Physical Insight on Mechanism of Photoinduced Charge Transfer in Multipolar Photoactive Molecules

Two series of novel dyes were designed based on the multipolar structures of the red dye D35 and blue dye DB, by introducing the furan (F), benzene ring (B) and benzo[c]thiophene (BT) groups into the conjugated bridge of D35 in proper order and adjusting the position of diketopyrrolopyrrole(DPP) unit and the incorporation of fluorine in the conjugated bridge of DB, respectively. We performed the quantum chemistry calculation to investigate the ground state and excited properties in a direct correlation with the spectra properties and abilities of losing or accepting electron for the original and designed molecules. Furthermore, the absorption spectra characteristics in consideration of the aggregation of dyes on the TiO2 layer and intermolecular charge transfer rate of the dimers were calculated. The obtained results indicate that the larger intermolecular charge transfer rate leads to the poor photoelectrical properties of the dyes, and the designed dyes D35-3 and DB-2 would exhibit the best photoelectrical properties among the investigated dyes due to their lower energy gaps, widened absorption spectra and prominent charge transfer properties.


Results
FMOs and energy gaps. The calculated energy levels and gaps of the original and designed dyes in acetonitrile are presented in Fig. 2. As shown, the HOMO energy level of DB (−4.89 eV) is higher than that of D35 (−5.04 eV), and the LUMO energy level (−2.85 eV) is below that of D35 (−2.72 eV), resulting in the lower energy gap of DB compared with that of D35. The results indicate that the introduction of DPP unit into the dye D35 has changed the energy levels and thereby improved the photoelectrical properties of DB. Noted that the HOMO energy levels for the original and designed molecules are not significantly different, and the largest and smallest HOMO energies are −4.87 eV and −5.04 eV for D35-3 and D35, respectively, implying that the modification of conjugated bridge for the dyes D35 and DB little affects the HOMO levels. However, it exhibits the obvious difference in the LUMO, i.e., DB-2 (−3.28 eV) < DB-1 (−3.09 eV) < DB-3 (−2.88 eV) < DB (−2.85 eV) < D35 (−2.72 eV) < D35-3 (−2.66 eV) < D35-1 = D35-2 (−2.58 eV). The results indicate that the energy levels of LUMO are more susceptible to be influenced by modification of conjugated bridge for the dyes D35 and DB.
In order to make the excited electron effectively injected into TiO 2 , dye higher LUMO is needed (here for TiO 2 conduction band, usually −4.00 eV); for regeneration process, it is effectively restored for the oxidized dye under the lower HOMO compared with electrolyte (usually −4.80 eV for I − /I 3 − ) 36,37 . As shown in Fig. 2, the higher LUMO energies for dyes and lower HOMO were found in comparison with the TiO 2 and electrolyte, meaning the smooth completion of two processes (electron injection and dye regeneration).
Energy gap, defined as the difference between HOMO and LUMO levels, is a key factor affecting the solar cell PCE. A low energy gap is contributed to the better intramolecular charge transfer (ICT) and strong absorption band in spectra 38 . As shown in Fig. 2, it can be found that for D35 and its derivatives, the energy gaps are in the order of D35-3 (2.21 eV) < D35-2 (2.30 eV) < D35 (2.32 eV) < D35-1 (2.33 eV), indicating that the dye D35-3 would have a strong absorption band, and the introduction of benzo[c]thiophene unit into D35 should obviously improve the photoelectrical properties of dye. For DB and its derivatives, the energy gaps are DB-2 (1.61 eV) < DB-1 (1.80 eV) < DB = DB-3 (2.04 eV), and DB-2 exhibits the lowest energy gap among all the original and designed dyes, implying that DB-2 would show the best optical properties among the investigated dyes. The above results suggest that the photoelectrical properties of dye can be improved effectively by properly adjusting the position of the DPP unit in the conjugated bridge of DB, and the fluorine atoms has no obvious influence on the energy gap of DB molecule.
Calculation on IPs and EAs. Calculated IPs and EAs of the original and designed dyes are shown in Fig. 3.
As shown in Fig. 3, the IP of DB (5.23 eV) is less than that of D35 (5.51 eV), indicating that the introduction of DPP unit into the dye D35 could result in the dye being easier to lose electrons, thereby making the dye DB exhibit better photoelectrical properties. Meanwhile, it can be found from Fig. 3 that the EA of DB (1.96 eV) is  greater than that of D35, which means that introducing the DPP unit into the dye D35 could improve the electron accepting ability.
By comparing the IPs and EAs of the original and designed dyes, it can be found that there is no significant difference between the IPs of the original and designed dyes, and the largest and smallest IPs are 5.51 eV and 5.21 eV for D35 and DB-1, respectively. However, the calculated EAs of the original and designed dyes show a great difference, and the EAs of the original and designed dyes are DB-2 (2. Excited state properties. Absorption spectra of the original and designed dyes in acetonitrile are presented in Fig. 4a and b. Table 1 shows the calculated peak site and oscillator strength (OS) as well as electron transition information. The absorption spectra of D35 and its derivatives with double-peaks characteristic are mainly distributed in the region of 250-550 nm (see Fig. 4a). The maximal absorption peaks corresponding to D35, D35-1, D35-2 and D35-3 are 447.49 nm, 446.63 nm, 420.34 nm and 464.27 nm, respectively, in which the maximal absorption peak corresponding to D35-1 appears a little change compared with that of D35. It is worth noting that the maximal absorption peaks corresponding to D35-3 and D35-2 exhibit a red and blue shift of 16.78 nm and 27.15 nm than D35, which implies that introduction of benzo[c]thiopheneorbenzene ring group into the conjugated bridge of D35-1 could result in the red or blue shift of absorption spectrum. As shown in Fig. 4a, it is interesting that the maximal peak OS of D35-2 is greater than that of D35, which is advantageous to the absorption of light. In addition, all the maximal peaks of D35 and its derivatives correspond to the S1 excited states, in which the S1 excited states of D35 and D35-1 correspond to the HOMO → LUMO transition. Those of D35-2 and D35-3 correspond to the HOMO-1 → LUMO. From the electron density in Fig. 5, the electron density of the above mentioned HOMO and HOMO-1 is distributed in whole molecules, and those of the LUMO levels reside in bridge and acceptor units of dyes, signifying ICT process for the dye D35 and its derivatives upon the photo-excitation.
Simultaneously, it can be found from Fig. 4b that the absorption spectra of DB and its derivatives show a good response to the solar spectrum, which covers almost the whole visible and even infrared light region. The absorption spectra of DB and its derivatives also show the double-peak characteristic, which is similar to the shapes of absorption spectra of D35 and its derivatives. Table 1 shows that absorption peaks are DB-2 (595.89 nm) > DB-1 (537.43 nm) > DB (528.88 nm) > DB-3 (524.58 nm), in which the maximal absorption peak of DB-2 shows the greatest bathochromic-shift of 67.01 nm compared with that of DB. In addition, it can be found that all the maximal absorption peaks of DB and its derivatives also correspond to the S1 excited states (HOMO → LUMO transition), and that of DB-1 and DB-2 is HOMO-1 → LUMO. The electron density indicates that upon the photo-excitation, the significant ICT occurs in the DB and DB-3 molecules (see Fig. 5).
The dye with longer excited state lifetime would behave with higher charge transfer efficiency 38 , and the excited state lifetime of dye is estimated by using the following equation 39 : (1) 2 where E stands for the excitation energy corresponding to different excited state, and f represents the excited state OS. The calculated first excited lifetimes of the original and designed dyes are presented in Fig. 6. It was found intuitively from Fig. 6 that the dye DB-2 exhibits the largest first excited-state lifetime among all the investigated dyes, and the calculated first excited-state lifetimes are in this order: DB-2 > DB-1 > DB-3 > DB > D35 > D35-3 > D35-1 > D35-2. Moreover, the dye D35-3 shows the longest excited state lifetime among the designed dyes based on D35. In summary, DB-2 and D35-3 could be used as the candidates for high efficiency dye due to their excellent optical properties among the investigated dye molecules. ICT is accompanied by the photo-excitation, and the excited state with highly efficient charge separation properties would be propitious to the ultrafast interfacial electron injection and reducing the electrons recombination rate 40 . Table 2 shows the parameters contain the charge-transfer length (D CT ), transferred charge (∆q), the half of the sum of two centroid axis along the electron transfer direction (H), the difference between H and D CT (t) and the exciton binding energy (E b ), in which the greater t results in the better separation between the density increment and depletion regions 41 . The average ∆q for dye DB and its derivatives (0.76 e) is greater than those for the dye D35 and its derivatives (0.73 e), indicating that the ICT is more likely to occur in the dye system based on DB compared with the dye system based on D35. For the dye D35 and its derivatives, the ∆q are in the order of D35 > D35-3 > D35-2 > D35-1, implying that the dye D35-3 would exhibit the better ICT properties compared with the other derivatives of D35. For the dye DB and its derivatives, the obtained ∆q follows the order of DB-2 > DB-3 > DB-1 > DB, which suggests that the dye DB-2 would have the best ICT characteristics among the dye DB and its derivatives. The obtained charge density difference is presented in Fig. 7, from which can be seen clearly that there is ICT process. In addition, from Table 2 it can be found that the obtained t for all the original and designed dyes are in the order of DB-2 > DB-1 > DB > DB-3 > D35-3 > D35-2 > D35-1 > D35, meaning that the dye DB and its derivatives would show the better charge separation compared with the dye D35 and its derivatives. Moreover, the dyes D35-3 and DB-2 show the largest t value among the dyes D35 and DB series, respectively, which signifies that the dyes D35-3 and DB-2 would present the best charge separation among the two dye series.
The exciton should be generated immediately as long as the ICT occurs under the photo-excitation. In order to effectively separate the exciton, the energy of exciton binding (E b ) must be overcome, which can be estimated by electronic and optical band gap 42 . Table 2 shows that the calculated E b for the original and designed dyes, i.e., the average E b value for the dye DB and its derivatives (0.40 eV) is lower than that for the dye D35 and its derivatives (0.50 eV), indicating that the excitons in the dye DB and its derivatives are easier to separate compared with that in the dye D35 and its derivatives.
Emission characteristics. Table 3 shows the obtained emission peaks, OS and radiative lifetimes of the original and designed dyes. All the emission peaks corresponding to S1 state are composed of HOMO → LUMO transition except for the dyes DB-1 and DB-2. For the dye D35 and its derivatives, the emission peaks are D35 In addition, the radiative lifetimes of the original and designed dyes were estimated from the following equation 44 :    Reorganization energies. The dye molecule with prominent performance should possess the good charge transfer rate, and the charge transfer rate arose from the standard Marcus/Hush model expressed as follows 45 : where Κ b stands for the Boltzmann constant, T represents the temperature, V is the electronic coupling matrix element between the two species, and λ is the reorganization energy, which contains the inter-and intra-molecular reorganization energy 46 . However, the intermolecular reorganization energy has no significant effect on the electron transfer, so the intramolecular reorganization energy was only focused on in this work, which can be calculated as follows 47 : represent neutral molecule optimized energy, charged molecular energy on the basis of neutral and charged ground state, respectively. Figure 8 displays that all the hole reorganization energies are lower than the electron reorganization energies of the investigated dyes, indicating that the investigated dyes have a better hole transport ability. For the dye D35 and its derivatives, the electron and hole reorganization energies are D35-2 < D35-3 < D35-1 < D35 and D35-3 < D35-2 < D35-1 < D35, respectively, implying that the dyes D35-2 and D35-3 have the better electron and hole transfer ability among the dye D35 and its derivatives. For the dye DB and its derivatives, the electron and hole reorganization energies follow the order of DB-1 < DB-3 < DB < DB-2 and DB-1 < DB-2 < DB-3 < DB, respectively, which indicates that the dye DB-1 would exhibit the best electron and hole transfer ability among the dye DB and its derivatives. Moreover, as shown in Fig. 8, DB-1 has the lowest reorganization energies among original and designed dyes, meaning that DB-1 would show the best charge transfer ability among the investigated dyes. In addition, it is worth noting from Fig. 8 that the electron and hole reorganization energies of DB and DB-3 show the lowest difference compared with that of the other dyes, indicating that the two dyes have the better charge transfer balance performance among the investigated dyes.
Key parameters associated with V oc and J sc . The PCE (η) of DSSC is determined by the open circuit voltage (V OC ), the short-circuit current density (J SC ) and the fill factor (FF), which can be expressed as following 48 : OC SC inc where P inc represents the incident light intensity. The V oc is defined as the difference between the Fermi level of the semiconductor (usually TiO 2 ) and the redox potential of the electrolyte (usually − − I /I 3 ) 49 : where E CB is the conduction band (CB) of the semiconductor, ∆E CB represents the shift of the CB of semiconductor, q is the elementary charge, κ B is the Boltzmann constant, T is the temperature, N CB is the effective density of state, n c is the number of electrons in the CB of semiconductor, and E redox is the redox potential of the electrolyte (usually −4.80 eV for − − I /I 3 ) 50 . ∆E CB can be expressed as following 51 :  where μ normal , γ, ε 0 (ε) are the dipole moment, the coverage of dye absorbed on the TiO 2 and the dielectric constant, respectively. As can be seen from the equations (7) and (8) that the greater μ normal and ∆E CB of dye would emerge, V OC is the larger. The density of state (DOS) and partial DOS (PDOS) charts of the dye/TiO 2 complexes, related to the ∆E CB , are shown in Fig. S1 (see Supplementary Fig. S1), and Table 4 shows the calculated μ normal and ∆E CB of the original and designed dyes. For original and designed dyes, the μ normal and ∆E CB are in the order of The above results indicate that the strategy of modification of different groups in the π-conjugated bridge or adjusting the position of the DPP unit in the π-conjugate bridge could improve the V OC of the dyes. In addition, J SC is mainly depended on the LHE, the inject efficiency Φ inj and collection efficiency η coll according to the following relationship 41,52 : SC inj coll 0 For the same DSSC, η coll can be considered as a constant. Therefore, the J SC is determined only by the factors of LHE and Φ inj , which are light absorption efficiency and injection efficiency of electron. The LHE is correlated with the calculated oscillator strength (f), which is represented as 53 : = − − LHE 1 10 f . The Φ inj is positively correlated with the driving force of electron injection (∆G inject ), which can be defined as 54,55 Table 4 shows the calculated LHE, * E OX dye and ∆G inject . The obtained LHE is in the range of 0.9558-0.9954, which exhibits no obvious difference. Moreover, the calculated values of ∆G inject for all molecules are far greater than 0.2 eV, which means the sufficient driving force is provided to fulfill electron injection process 56 . In addition, the relatively lower E b can generate the better Φ inj 41 . As listed in Table 2, the obtained E b for the dye D35 and DB are 0.45 eV and 0.30 eV, respectively. The results indicate that the dye DB would have a better Φ inj , thereby showing the better photoelectrical performance, which is consistent with the experimental results 34 . The average value of E b for the dye DB and its derivatives (0.40 eV) is lower than that for the dye D35 and its derivatives (0.50 eV), implying that the dye DB and its derivatives would show the better Φ inj .
Excited state properties of dye/TiO 2 complexes. For understanding the dyes and TiO 2 interaction, the structure and CT properties of the dye/TiO 2 complexes were investigated. Table 5 and Table S1-S2 (see  Supplementary Table S1-S2) show the excited information about ten excited states of the dye/TiO 2 complexes. The simulated absorption spectra of the dye/TiO 2 complexes are presented in Fig. 9 and Fig. S2 (see Supplementary  Fig. S2). Figure 9 and Fig. S2 show the spectra of DB/TiO 2 and DB-3/TiO 2 complexes emerge a new absorption band (301.12 nm and 300.67 nm for DB/TiO 2 and DB-3/TiO 2 , respectively). Except for the DB/TiO 2 and DB-3/ TiO 2 complexes, the absorption spectra of the other complexes do not show extra absorption band in comparison with the isolated dyes.
The selected transition properties corresponding to the first three absorption peaks of the dye/TiO 2 complexes are listed in Table 5. As shown, the maximal absorption peaks of all the complexes correspond to the S1 excited state. For the dye D35 and its derivatives, the S1 excited states for D35/TiO 2 , D35-1/TiO 2 , D35-2/TiO 2 and D35-3/TiO 2   To investigate the electron transfer process in the excited states of dye/TiO 2 complexes, the charge density difference (CDD) diagrams corresponding to some excited states of the dye/TiO 2 complexes are shown in Fig. 10. As illustrated in Fig. 10, taking the D35/TiO 2 complex as an example, the S1 excited state belongs to a local excitation state, for which the electrons and holes are distributed over the complex alternately. Similarly, it can be found from Fig. S3 (see Supplementary Fig. S3) that the excited states S2-S6, S10, S13-S16, S18-S20 are attributed to the local excited state. In addition, the holes and electrons for the S7 are entirely separated in complex system, which can be vested in the charge-transfer excitation and is similar to the charge distribution of the excited states S11 and S17 (See Supplementary Fig. S3). It is interesting that for the excited state S8, the holes and electrons are fully distributed in the dye and TiO 2 cluster, respectively, which is similar to the charge distribution of the excited states S9 and S12 (See Supplementary Fig. S3). Figure 11 shows the calculated chemical reactivity parameters of the original and designed dyes (the various parameters are listed in Table S3). As shown in Fig. 11, D35-3 has the lowest chemical hardness and highest electroaccepting power among the dye D35 and its derivatives, which would result in the greater short-circuit current density, thereby obtaining a better PCE 57 . Moreover, the dye DB-2 shows the lowest chemical hardness and highest electroaccepting power among the dye DB and its derivatives. It is surprising that DB-2 exhibits the lowest chemical hardness and highest electroaccepting power among the investigated dyes, suggesting that the dye DB-2 would have the prominent Jsc, and consequently bring the prominent PCE. With regard to electrophilicity(ω), the higher electrophilicity leads to the higher energetic stability by acquiring electrons from the environment 58 . It can be found from Fig. 11 that the dye D35-3 and DB-2 exhibit the greatest electrophilicity among the two series dyes, respectively, which indicates that the two dyes possess the highest energetic stability by acquiring electrons from the environment. In addition, the calculated electron-donating powers of the original and designed dyes show the same tendency as the obtained electrophilicities and electroaccepting powers, which make against improving the donating electrons ability of the dye D35-3 and DB-2 59 .

Ground-and excited-state properties under external electric field. The geometries of the dyes D35
and DB were optimized under the external electric field of −3.0 × 10 −3~3 .0 × 10 −3 a.u. In this work, the direction from the electron donor to the electron acceptor was determined to be the positive direction. The trend of obtained HOMO and LUMO energies with the increasing electric field intensity is presented in Fig. 12a,b. It can be found in Fig. 12a that for the dye D35, the HOMO energies have no obvious change under the electric field of −3.0 × 10 −3~3 .0 × 10 −3 a.u. However, the LUMO energies of D35 increase gradually with the electric field increasing from 1.0 × 10 −3 a.u. to 3.0 × 10 −3 a.u. resulting in gradually increasing energy gaps under the same variation tendency of electric field (see Table S4). To the contrary, the LUMO energies of D35 decrease gradually with the electric field increasing from −1.0 × 10 −3 a.u. to −3.0 × 10 −3 a.u. leading to the decrease of energy gap under the same variation tendency of electric field. In addition, it can be found from Fig. 12b that for the dye DB, the HOMO and LUMO energies are increased gradually along with the increased electric field from 1.0 × 10 −3 a.u. to 3.0 × 10 −3 a.u., and the energy gaps are decreased by degrees under the same variation tendency of electric field. Moreover, the HOMO energies first increase and then decrease when the electric field is increased from −1.0 × 10 −3 a.u. to −3.0 × 10 −3 a.u. and the LUMO energies first decrease and then increase under the same variation tendency of electric field, in which the energy gap reaches the minimum value under the electric field of −2.0 × 10 −3 a.u.
Under the different external electric field, the excited state properties of the dyes were calculated in the electric field, and the spectra of the two dyes under the external electric field of −3.0 × 10 −3~3 .0 × 10 −3 a.u. are presented in Fig. 13a,b, and Table S5 shows the corresponding excited state properties with oscillator strength f > 1. It can be found from Fig. 13a that for the dye D35, the maximum absorption peak is red-shifted along with the gradual increase of the electric field intensity from −1.  of energy gap in the electric field, it can be found that the decrease or increase of energy gap in the electric field would cause the red-or blue-shift of absorption peak. Moreover, as shown in Fig. 13b for the dye DB, the red-shift of maximum absorption peak occurs with the increase of electric field from 1.0 × 10 −3 to 3.0 × 10 −3 a.u., which corresponds to the decrease of energy gap. In addition, the maximum absorption peaks are 585. Absorption and intermolecular charge transfer of the dimers. For studying an impact of aggregation on the optical properties of dyes, absorption spectra for the dimers corresponding to the researched dyes were calculated based on the dimers geometries. The obtained absorption spectra of the dimers are presented in Fig. 14 and Fig. S4 (see Supplementary Fig. S4), and Table S6 shows the transition properties corresponding to the main absorption peaks. The absorption spectra of dimers have the same shape with that of the corresponding monomers except the dyes DB and DB-3, in which the absorption spectra of (DB) 2 and (DB-3) 2 present an extra absorption band in comparison with the corresponding monomers. However, noted that the peak strengths for all dimers are greater than those of the monomers. In addition,  Table 5. Calculated excited state properties of the dye/TiO 2 complexes in acetonitrile. In order to intuitively observe the charge transfer process in the dimers under photo-excitation, the CDD analysis method was adopted, and CDD results for the first thirty excited states of the dimers are shown in Fig. S5-S12 (see Supplementary Fig. S5-S12). The selected charts corresponding to the first charge completely separated state of the dimers are presented in Fig. 15, in which the electrons and holes are distributed on the two monomers, respectively. It can be found from Fig. S5 that for the dimer (D35) 2 , the charge distribution of excited states S4, S10, S11, S20 and S23 are similar to that of the excited state S3. It is noteworthy that for the excited states S20 and S23, the holes are distributed in the donor part of a monomer and the electrons are distributed in the conjugated bridge and acceptor part of another monomer. Similarly, as shown in Fig. S6-S12, the excited states S4, S5, S11, S13, S23, S25, S26 for (D35-1) 2 , S5, S6, S14, S21, S24, S29, S30 for (D35-2) 2 , S7, S8, S12, S16, S25, S26 for (D35-3) 2 , S7, S9, S13, S14, S24, S30 for (DB) 2 , S5-S7, S11, S23-S25 for (DB-1) 2 , S3, S4, S7, S8, S18, S20, S29 for (DB-2) 2 , S4, S6, S11, S14-S16, S24, S28 for (DB-3) 2 , all belong to the charge completely separated state.
In order to investigate the intermolecular charge transfer in the dye aggregation, the lateral intermolecular charge transfer rate between dimers was calculated based on the non-adiabatic Marcus theory, in which the Gibbs free energy has no obvious change at the initial and final state due to the two identical dyes for the stacked dimers 60,61 : where h is the Planck's constant, κ B represents the Boltzmann constant, T is the temperature, | | V ij and λ are the intermolecular electronic coupling and the reorganization energy, respectively. With the direct method, the value of | | V ij should be estimated as 62 : Figure 11. Calculated chemical reactivity parameters of the original and designed dyes.  where operator F is the Kohn-Sham-Fock matrix for the dimer, and ϕ j/i stands for the two near molecular orbitals. Table 6 shows the values of λ e , V ij and κ e . The κ e for (D35) 2 is two orders of magnitude greater than that for (DB) 2 . The greater κ e for (D35) 2 increases the electron loss in the process of Dye → TiO 2 61 . That is to say, the electron injection rate from the dye to TiO 2 for D35 would be lower than that for DB, thereby weakens the photoelectrical properties of the dye D35, which is consistent with the experimental results 34 . Moreover, for the designed dyes based on the dye D35, the κ e are in the order of (D35-3) 2 < (D35-1) 2 < (D35-2) 2 , indicating that the dye D35-3 would show the most efficient electron injection from the dye to TiO 2 among the three designed dyes. For the derivates of DB, the κ e follow the order of (DB-3) 2 < (DB-2) 2 < (DB-1) 2 , implying that DB-3 would have a more efficient electron injection compared with the other two DB derivates.

Discussion
In this work, two series of novel dyes were designed with the multipolar structures for the dyes D35 and DB by the modification for their conjugated bridges. The ground-and excited-state properties of the original and designed dyes were investigated systematically via quantum chemistry methods. Moreover, the key parameters associated with V OC and J SC containing dipole moment (μ normal ), shift of the CB of semiconductor (∆E CB ), light harvesting efficiency (LHE), driving force of electron injection (∆G inject ), exciton binding energy (E b ) and chemical reactivity parameters were calculated. The effects of external electric field on the optical and electric properties of dyes were investigated. In order to investigate the intermolecular charge transfer in the dye aggregation, the lateral intermolecular charge transfer rate between dimers was calculated based on the non-adiabatic Marcus theory. From the above results, it can be concluded that D35-3 and DB-2 would exhibit the better optical and electrical properties due to their narrower energy gaps, widened optical absorption, longer excited state lifetimes, and larger transferred charge (∆q) among the two series of designed dyes. Furthermore, D35-3 and DB-2 possess the lower chemical hardness, higher electroaccepting power and electrophilicity among the two series of dyes, which would result in their prominent J sc , and consequently bring the better PCE. Considering the charge transfer  process, the ability of hole transfer of the two series of dyes would be higher than that of the electron transfer arising from their lower hole reorganization energies. D35-3 and DB-3 would show the most efficient electron injection from the dye to TiO 2 among the two series of designed dyes because of their lower intermolecular electron transfer rate (κ e ). Therefore, DB-2 could be used as a candidate for high performance dyes in the field of DSSC, and rational molecular design can provide valuable reference for the synthesis of dyes with higher efficiency in the experiment.

Methods
All calculations in this work were performed by using Gaussian 09 package 63 . The geometries of the investigated dyes were optimized without any constraint in the DFT framework 64,65 , with B3LYP 66-68 functional at 6-31 G(d) basis set. Moreover, the excitation and emission characteristics of the dyes have been investigated with TD-DFT method 69,70 , with CAM-B3LYP 71 functional at 6-31 G(d). The calculations in solvent employed the Conductor-like PCM (C-PCM) model 72 , and the solvent acetonitrile was adopted, which was used in the experiment 34 . In order to save computing time, the alkyl chains in the original dye molecules were replaced by the methyl due to the negligible influence of the alkyl chain length on the electronic structures of dyes 73 .
Moreover, the ground-and excited-state performances of the dye/TiO 2 complexes have been obtained with the Ti(OH) 3 H 2 O cluster model reported by Peng et al. 74 , which has been proved the feasibility to reveal the photoelectrical properties of dyes by Ramkumar et al. 75 . The ground state structures of the dye/TiO 2 complexes were optimized via DFT//B3LYP/6-31 G(d) for C, H, O, N, S, F atoms and effective core potential (ECP) LANL2DZ [76][77][78] and the accompanying basis set for Ti atom. Three-dimensional (3D) real space CDD analysis method was employed to intuitively display the electron transfer performances in the isolated dyes, dye/TiO 2 complexes and dimers under the photo-excitation, which has been validated in the previous works [79][80][81][82] . The charts of density of state (DOS) and partial density of state (PDOS) for the dye/TiO 2 complexes were displayed via the Multiwfn 3.3.7 package 83 . According to the previous literatures 84,85 , under the obtained ionization potentials (IPs) and electron affinities (EAs) of the dyes, we calculate the chemical hardness (h), electrophilicity (ω), electrodonating power (ω − ) and electroaccepting power (ω + ) of dyes via the following equations:  where, E neutral , E ca and E an represent the energies of neutral molecule, cation and anion, respectively.   Table 6. Calculated the electron reorganization energies (λ e ), intermolecular electronic couplings ( V ij ) and lateral intermolecular electron transfer rates (κ e ) for the dimers.