difference

A

in binding mode does not lead to noticeable change in the CT property. To further emphasize the above arguments, we roughly estimated the electron

injection times (𝜏) by the procedure based on Newns-Anderson approach [85–87]. The results for the binding mode I are displayed in Table 9 and Figure S9, where it is seen that the adsorbate LUMO energies, εLUMO (ads), are shifted by at least 0.27 eV compared to those of the isolated dyes, εLUMO (free), due to the couplings with (TiO2)38. The electron injection

19

times were estimated to be within 6 fs for all the dye systems investigated. The fast injection times of 3 fs for P1/(TiO2)38 and AN/(TiO2)38 are consistent with the above discussion that the direct injection mechanism is expected for these systems.

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In summary, elongation of the acyclic linker increases the weight of the indirect mechanism in electron injection, whereas dyes with cyclic linkers, except for AN, are similar with dyes previously studied and effectively illustrate the coexistence of direct and indirect mechanisms [50,106,109].

3.2.3. Exciton binding energy

The exciton binding energy (EB) determines the efficiency of electron-hole pair

U

binding and thus the accessibility of CT from the dye to the metal oxide. Therefore, the higher

N

Jsc of P2 over P1 could be substantiated based on the EB values as well. The EB was calculated

A

as a difference between εg and optical gap [110]. The low EB value means the small energy needed by dissociation of electron-hole pair binding. The EB of the isolated dyes and that of

M

the dye/(TiO2)38 systems with binding mode I are depicted in Figure 8. The decrease in EB supports good performance of sensitizers in DSSC [111]. For the isolated dyes, elongating

D

π-conjugated linkers decreases EB which is favorable for photo-to-current conversion. As can

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be seen in Table 5, P1/(TiO2)38 has much small LHE with higher EB, whereas both LHE and EB of P2/(TiO2)38 show better performance than those of P1/(TiO2)38. This could be one of

EP

the reasons of the better performance of P2 over P1. Furthermore, the dye/(TiO2)38 systems of cyclic linkers can surpass the performance of P2 in DSSC via reasonable EB in the range

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of 0.25-0.27 eV, which is lower than that of P2 (0.34 eV. The results based on the exciton binding energies show that the AO and AS are expected to be good dyes in the DSSCs, in

A

consistent with the results obtained above.

4. Conclusions Density functional theory (DFT) and time-dependent DFT (TD-DFT) methods have been used to investigate the performance of some bis-N,N-dimethylaniline-based dyes as

20

sensitizers in the dye-sensitized solar cells (DSSCs). The results obtained can be summarized as follows: 1-

Shorter acyclic π-conjugated linkers help in electron injection and dye regeneration

2-

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processes. Increasing the length of acyclic π-conjugated linkers lowers free energy of injection, decreases probability of dye regeneration, induces the probability of dye aggregation, and enhances indirect injection.

3 - Cyclic π-conjugated linkers exhibit better performance regarding LHE, high free energy of injection, decrease probability of dye aggregation, and coexistence of direct and indirect mechanisms.

U

4- The Dye with pyrrole linker and the one with the shortest acyclic linker (P1) illustrate

N

direct electron transfer from the dye to the photoanode.

A

5- The better performance of P2 over P1 could be explained in terms of better free energy of regeneration, participation of direct and indirect injections, lower EB, and higher LHE in

M

P2 relative to P1.

6- All binding modes for the dye/TiO2 systems carried out in this study are energetically

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TE

D

stable and give comparable data.

Author information

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Corresponding Author Ahmed M. El-Nahas. Phone +2-1064607974

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E-Mail: [email protected]

Acknowledgments We are grateful to Egyptian Cultural office in Japan. This study was supported by Egyptian mission. AE.-M. thanks Dr. Morad El-Hendawy for discussion at the beginning of this study.

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All the computational calculations were performed using the Nagoya university supercomputer.

Supporting Information

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Associated conten The Supporting Information for this paper is available online at

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SC RI PT

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TE

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EP

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A

CC

EP

TE

D

M

A

N

U

(2013) 5461–5481.

33

N

N O O

N

CN

P1

SC RI PT

OH N

N O OH

N

P3

NC

OH

N

D TE

EP P4

O

O AO

N

N

O OH CN N

N H NC AN

O OH

N

CC A

M

OH CN

A

N

N

O

N

OH

U

N

N

NC

AS

N

OH

O

S

CN

P2

NC

AC

N

O OH CN N

AB

Figure 1. Molecular structures of the investigated dyes. The spacers inserted between the donor and acceptor groups are given in magenta.

34

HOMO

LUMO

SC RI PT

HOMO-1

U

P1

TE

D

M

A

N

P2

A

CC

EP

P3

P4

Figure 2. Frontier orbitals of the P1-P4 dyes. 35

SC RI PT U N A

Figure 3. Energy levels of HOMO and LUMO for the dyes calculated at B3LYP/6-31G(d,p)

M

level in acetonitrile. The upper and lower horizontal dashed lines indicate the conduction band minimum of TiO2 (- 4.0 eV) and the redox potential of the I- /I3- electrolyte (-4.8 eV),

A

CC

EP

TE

D

respectively.

36

c)

d)

SC RI PT

b)

M

A

N

U

a)

f)

CC

EP

TE

D

e)

A

Figure 4. The simulated UV/Vis absorption spectra of the dyes with acyclic linker (a), cyclic linker (b), acyclic-linker-based dyes bound to (TiO2)38 cluster with binding mode I (c), binding mode II (d), and binding mode I′ (f). Comparison of spectra among different binding modes (e). The full width at half maximum value was assumed to be 3000 cm-1.

37

N

N

N

N

H

H

CH

SC RI PT

C

C

N

N

Linker

C

Ti

C

O O Ti

C O Ti

C

C

N Ti

N

O

N

U

C

C

(I)

(II)

A

CC

EP

TE

D

M

A

Figure 5. Schematic representation of bridging modes I, II and I′.

38

O

Ti

C

C

O

Ti

(I')

N

SC RI PT

(a) P1/(TiO2)38, S12, λ = 0.76 (left pair) and 0.24 (right pair)

(c) P3/(TiO2)38, S4

(e) AC/(TiO2)38, S4

EP

TE

D

(d) P4/(TiO2)38, S2

M

A

N

U

(b) P2/(TiO2)38, S4

CC

(f) AS/(TiO2)38, S4 (g) AO/(TiO2)38, S4 Figure 6. Natural transition orbitals for the excited states (Sn) with relatively large oscillator strengths of dye/(TiO2)38 systems with binding mode I. The hole (left) and particle (right) for each pair are shown. The eigenvalue of each pair is larger than 0.99 except for P1/(TiO2)38

A

for which the eigenvalues are illustrated.

39

SC RI PT (i) AB/(TiO2)38, S4

A

CC

EP

TE

D

M

A

N

U

(h) AN/(TiO2)38, S6 Figure 6. Continued

40

(b) P2/(TiO2)38, S5

SC RI PT

(a) P1/(TiO2)38, S7

(d) P4/(TiO2)38, S3

U

(c) P3/(TiO2)38, S3

(f) AS/(TiO2)38, S3

D

M

A

N

(e) AC/(TiO2)38, S3

TE

(g) AO/(TiO2)38, S3 (h) AN/(TiO2)38, S5 Figure 7. Natural transition orbitals for the excited states (Sn) of dye/(TiO2)38 systems with

EP

binding mode II. The hole (left) and particle (right) for each pair are shown. The eigenvalues

A

CC

of the pairs are larger than 0.97 so that the transition is characterized by one single pair.

41

(i) AB/(TiO2)38, S3

A

CC

EP

TE

D

M

A

N

U

SC RI PT

Figure 7. Continued

42

SC RI PT

EP

TE

D

M

A

N

U

Figure 8. EB (eV) of isolated dyes and dye/(TiO2)38 systems.

Table 1. Contributions (%) of atomic orbitals of the donor (D), π-conjugated linker (π), and

CC

the acceptor (A) to the HOMO-1, HOMO, and LUMO of the isolated dyes in acetonitrile at

A

B3LYP/6-31G(d,p) level. dye

HOMO-1

HOMO

LUMO

D

π

A

D

π

A

D

π

A

P1

99

1

0

68

15

18

50

24

26

P2

99

1

0

61

25

14

37

40

23

P3

99

1

0

55

34

11

28

51

21

43

99

1

0

50

41

9

21

60

19

P3-cEcEt

99

1

0

55

35

11

28

53

19

AC

99

1

0

54

34

13

27

53

20

AS

99

1

0

63

29

9

23

54

23

AO

99

1

0

61

29

AN

99

1

0

60

29

AB

99

1

0

71

25

SC RI PT

P4

23

52

25

11

22

54

25

4

16

55

29

A

CC

EP

TE

D

M

A

N

U

10

44

Table 2. Excitation energies (Eex), oscillator strengths (f), light harvesting efficiencies (LHE) and electronic transitions configurations of the isolated dyes at TD-B3LYP/6-31G(d,p) level in acetonitrile. excited state S0→ S1 S0→ S2

Eex (eV (nm)) 2.53 (491) 2.64 (470)

0.3695 0.8135

0.5729 0.8464

P2

S0→ S1 S0→ S2

2.28 (544) 2.43 (511)

0.8781 0.6041

0.8676 0.7512

P3

S0→ S1 S0→ S2

2.07 (598) 2.30 (538)

1.4125 0.4008

0.9613 0.6026

P3-cEcEt

S0→ S1 S0→ S2

1.94 (638) 2.22 (558)

1.0043 0.5274

0.9010 0.7031

P4

S0→ S1 S0→ S2

1.91 (650) 2.23 (557)

1.8501 0.2858

0.9859 0.4822

AC

S0→ S1 S0→ S2

2.04 (607) 2.35 (529)

0.9826 0.3069

0.8959 0.5067

H→L (97%) H-1→L (96%)

AS

S0→ S1 S0→ S2

2.07 (598) 2.32 (535)

0.8776 0.3104

0.8674 0.5107

H→L (95%) H-1→L (95%)

AO

S0→ S1 S0→ S2

2.18 (568) 2.42 (513)

0.8622 0.2363

0.8627 0.4196

H→L (96%) H-1→L (96%)

AN

S0→ S1 S0→ S2

2.30 (539) 2.59 (478)

0.9222 0.2088

0.8804 0.3817

H→L (98%) H-1→L (98%)

2.07 (599) 2.34 (530)

0.6984 0.2549

0.7997 0.4440

H→L (96%) H-1→L (96%)

a

EP

AB

S0→ S1 S0→ S2

transition assignmenta

SC RI PT

LHE

H-1→L (60%), H→L (40%) H-1→L (40%), H→L (60%) H→L (86%) H-1→L (86%) H→L (96%) H-1→L (96%) H→L (94%) H-1→L (93%)

A

N

U

f

M

TE

P1

D

dye

H→L (98%) H-1→L (98%)

A

CC

Contributions above 20% are presented. H and L represent HOMO and LUMO, respectively.

45

dye

Table 3. Oxidation potentials (𝐸ox , eV), free energies of injection (∆𝐺 inject , eV), dipole moments (µ, Debye), static polarizabilities (α, Bohr3), electronic open-circuit photovoltages (eVoc, eV), and free energies of regeneration (ΔGregen, eV) calculated with B3LYP/6-31G(d,p)

SC RI PT

and TD-B3LYP/6-31G(d,p) in acetonitrile. dye dye∗ µ µa αa eVoc ΔGregen ∆𝐺 inject 𝐸ox 𝐸ox 5.22 2.58 -1.42 4.88 3.32 345.30 1.61 0.42 P1 (5.50)b 5.05 2.77 -1.23 13.98 10.11 426.41 1.44 0.25 P2 (5.31)b 4.92 2.84 -1.16 17.56 12.73 527.98 1.32 0.12 P3 4.91 2.97 -1.03 15.17 10.95 499.58 1.26 0.11 P3-cEcEt 4.81 2.91 -1.09 19.98 14.53 649.11 1.23 0.01 P4 4.86 2.82 -1.18 13.30 9.86 468.88 1.43 0.06 AC 4.96 2.88 -1.12 12.95 9.64 465.29 1.37 0.16 AS (5.31)b 4.96 2.77 -1.23 12.30 9.24 435.02 1.48 0.16 AO 4.86 2.56 -1.44 10.83 8.45 435.05 1.69 0.06 AN 4.94 2.88 -1.12 10.79 8.49 455.39 1.41 0.14 AB a B3LYP/6-31G(d,p) in vacuum. b The experimental oxidation potentials of P1, P2, and AS

M

A

N

U

dye

D

are 1.06, 0.87 and 0.87 V, respectively,34 by considering the absolute hydrogen electrode

A

CC

EP

TE

potential 4.44 eV.

46

Table 4. HOMO and LUMO energies (εHOMO and εLUMO, eV) and HOMO-LUMO gaps (εg, eV) of dye/(TiO2)38 cluster systems with binding modes I, II, and I′ at B3LYP/6-31G(d,p) level in acetonitrile.

εLUMO

-5.39 -5.37a -5.23 -5.11a

-3.10 -3.14a -3.11 -3.15a

2.29 2.23a 2.12 1.96a

-5.38

-3.15

-5.18

-3.14

P3/(TiO2)38

-5.04

-3.10

1.94

-5.03

-3.14

P4/(TiO2)38

-4.91

-3.10

1.81

-4.91

-3.14

AC/(TiO2)38

-4.99

-3.10

1.89

-4.98

AS/(TiO2)38

-5.04

-3.11

1.93

AO/(TiO2)38

-5.05

-3.11

1.94

AN/(TiO2)38

-4.96

-3.11

1.86

AB/(TiO2)38

-4.98

-3.12

D

P2/(TiO2)38

εg

εHOMO

εLUMO

εg

2.23

-

-

-

2.04

-

-

-

1.89

-

-

-

1.77

-

-

-3.14

1.84

-4.99

-3.10

1.89

-5.03

-3.15

1.89

-5.05

-3.11

1.94

-5.03

-3.15

1.88

-4.99

-3.11

1.88

-4.96

-3.15

1.81

-4.95

-3.11

1.84

1.86

-4.99

-3.16

1.82

-4.98

-3.12

1.86

U

εHOMO

N

εg

M

εLUMO

binding mode I′

SC RI PT

binding mode II

εHOMO P1/(TiO2)38

TE

ref. [50] calculated at B3LYP /6-31G(d).

A

CC

EP

a

binding mode I

A

dye/(TiO2)38

47

Table 5. The excitation energies (Eex, eV), oscillator strengths (f > 0.10), and their transition

State

Eex b

f

P1/(TiO2)38

5

2.14 (580)

0.1372

H → L+3 (30%), H→L+4 (27%)

7

2.16 (574)

0.1418

H-1→ L+2 (29%), H→L+5 (24%)

12

2.25 (550)

0.2901

H-1→ L+3 (42%)

13

2.28 (543)

0.2831

H-1→L+5 (45%)

4

1.97 (629)

0.8186

H→ L+3 (82%)

12

2.15 (578)

0.3827

H-1→L+3 (39%)

13

2.16 (575)

0.1807

H→L+8 (48%)

4

1.80 (688)

1.5077

U

13

2.06 (603)

0.3018

H-1→L+1 (61%)

2

1.65 (754)

1.2163

H→L+1 (62%), H→L+3 (33%)

4

1.67 (741)

0.9782

H→L+1 (29%), H→L+3 (59%)

13

1.99 (624)

0.3034

H-1→L+1 (86%)

P4/(TiO2)38

a

H→L+1 (83%)

N

P3/(TiO2)38

M

P2/(TiO2)38

Assignmentc

SC RI PT

dye/(TiO2)38

A

characters for P1-P4/(TiO2)38 with binding mode I.a

At the B3LYP/6-31G(d,p) level with solvent effects of acetonitrile through C-PCM. Values in parentheses are given in nm. c Only contributions above 20% are shown, where H and L represent HOMO and LUMO, respectively.

A

CC

EP

TE

D

b

48

Table 6. Excitation energies (Eex, eV), oscillator strengths (f > 0.10), and their transition

State

Eex b

f

P1/(TiO2)38

7

2.18 (570)

0.3091

H → L+4 (34%), H→ L+5 (54%)

11

2.26 (548)

0.1381

H-1→ L+5 (23%), H →L+4 (20%)

18

2.38 (521)

0.1451

H→ L+12 (42%)

5

1.99 (623)

0.7188

H→L+4 (87%)

9

2.09 (593)

0.1096

H→L+5 (67%), H→L+7 (20%)

10

2.13 (583)

0.1051

13

2.18 (569)

0.1533

H→L+5 (20%), H→L+7 (22%), H→L+8 (39%) H-1→L+4 (29%)

14

2.20 (563)

0.2441

H-1→L+2 (32%)

15

2.21 (561)

0.1380

H-1→L+2 (63%)

3

1.83 (678)

0.8584

A

4

1.84 (674)

0.5689

H→L+2 (26%), H→L+3 (39%), H→L+4 (29%) H→L+3 (40%), H→L+4 (50%)

6

1.93 (643)

0.1157

H→L+6 (70%)

8

1.99 (622)

0.1045

H→L+7 (25%), H→L+8 (46%)

16

2.11 (587)

0.2585

H-1→L+3 (65%)

1

1.50 (825)

0.1018

H→L (73%), H→L+1 (20%)

3

1.70 (730)

1.9948

H→L+2 (85%)

13

2.00 (620)

0.2536

EP

P4/(TiO2)38

U

N

M

P3/(TiO2)38

TE

P2/(TiO2)38

Assignmentc

SC RI PT

dye/(TiO2)38

D

characters for P1-P4/(TiO2)38 with binding mode II.a

A

CC

H-1→L (37%), H-1→L+1 (29%), H-1→L+2 (29%) a At the B3LYP/6-31G(d,p) level with solvent effects of acetonitrile through C-PCM. b Values in parentheses are given in nm. c Only contributions above 20% are shown, where H and L represent HOMO and LUMO, respectively.

49

Table 7. Contributions (%) of the dye atomic orbitals to natural transition orbital pairs (holes and particles) for the excitation with significant and small but non-negligible oscillation strengths for dye/(TiO2)38 systems with binding mode I.a

dye/(TiO2)38

state

dye AOs (%) λb

particle

hole

0.86 0.65 0.76 0.89

23 23 26 31

99 99 100 100

0.14 0.35 0.24 0.11

3 8 9 1

100 99 99 99

P2/(TiO2)38

4 12

0.99 0.67

68 67

99 100

0.33

9

99

4 13

0.99 0.72

71 75

99 100

0.28

1

99

P4/(TiO2)38

2 4

0.99 0.99

AC/(TiO2)38

4

AS/(TiO2)38

4

AO/(TiO2)38

4

AN/(TiO2)38

6

N

A

4

43 37

99 99

0.99

67

99

0.99

66

99

0.99

57

99

0.99

19

99

0.99

60

100

D

TE

AB/(TiO2)38

U

5 7 12 13

M

hole

P1/(TiO2)38

P3/(TiO2)38

EP

At the B3LYP/6-31G(d,p) level with solvent effects of acetonitrile through C-PCM. Eigenvalues of the pairs.

A

CC

b

dye AOs (%)

λb

particle

a

NTO pair

SC RI PT

NTO pair

50

Table 8. Contributions (%) of the dye atomic orbitals to natural transition orbital pairs (holes and particles) for the excitation with significant and small but non-negligible oscillation strengths for dye/(TiO2)38 systems with binding mode II.a

dye/(TiO2)38

state

dye AOs (%) λb

hole

particle

hole

0.99 0.55 0.78

20 53 17

99 100 99

0.45 0.22

1 2

99 100

5 14

0.97 0.58

40 36

99 99

0.42

3

100

P3/(TiO2)38

3 4

0.99 0.99

36 25

P4/(TiO2)38

3 13

0.99 0.96

71 69

99 100

AC/(TiO2)38

3

0.99

69

99

AS/(TiO2)38

3

0.99

74

99

AO/(TiO2)38

3 14

0.99 0.74

66 68

99 100

0.26

2

99

0.99 0.98

24 12

99 99

0.99

63

100

3

99 99

N

A

EP

AB/(TiO2)38

5 9

D

AN/(TiO2)38

TE

P2/(TiO2)38

U

7 11 18

M

P1/(TiO2)38

dye AOs (%)

λb

particle

a

NTO pair

SC RI PT

NTO pair

At the B3LYP/6-31G(d,p) level with solvent effects of acetonitrile through C-PCM. Eigenvalues of the pairs.

A

CC

ｂ

51

Table 9. The calculated LUMO energies of isolated dyes (εLUMO (free)), the adsorbate LUMO energies (εLUMO (ads)), the energy shifts (Δε), the widths of the adsorbate LUMO (Δ), and the Δεb

Δ (meV)

τ(fs)c

P1/(TiO2)38

-2.38

-2.95

-0.57

61.74

3

P2/(TiO2)38

-2.55

-2.86

-0.31

144.52

5

P3/(TiO2)38

-2.67

-2.96

-0.28

116.37

6

P4/(TiO2)38

-2.77

-3.04

-0.27

101.39

6

AC/(TiO2)38

-2.57

-2.86

-0.29

129.14

5

AS/(TiO2)38

-2.62

-2.91

-0.28

137.77

5

AO/(TiO2)38

-2.52

-2.79

-0.27

196.82

3

AN/(TiO2)38

-2.30

-2.63

-0.32

204.94

3

AB/(TiO2)38

-2.58

-0.33

160.24

4

A

N

U

εLUMO (ads) (eV)

-2.92

The structures with the binding mode I were employed. Δε =εLUMO (ads) -εLUMO (free). τ=ћ/Δ. [85–87]

A

CC

EP

TE

D

c

εLUMO (free) (eV)

M

a

dye/(TiO2)38

SC RI PT

injection times (τ)a in acetonitrile.

52

b