Photophysical Properties of Phenyl- or Thiophene-Cored

Article pubs.acs.org/JPCC

Photophysical Properties of Phenyl- or Thiophene-Cored Branched Molecules with Thiophene and/or Thienylenevinylene Arms toward Broad Absorption Spectra for Solar Cells: A Theoretical Study Shanshan Tang,†,‡ Bo Li,† and Jingping Zhang*,† †

Faculty of Chemistry, Northeast Normal University, Changchun 130024, People’s Republic of China College of Resource and Environmental Science, Jilin Agricultural University, Changchun 130118, People’s Republic of China

‡

S Supporting Information *

ABSTRACT: The aim of this work is to provide an in-depth study of the optical and electronic properties for branched molecules possessing thiophene- or phenyl-core with two-, three-, or four-branches, where the branch varies from thiophene to thienylenevinylene, for solar cells. Equilibrium ground state geometry configurations and their relevant electronic properties of investigated molecules for photovoltaic applications were optimized at the PBE0/6-31G(d) level. The absorption spectra were evaluated by the TD-PBE0/6-31+G(d,p) method. For the molecules possessing the thiophene core with thiophene and thienylenevinylene branches, the red shift is observed in absorption spectra, relative to ones with the phenyl-core and the thiophene branch. Moreover, the ortho- or para-substituted phenyl-cored (2,3- or 2,5-substituted thiophene-core) molecule contributes a red shift for the absorption spectra compared with the meta-substituted (2,4-substituted thiophene-core) one. The calculated reorganization energies of electrons and holes for the investigated molecules indicated them to be potential ambipolar charge transport materials under the proper operating conditions. We have also predicted the mobility of the recommended molecule possessing 2,3,5-subsititued thiophene-core and thiophene and thienylenevinylene side fragments with better performance in two different space groups.

1. INTRODUCTION Since Tang reported the first thin film organic photovoltaic cell based on a donor−acceptor heterojunction in 1986,1 there have been a lot of reports on organic solar cells (OSCs) using a variety of semiconducting polymers and dyes.2,3 Branched macromolecules or dendrimers have provided a rich stream of research in terms of both innovative chemistry and application.4 Polythiophene derivatives are the most extensively investigated conjugated polymers, because of their strong absorption in the visible region, high charge carrier mobility, and synthetic accessibility. Among them, soluble poly(3-alkylthiophene)s are the most important semiconducting polymers for the applications in OSCs.5 A series of poly(thienylenevinylene) derivatives with bi(thienylenevinylene) side chains have been synthesized for the conjugated polymers with broad and strong visible absorption spectra. Moreover, the absorption peak of spectra was red-shifted to the visible region, when bi(thienylenevinylene) is the conjugated side chain.4d,6 Thiophene derivatives with different electron-withdrawing groups have been applied for OSCs cells, offering the highest power conversion efficiency (PCE) value of 7.7%.7 However, the PCE still needs to be improved for actual applications.8 It is wellknown that the PCE is determined by the open circuit voltage (Voc), short circuit current (Jsc), and fill factor (FF) of the OSCs. Therefore, the three steps to improve the PCE of OSCs are as follows: first, reducing the highest occupied molecular © 2013 American Chemical Society

orbital (HOMO) energy of molecule to increase Voc; second, decreasing the HOMO−LUMO (the lowest unoccupied molecular orbital) gap of molecule to harvest more sunlight, which leads to higher Jsc; third, increasing the charge carrier mobility to enlarge Jsc and raise FF.9 With the above considerations, in this work, we investigated a series of phenyl-cored and thiophene-cored branched molecules with thienylenevinylene and thiophene arms in various topologies, i.e., two-, three-, and four-arms for photovoltaic applications (Scheme 1). The purpose of this molecular architecture was to investigate the relationship between topologic structure and optical as well as electronic properties resulting in a broad absorption region and high charge transfer rate, rendering it a good candidate for solar cell materials. Moreover, the computational results such as the frontier molecular orbitals (FMOs) including HOMO and LUMO energies, the HOMO−LUMO gaps (Eg) as well as the absorption spectra were investigated here. On the basis of detailed investigation of designed oligomers, the most promising candidates were designed as 1−5 (Scheme 2) and their various properties were predicted. According to the Marcus model,10−12 we calculated reorganization energies of all Received: September 24, 2012 Revised: January 28, 2013 Published: February 7, 2013 3221

dx.doi.org/10.1021/jp309495a | J. Phys. Chem. C 2013, 117, 3221−3231

The Journal of Physical Chemistry C

Article

Scheme 1. Different Cores and Branches Utilized to Design Novel Molecules

1 x(t )2 1 D = lim ≈ t →∞ 2n t 2n

Scheme 2. Chemical Structures of 1−5 as the Most Promising Candidates

2 2

∑ i

di2kipi

1 ∑i di ki = 2n ∑i ki

(2)

where n = 3 means the spatial dimension of the crystal and d is the center-to-center distance between adjacent molecules. The inverse of the rate constant 1/k corresponds to the hopping time between adjacent molecules. Pi = ki/Σiki represents a probable specific hopping route. In other words, it is a threedimensional averaged diffusion process. One can clearly see that the mobility and electron transfer rate have a linearly proportion. Utilizing this mechanism, one can deduce that the localized electron is only hopping between adjacent molecules. In the present work, the charge transfer reaction is the selfexchange reaction. That is to say, the free energy difference (ΔG°) can be approximately assumed as zero in the transfer process between the initial and final states. As a result, the charge transfer rate can be represented as follows:

designed molecules and carrier mobility of the molecule with better performance as representation whose charge transport properties was investigated as well.

k=

2. COMPUTATIONAL DETAILS The density functional theory (DFT)13 method at the PBE0 level with the 6-31G(d) basis set was used for the optimization of all the investigated molecules. The reason was consistent with our previous work14−18 and the reports by Jacquemin et al.19−22 in which the PBE0 was proven to be a method of choice for systems bearing sulfur atoms. Thus the PBE0/631G(d) method was used for all of the geometry optimization in our work. Time-dependent DFT (TD-DFT) calculations at the PBE0/6-31+G(d,p) level were used to obtain the absorption spectra and some account of electron correlation for all of the designed molecules. Generally, the charge transport can be considered as a hopping process in the organic solid, which can be evaluated by the Marcus model. According to the Einstein relation, the carrier mobility can be obtained on the basis of the following equation: e μ= D kBT (1)

V2 ℏ

⎛ π λ ⎞ exp⎜ − ⎟ λkBT ⎝ 4kBT ⎠

(3)

where T is the temperature, kB represents the Boltzmann constant, λ means the reorganization energy due to geometric relaxation accompanying charge transfer, and V corresponds to the electronic coupling matrix element (transfer integral) between the two adjacent species largely dictated by orbital overlap. From eq 3, one can find that the charge transfer rates are dependent on two key parameters: (i) λ, which should be small, and (ii) V, which should be maximized for effective transport. Recently, the B3LYP/6-31G(d,p) functional was successfully used to calculate charge transport parameters for thiophene derivatives.24−27 The reorganization energies for electrons (λe) and holes (λh) of molecules were calculated at the B3LYP/6-31G(d,p) level on the basis of the single point energy.28,29 The reorganization energy is composed of two parts, internal reorganization energy (λint) and external reorganization energy (λext). λint is a measure of the fast change in the molecular geometry;30 λext represents the effect of the polarized medium in the surrounding medium. In this work, the designed molecules are candidates for donors of solar cells in the solid film; the dielectric constants of their media are low.31 The predicted values of the external reorganization energy are small, which are much smaller than their internal parts in pure

where D represents the diffusion constant. If the phenomenon of charge transfer is assumed as a homogeneous random walk, then the diffusion constant can be evaluated as follows:23 3222



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organic condensed phases.32−35 In addition, λint and charge transfer rate have a clear correlation as previous works reported.30,36,37 Thus, we mainly study the λint of the isolated active organic π-conjugated systems, ignoring the environmental changes and relaxation in this work. Hence, the λe and λh can be defined by eqs 4 and 5:31 λe = [E0− − E−] + [E−0 − E0]

(4)

λh = [E0+ − E+] + [E+0 − E0]

(5)

E0+

−

where (E0 ) is the energy of the cation (anion) calculated with the optimized structure of the neutral molecule. Similarly, E+ (E−) represents the energy of the cation (anion) calculated with the optimized cation (anion) structure, and E+0 (E−0) corresponds the energy of the neutral molecule calculated at the cationic (anionic) state. Finally, E0 is the energy of the neutral molecule at ground state. In order to predict the transfer integral, the single-crystal structures were used to generally all of the possible nearest neighboring intermolecular hopping pathways. Through a direct approach evaluating the electronic coupling between two adjacent molecules, the electronic coupling matrix element is obtained. For the hole (electron) transport, the coupling between frontier orbitals of two adjacent molecules can be represented as follows:38,39 Figure 1. The FMOs of phenyl-cored molecules with thiophene branches.

0

Vij = ϕ10 F ̂ ϕ20

(6)

Vij is the transfer integral, ϕ01 represents the unperturbed frontier orbital of molecule 1, ϕ02 corresponds to molecule 2 in the dimer. F̂0 is the Kohn−Sham−Fock operator of the dimer obtained with the unperturbed density matrix. F̂0 is evaluated by the molecular orbitals and density matrix of the two individual molecules, which can be separately studied by using the standard self-consistent field procedure. The pw91pw91/631G(d) method was employed to calculate the transfer integral. This method gave a reasonable description for the intermolecular coupling term previously.24,40−42 The molecular crystal structure was predicted by the Polymorph module of Materials Studio software package.43 The Compass force field was used for the prediction. van der Waals and Coulomb interactions were calculated by using the Ewald summation method with a cutoff of 6 Å, and the Ewald accuracy tolerance was set to 0.0001 kcal·mol−1. All calculations for individual molecules were carried out with the aid of the Gaussian 03.44

of p-1t-2t-3t-4t are mainly centered on the core and two arms (1, 4-positions). These results reveal that different substituted positions significantly affect the distribution patterns of FMOs for phenyl-cored molecules with three and four thiophene branches. The meta-substitution causes poor conjugation. It is worth noting that unlike linear oligomers where thiophene units had anti conformations leading to a planar structure of the oligothiophene chain,45 the most stable conformation of branched molecules including thiophene results in the nonplanar geometry due to steric hindrances. The nonplanar geometry leads to a poorly conjugated system, and it would give a blue shift for the absorption spectrum. As shown in Figure 2, for two arms molecules, the HOMO energies are in the order of p-1t-3t < p-1t-2t < p-1t-4t, and the sequence of LUMO energies is p-1t-2t > p-1t-3t > p-1t-4t. Thus, the Eg values are in the order of p-1t-3t > p-1t-2t > p-1t4t. It implies that the molecule of meta-substitution has larger Eg value than that of ortho- or para-substitution. It is due to the meta-substitution induced poor conjugation in comparison with

3. RESULTS AND DISCUSSION 3.1. Phenyl-Cored Molecules with Thiophene Branches. Scheme S1 (see the Supporting Information, SI) shows the models of phenyl-cored molecules with thiophene branches in our study. 3.1.1. Frontier Molecular Orbitals. The FMOs sketches of the branched molecules are shown in Figure 1. For two arms molecules, strong delocalization is presented in the FMOs of the entire molecules. It shows that the different substituted positions exert slight effects on the distribution patterns of FMOs for phenyl-cored molecules with two thiophene branches. For three arms molecules, the electronic cloud distribution of HOMO is mainly delocalized on the two arms of p-1t-2t-3t (1,2-positions), on the whole molecule of p-1t-2t-4t. The orbital in the LUMO mainly resides at the core and two arms of p-1t-2t-3t (1,2-positions). The LUMO of p-1t-2t-4t is localized on the core, two arms (1,4-positions) and partially on the third one (2-position). For four arms molecules, the FMOs

Figure 2. Evaluation of HOMO and LUMO energies for phenyl-cored molecules with thiophene branches. 3223



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cell material with intense broad absorption spectra. In addition, most of the transitions correspond to the excitation from the HOMO to the LUMO. 3.1.3. Reorganization Energy. Understanding the relationship between molecular structure and charge transport property of a material is a key point for providing good candidates for solar cell devices design. To compare the charge transport properties of the investigated molecules, we calculated the reorganization energies associated with different geometries of two states (anion and cation). The calculated reorganization energies for holes (λh) and electrons (λe) according to eqs 4 and 5, respectively, are listed in Table 2.

para-substitution, which is also in good agreement with earlier experimental observation46 and theoretical investigation (at the B3LYP/6-31G(d) level)31 for similar systems. For three arms molecules, the HOMO energy of p-1t-2t-3t is equal to that of p-1t-2t-4t, and the LUMO energy of p-1t-2t-3t is larger than that of p-1t-2t-4t. Hence, their Eg values are in the order of p1t-2t-3t > p-1t-2t-4t. The Eg value of p-1t-2t-3t is similar with that of p-1t-2t, which shows that increasing the 3-position substituent slightly affects the Eg value due to the steric hindrances preventing the effective conjugation. For four arms molecules, the HOMO (LUMO) energy of p-1t-2t-3t-4t is higher (lower) than that of p-1t-2t-3t. Therefore, the prediction of Eg value of p-1t-2t-3t-4t is lower than that of p-1t-2t-3t. In addition, the HOMO and LUMO energies are similar for p-1t2t and p-1t-2t-3t as well as p-1t-4t and p-1t-2t-3t-4t, respectively. This can be attributed to their similar distribution patterns of the FMOs. 3.1.2. Absorption Spectra. The absorption region (R denotes for the difference of the longest and shortest wavelength values with oscillator strength larger than 0.01 considering the first fifteen excited states, see Table S1 of the SI), the longest wavelength of absorption spectrum (λmax), and corresponding oscillator strength (f) values of phenyl-cored molecules with thiophene branches as shown in Scheme S1 (SI) were calculated and the results are listed in Table 1. The

Table 2. Calculated λe and λh (eV) for Phenyl-Cored Molecules with Thiophene Branches

species

p-1t-3t p-1t-4t p-1t-2t-3t p-1t-2t-4t p-1t-2t-3t-4t

assignment

λmax (nm)

f

R (nm)

H-1→L+1 (−0.10) H→L (0.66) H-1→L (0.50) H→L+1 (0.42) H-1→L+1 (−0.12) H→L (0.65) H→L (0.65) H→L (0.65) H→L (0.65)

438.96

0.64

56.54

415.32

1.93

40.36

480.69

2.30

123.25

437.62 455.26 463.80

0.73 1.34 1.60

41.90 71.62 75.12

λe

λh

0.300 0.230 0.244 0.171 0.294 0.238

0.209 0.209 0.255 0.155 0.273 0.197

It is well-known that the smaller the reorganization energy, the larger the charge transfer rate becomes.47 As shown in Table 2, the differences between λe and λh values of phenylcored molecules (except p-1t-2t) with thiophene branches are in the region of 0.011−0.041 eV, respectively. As a consequence, these materials are potential ambipolar charge transport materials (electron and hole) under the proper operating conditions for solar cells. The values of λe for p-1t-3t and p-1t-4t are similar, and they are smaller than that of p-1t2t. The values of λh for p-1t-2t and p-1t-3t are the same, and they are smaller than that of p-1t-4t. For three arms molecules, the values of λe and λh for p-1t-2t-3t are smaller than those of p-1t-2t-4t, respectively. It reveals that the 3-position substituent results in larger charge transfer rate than 4-position substituent for phenyl-cored molecules with three thiophene branches in the same environment. For four arms molecules, the λe and λh values of p-1t-2t-3t-4t are larger than those of p-1t-2t-3t, respectively. It shows that increasing the 3-position substituent will decrease the charge transfer rate (considering the same environment). Among these molecules, p-1t-2t-3t owns the largest charge transfer rate ignoring any environmental relaxation and changes. It can be a good ambipolar charge transport material. 3.2. Thiophene-Cored Molecules with Thiophene Branches. The structures of thiophene-cored molecules with thiophene branches in our calculations are displayed in Scheme S2 (SI). 3.2.1. Frontier Molecular Orbitals. From Figure 3, one can observe that, for two arms molecules, the distribution patterns of FMOs for t-2t-3t and t-2t-5t are spread over the whole molecules. For t-2t-4t, the HOMO mainly delocalizes on the entire molecule, while its LUMO mainly localizes on the core and one arm (2-position). For three arms molecules, the HOMO of t-2t-3t-4t is distributed on the thiophene core and two arms (2,4-positions), and its LUMO is centralized on the thiophene core and two arms (3,4-positions). The HOMO of t2t-3t-5t is spread on the whole molecule, and its LUMO is localized on the thiophene core and two arms (2,5-positions), and partially on the third one (3-position). One can see that t-

Table 1. Comparative Study of Predicted R, λmax, and Corresponding f for Phenyl-Cored Molecules with Thiophene Branches Obtained at the TD-PBE0/631+G(d,p)//PBE0/6-31G(d) Level p-1t-2t

species p-1t-2t p-1t-3t p-1t-4t p-1t-2t-3t p-1t-2t-4t p-1t-2t-3t-4t

results presented in Table 1 show that, for two arms molecules, the λmax values are in the order of p-1t-4t > p-1t-2t > p-1t-3t, which is in excellent agreement with the corresponding reverse order of E g values displayed in section 3.1.1. Their corresponding f values are in the sequence of p-1t-4t > p-1t3t > p-1t-2t. The order of their R values are predicted in the decreasing order of p-1t-4t > p-1t-2t > p-1t-3t. It indicates that the meta-substitution results in smaller λmax and R value than ortho- or para-substitution. For three arms molecules, the λmax and f values are in the same order of p-1t-2t-4t > p-1t-2t-3t, the R value of p-1t-2t-3t is larger than that of p-1t-2t-4t. The λmax values are similar for p-1t-2t and p-1t-2t-3t as well as p-1t-4t and p-1t-2t-4t, respectively. It confirms the deduction in section 3.1.1. However, their R values are not identical. This can be reasonably attributive to their similar distribution patterns of FMOs and Eg energies, but the structures of molecules and the assignments of transition are different. For four arms molecules, the λmax, f, and R values of p-1t-2t-3t-4t are similar with those of p-1t-2t-4t. As a result, among phenylcored molecules with thiophene branches, p-1t-4t owns the largest λmax, f, and R values. Thus, p-1t-4t could be used as solar 3224



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prohibiting the effective conjugation. The Eg value of t-2t-3t-5t is smaller than that of t-2t-3t, which shows that the 5substitution is responsible for the smaller Eg value. The Eg value of t-2t-3t-4t-5t is smaller than that of t-2t-5t. The Eg value of each thiophene-cored molecule with thiophene branches is smaller than that of the corresponding phenyl-cored molecule with thiophene branches. It reveals that the thiophene-core can decrease the Eg value in comparison with the phenyl-core when the branches are the same. 3.2.2. Absorption Spectra. The R (considering the first fifteen excited states, see Table S2 of the SI), λmax, and corresponding f values of thiophene-cored molecules as shown in Scheme S2 (SI) were summarized in Table 3. For two arms Table 3. Comparative Study of Predicted R, λmax, and Corresponding f for Thiophene-Cored Molecules with Thiophene Branches Obtained at the TD-PBE0/631+G(d,p)//PBE0/6-31G(d) Level assignment

λmax (nm)

f

R (nm)

H→L (0.66) H-1→L (−0.18) H→L (0.54) H→L+1 (0.31) H→L (0.65) H-1→L (0.28) H→L (0.58) H→L+2 (0.14) H→L (0.66) H→L (0.66)

468.74 446.63

0.77 1.43

94.74 59.59

529.03 446.72

2.30 0.97

170.00 54.89

509.55 530.49

1.48 1.38

112.12 95.30

species t-2t-3t t-2t-4t

t-2t-5t t-2t-3t-4t

Figure 3. The FMOs of thiophene-cored molecules with thiophene branches.

2t-3t-4t shows strong charge transport properties from one part to another for the HOMO−LUMO transition. For four arms molecules, the HOMO and LUMO of t-2t-3t-4t-5t mainly concentrate on the two arms (1,4-positions) and minor contribution from the other two arms (2,3-positions). Figure 4 clearly shows that for two arms molecules, the FMOs values are similar for t-2t-3t and t-2t-4t. The HOMO

t-2t-3t-5t t-2t-3t-4t-5t

molecules, the λmax and R values are in the order of t-2t-4t < t2t-3t < t-2t-5t, which is just the reverse of the corresponding order of Eg values as shown in 3.2.1. Their corresponding f values are in the sequence of t-2t-3t < t-2t-4t < t-2t-5t. For three arms molecules, the R, λmax, and corresponding f values of t-2t-3t-4t are smaller than those of t-2t-3t-5t. The λmax value of t-2t-3t-4t-5t is similar with that of t-2t-5t, and the R and f value of t-2t-3t-4t-5t are smaller than those of t-2t-5t. The λmax and R values of thiophene-cored molecules with thiophene branches are larger than those of corresponding phenyl-cored ones, because of the smaller Eg value for thiophene-cored molecules with thiophene branches in comparison with the corresponding phenyl-cored ones. It is worth noting that, among thiophenecored molecules with thiophene branches, t-2t-4t has the smallest λmax value, and t-2t-3t-4t-5t has the largest one. Moreover, t-2t-5t shows the most intense broad absorption spectrum, and t-2t-3t-4t has the narrowest R. Therefore, t-2t-5t is the best candidate with intense broad absorption spectra for solar cell material among these molecules. 3.2.3. Reorganization Energy. As listed in Table 4, for two arms molecules, the predicted λe and λh values are in the same

Figure 4. Evaluation of HOMO and LUMO energies for thiophenecored molecules with thiophene branches.

Table 4. Calculated λe and λh (eV) for Thiophene-Cored Molecules with Thiophene Branches

(LUMO) energies of t-2t-3t and t-2t-4t are lower (higher) than that of t-2t-5t. Thus, their Eg values are in the order of t-2t-4t > t-2t-3t > t-2t-5t. It implies that the molecule of 2,4substitutions has larger Eg value than that of 2,3-substitutions or 2,5-substitutions. For three arms molecules, the HOMO (LUMO) energy of t-2t-3t-4t is lower (higher) than that of t2t-3t-5t. Therefore, the Eg value of t-2t-3t-4t is larger than that of t-2t-3t-5t. The Eg value of t-2t-3t-4t is close to that of t-2t-4t, which indicates that increasing the 3-substituted branch has a slight effect on the Eg value due to the steric hindrances, 3225

species

λe

λh

t-2t-3t t-2t-4t t-2t-5t t-2t-3t-4t t-2t-3t-5t t-2t-3t-4t-5t

0.328 0.154 0.217 0.306 0.310 0.211

0.264 0.220 0.250 0.245 0.295 0.249



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order of t-2t-3t > t-2t-5t > t-2t-4t. It indicates that 2,3substituted or 2,5-substituted molecule presents lower charge transfer rate compared with the 2,4-substituted molecule for thiophene-cored molecules with thiophene branches (considering the same environment). For three arms molecules, their λe and λh values are similar, respectively. Moreover, the differences between λe and λh of thiophene-cored molecules with thiophene branches are in the region of 0.015−0.066 eV, respectively, which is so small that these molecules can act as potential ambipolar charge transport materials (electron and hole) under the proper operating conditions for photovoltaic devices. 3.3. Phenyl-Cored Molecules with Thiophene and Thienylenevinylene Branches. The structures of phenylcored molecules with thiophene and thienylenevinylene branches in our calculations are displayed in Scheme S3 (SI). 3.3.1. Frontier Molecular Orbitals. As shown in Figure 5, for two arms molecules, the FMOs are mainly delocalized on the

Figure 6. Evaluation of HOMO and LUMO energies for phenyl-cored molecules with thiophene and thienylenevinylene branches.

energies are in the sequence of p-1t-2e > p-1t-3e > p-1t-4e. Their Eg values are in the order of p-1t-3e > p-1t-2e > p-1t-4e. It implies that the molecule of meta-substitutions has the larger Eg value than that of ortho-substitutions or para-substitutions. For three arms molecules, the HOMO and LUMO energies of p-1t-2e-3t are higher than those of p-1t-2e-4t, respectively. The Eg value of p-1t-2e-3t is larger than that of p-1t-2e-4t. The Eg value of p-1t-2e-3t is close to that of p-1t-2e, which indicates that increasing the 3-position thiophene branch has a slight effect on the Eg value due to the steric hindrances which prohibits the effective conjugation. The four arms molecule p1t-2e-3e-4t has higher HOMO and LUMO energies and smaller Eg value than those of p-1t-2e-4t. It reveals that adding the 3-position thienylenevinylene branch can increase the FMOs energies and decrease Eg value. In addition, phenylcored molecules with thiophene and thienylenevinylene branches have higher HOMO energies, lower LUMO energies, and smaller Eg values than those of corresponding phenyl-cored molecules with thiophene branches. Hence, adding the thienylenevinylene branch can increase HOMO energies, decrease HOMO energies and Eg values in comparison with the thiophene branch when cores are the same. 3.3.2. Absorption Spectra. The predicted λmax and corresponding f for phenyl-cored molecules with thiophene and thienylenevinylene branches are shown in Table 5. For two Table 5. Comparative Study of Predicted λmax, and Corresponding f for Phenyl-Cored Molecules with Thiophene and Thienylenevinylene Branches Obtained at the TD-PBE0/6-31+G(d,p)//PBE0/6-31G(d) Level

Figure 5. The FMOs of phenyl-cored molecules with thiophene and thienylenevinylene branches.

whole molecule for p-1t-2e and p-1t-4e. The HOMO of p-1t3e mainly resides at the phenyl core, the thienylenevinylene branch, and the partial thiophene branch. Its LUMO is mainly localized on the phenyl core and the thienylenevinylene branch. For three arms molecules, the orbitals in the HOMOs mainly resides at the phenyl core and two arms for p-1t-2e-3t (2, 3positions), while its LUMO is localized on the phenyl core, the thienylenevinylene branch and partially on two thiophene branches. The FMOs are delocalized on the whole molecule for p-1t-2e-4t. For four arms molecules, the FMOs are distributed in the phenyl core and thienylenevinylene branches. These results reveal that different positions of arms influence significantly on distributions of FMOs. Figure 6 shows FMOs energies for phenyl-cored molecules with thiophene and thienylenevinylene branches. It can be clearly found that for two arms molecules, the HOMO energies are in the order of p-1t-4e > p-1t-2e > p-1t-3e, their LUMO

species p-1t-2e

p-1t-3e

p-1t-4e p-1t-2e-3t p-1t-2e-4t p-1t-2e-3e-4t

3226

assignment

λmax

f

HOMO-1−LUMO+1 (−0.12) HOMO-1−LUMO (0.13) HOMO−LUMO (0.62) HOMO−LUMO+1 (−0.14) HOMO-1−LUMO+1 (−0.26) HOMO-1−LUMO (0.31) HOMO−LUMO (0.46) HOMO−LUMO+1 (0.19) HOMO−LUMO (0.64) HOMO-1−LUMO+1 (0.10) HOMO-1−LUMO+1 (0.11) HOMO−LUMO (0.65) HOMO−LUMO (0.65) HOMO−LUMO (0.66) HOMO−LUMO+1 (0.10)

460.35

0.96

443.07

2.40

504.97

2.87

470.28

0.41

480.82 489.06

1.12 0.32



Article

arms molecules, the prediction of λmax values is in the order of p-1t-4e > p-1t-2e > p-1t-3e, which is in excellent agreement with the corresponding reverse order of Eg values displayed in section 3.3.1. Their corresponding f values are in the sequence of p-1t-4e > p-1t-3e > p-1t-2e. For three arms molecules, the λmax and f values of p-1t-2e-4t are larger than those of p-1t-2e3t. The four arms molecule p-1t-2e-3e-4t had larger λmax and smaller f values than those of p-1t-2e-4t, which indicates that the 3-position thienylenevinylene branch can result in a red shift in the absorption spectra. Moreover, the λmax values of phenyl-cored molecules with thiophene and thienylenevinylene branches are larger than corresponding phenyl-cored molecules with thiophene branches due to their smaller Eg values. 3.3.3. Reorganization Energy. The λe and λh values of phenyl-cored molecules with thiophene and thienylenevinylene branches are listed in Table 6. For two arms molecules, the λe Table 6. Calculated λe and λh (eV) for Phenyl-Cored Molecules with Thiophene and Thienylenevinylene Branches species

λe

λh

p-1t-2e p-1t-3e p-1t-4e p-1t-2e-3t p-1t-2e-4t p-1t-2e-3e-4t

0.309 0.161 0.238 0.293 0.231 0.247

0.221 0.165 0.247 0.174 0.204 0.219

Figure 7. The FMOs of thiophene-cored molecules with thiophene and thienylenevinylene branches.

vinylene branches. These results reveal that different positions of arms have significant effects on distributions of FMOs. Figure 8 shows FMOs energies for thiophene-cored molecules with thiophene and thienylenevinylene branches.

and λh values of p-1t-3e are smaller than those of p-1t-2e and p-1t-4e, respectively. It reveals that meta-substitution results in the higher charge transfer rate than that of ortho- or parasubstitution, ignoring any environmental relaxation and changes. For three arms molecules, the λe value of p-1t-2e-3t is larger than that of p-1t-2e-4t, and its λh is smaller than that of p-1t-2e-4t. Their λe and λh values are both smaller than those of p-1t-2e. It indicates that increasing the 3- or 4-position thiophene branch can results in the higher charge transfer rate in the same environment. The four arms molecule p-1t-2e-3e4t has larger λe and λh values than those of p-1t-2e-4t. It shows that increasing the 3-position thienylenevinylene branch can result in the lower charge transfer rate considering the same environment. The differences between λe and λh values of phenyl-cored molecules with thiophene and thienylenevinylene branches (except p-1t-2e and p-1t-2e-3t) are in the region of 0.004−0.028 eV, respectively. As a consequence, these materials are potential ambipolar charge transport materials. 3.4. Thiophene-Cored Molecules with Thiophene and Thienylenevinylene Branches. The structures of phenylcored molecules with thiophene and thienylenevinylene branches in our calculations are displayed in Scheme S4 (SI). 3.4.1. Frontier Molecular Orbitals. As shown in Figure 7, for two arms molecules, the FMOs are mainly delocalized on the whole molecule for t-2t-3e and t-2t-5e. The HOMO of t-2t-4e is mainly resided at the whole molecule, and its LUMO is mainly localized on the phenyl core and the thiophene branch. For three arms molecules, the FMOs mainly reside at the phenyl core and two arms for t-2t-3e-4t (1,2-positions). The FMOs are delocalized on the whole molecule for t-2t-3e-5t. For four arms molecules t-2t-3e-4e-5t, the HOMO is distributed in the whole molecule, and its LUMO is mainly localized on the phenyl core, thiophene branches, and partially on thienylene-

Figure 8. Evaluation of HOMO and LUMO energies for thiophenecored molecules with thiophene and thienylenevinylene branches.

One can find that for two arms molecules, the HOMO energies are in the order of t-2t-5e > t-2t-3e > t-2t-4e, their LUMO energies are in the sequence of t-2t-4e > t-2t-3e > t-2t-5e. Thus, their Eg values are in the order of t-2t-4e > t-2t-3e > t-2t5e. It implies that the molecule of 2, 4-substitutions has larger Eg value than that of 2, 3-substitutions or 2, 5-substitutions. For three arms molecules, the HOMO and LUMO energies of t-2t3e-4t are lower and higher than those of t-2t-3e-5t, respectively. Therefore, the Eg value of t-2t-3e-4t is larger than that of t-2t-3e-5t. The Eg value of t-2t-3e-4t is close to that of t-2t-3e, which indicates that increasing the 4-position thiophene branch has slight effect on Eg value due to the steric hindrances prohibiting the effective conjugation. The Eg value of t-2t-3e-5t is smaller than that of t-2t-3e, which shows that the 5-position thiophene branch is responsible for smaller Eg value. The four arms molecule t-2t-3e-4e-5t has lower 3227



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Table 8. Calculated λe and λh (eV) for Thiophene-Cored Molecules with Thiophene and Thienylenevinylene Branches

HOMO, higher LUMO energies, and a larger Eg value than those of t-2t-3e-5t. It reveals that increasing the 4-position thienylenevinylene branch can increase the Eg value. Additionally, thiophene-cored molecules with thiophene and thienylenevinylene branches have higher HOMO energies, lower LUMO energies, and smaller Eg values than those of corresponding phenyl-cored molecules with thiophene and thienylenevinylene branches (except t-2t-4e). It reveals that the thiophene core can increase HOMO energies, decrease LUMO energies and Eg values in comparison with the phenyl core when the branches are the same. Thiophene-cored molecules with thiophene and thienylenevinylene branches have higher HOMO energies, lower LUMO energies, and smaller Eg values than those of corresponding thiophene-cored molecules with thiophene branches. It indicates that the thienylenevinylene branch can increase HOMO energies, decrease LUMO energies and Eg values in comparison with the thiophene branch when the cores are the same. 3.4.2. Absorption Spectra. The predicted λmax and corresponding f for thiophene-cored molecules with thiophene and thienylenevinylene branches are shown in Table 7. For two

species

t-2t-5e t-2t-3e-4t t-2t-3e-5t t-2t-3e-4e-5t

assignment

λabs

f

HOMO−LUMO (0.65) HOMO-1−LUMO (0.19) HOMO−LUMO (0.54) HOMO−LUMO+1 (0.33) HOMO−LUMO (0.64) HOMO−LUMO (0.65) HOMO−LUMO (0.65) HOMO−LUMO (0.66)

500.57 460.28

1.12 1.50

549.84 493.24 538.73 532.98

2.77 0.88 1.30 0.93

λe

λh

t-2t-3e t-2t-4e t-2t-5e t-2t-3e-4t t-2t-3e-5t t-2t-3e-4e-5t

0.351 0.161 0.235 0.340 0.266 0.216

0.269 0.198 0.258 0.220 0.230 0.227

is larger than that of t-2t-3e-5t, and its λh is smaller than that of t-2t-3e-5t. Their λe and λh values are both smaller than those of t-2t-3e. It indicates that increasing the 4- or 5-position thiophene branch can result in the higher charge transfer rate in the same environment. The four arms molecule t-2t-3e-4e-5t has smaller λe and λh values than those of t-2t-3e-5t. It shows that increasing the 4-position thienylenevinylene branch can lead to the higher charge transfer rate for three arms molecules considering the same environment. The differences between λe and λh values of thiophene-cored molecules with thiophene and thienylenevinylene branches (except t-2t-3e and t-2t-3e-4t) are in the region of 0.011−0.037 eV, respectively, showing that they are potential ambipolar charge transport materials. 3.5. Properties of 1−5 As the Most Promising Candidates. Considering the optical and electric properties for designed molecules above, the rational way to design molecules toward charge transport materials should possess 2,3,5-substituted thiophene core with longer thiophene and thienylenevinylene side fragments (1−5) as shown in Scheme 2. The 3,5-positions substituent contributes to the higher charge transfer rate. However, the 2,5-position substituent, the thiophene core, and thienylenevinylene fragments contribute to the better optical and stability properties. The HOMO, LUMO, Eg, λmax, λe, and λh values of 1−5 were investigated, and the corresponding values are listed in Tables S3 and S4 (SI). The results indicate that along with molecular length increasing, the values are increasing for HOMO and λmax and decreasing for LUMO, Eg, λe, and λh. Then, we calculated the mobility of 1 as representation to study its charge transport property. The crystal structures of 1 predicted by Material Studio are shown in Figure 9. The crystal structures of 1 with two lowest total energies belong to space groups Pna21 and P212121. Thus, we predict the mobility of 1 in these two space groups. The total energies and lattice constants for the rest investigated space groups are listed in the Table S5 (SI). For the crystal structures, we arbitrarily choose one molecule as the initial position for the charge to diffuse. The intermolecular transfer integrals with all of the adjacent molecules in a dimer model are evaluated. Figure 10 shows the most important pathways (dimers). The transfer integrals of 1 for holes and electrons within the two different space groups are calculated, and the results are listed in Table 9. The data in Table 9 demonstrate that the electronic coupling is determined by the relative distance and orientations of the interacting molecules.48 Furthermore, 1 possesses the largest absolute electron coupling value in pathways 1 and 2 and the largest absolute hole coupling value in pathway 6 for Pna21, and pathways 1 and 2 for P212121 space group. It reveals that the orientation of the interacting molecules is the key factor of hole or electron coupling for 1, because the cofacial stacking

Table 7. Comparative Study of Predicted λmax, and Corresponding f for Thiophene-Cored Molecules with Thiophene and Thienylenevinylene Branches Obtained at the TD-PBE0/6-31+G(d,p)//PBE0/6-31G(d) Level t-2t-3e t-2t-4e

species

arms molecules, the λmax values are in the order of t-2t-5e > t2t-3e > t-2t-4e, which is in excellent agreement with the corresponding reverse order of Eg values displayed in section 3.4.1. Their corresponding f values are in the sequence of t-2t5e > t-2t-4e > t-2t-3e. For three arms molecules, the predictions of λmax and f values show the same decreasing order of t-2t-3e-5t > t-2t-3e-4t. The four arms molecule t-2t3e-4e-5t has smaller λmax and f values than those of t-2t-3e-5t, which indicates increasing the 4-position thienylenevinylene branch can result in a blue shift in the absorption spectra. Moreover, the λmax values of thiophene-cored molecules with thiophene and thienylenevinylene branches are larger than corresponding phenyl-cored molecules with thiophene and thienylenevinylene branches due to their smaller Eg values, respectively. The λmax values of thiophene-cored molecules with thiophene and thienylenevinylene branches are larger than corresponding thiophene-cored molecules with thiophene branches because of their smaller Eg values. 3.4.3. Reorganization Energy. Calculated λe and λh values for thiophene-cored molecules with thiophene and thienylenevinylene branches are listed in Table 8. For two arms molecules, the λe and λh values of t-2t-4e are smaller than those of t-2t-3e and t-2t-5e. It reveals that 2,4-substitutions result in the higher charge transfer rate than that of 2,3- or 2,5substitutions, ignoring any environmental relaxation and changes. For three arms molecules, the λe value of t-2t-3e-4t 3228



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Figure 9. Herringbone structures of 1 in different space groups.

Figure 10. Crystal structures and hopping routes of 1 in different space groups.

these two different space groups. It shows that different space groups lead to different mobility values, that is to say, the stacking structure is the most important factor for molecular mobility property.

Table 9. Center−Center Distance and the Corresponding Hole and Electron Coupling Between the Dimer in All of the Nearest Neighbor Pathways for 1 in Different Space Groups [T = 298 K, in cm2/(V s)] pathway Pna21

1 2 3 4 5 6 drift mobility pathway

P212121

1 2 3 4 5 6 7 8 drift mobility

distance (Å) 5.82 5.82 23.96 23.24 23.24 23.96

distance (Å) 8.39 8.39 21.50 21.50 21.50 21.50 24.55 24.55

electron coupling (eV) 1.60 1.60 −6.11 −6.11 6.62 5.91 2.31

× × × × × × ×

10−2 10−2 10−5 10−5 10−4 10−4 10−2

electron coupling (eV) −2.00 −2.00 1.00 −6.01 −5.25 −5.25 1.00 1.00 7.37

× × × × × × × × ×

10−3 10−3 10−5 10−4 10−5 10−5 10−5 10−5 10−4

hole coupling (eV) −8.60 −8.60 −4.81 −4.81 −5.15 −1.10 1.53

× × × × × × ×

4. CONCLUSIONS In the present work, we report a theoretical investigation of the optical and electronic response of the branched molecules for photovoltaic applications. The results show that molecular topology play a key role in changing the FMOs energies, and the derivatives with meta-substituted phenyl-core (2,4thiophene core) will increase the Eg value, which is due to the poor conjugation. The molecules with the thiophene core and thiophene and thienylenevinylene branches (vs phenyl-core and thiophene branch) have a red shift in absorption spectra. In addition, the ortho- or para-substituted phenyl-cored (2,3- or 2,5-substituted thiophene-core) molecule contributes a red shift for the absorption spectra in comparison with the metasubstituted (2, 4-substituted thiophene-core) one. The reorganization energy results reveal that meta-substituted phenyl core or 2,4-substituted thiophene-core will increase the charge transfer rates for molecules in the same environment. On the basis of investigated results, we predicted the properties of 1−5 as the most promising candidates. The electron mobility value of 1 in space group Pna21 is the largest [2.31 × 10−2 cm2/(V s)] and the hole mobility value of 1 in space group P212121 is the largest [5.93 × 10−2 cm2/(V s)]. Using theoretical methodologies, it is possible to predict reasonable optical and electronic properties of the branched derivatives for organic solar cells.

10−4 10−4 10−6 10−6 10−4 10−3 10−3

hole coupling (eV) −1.31 −1.31 −2.43 1.200 −4.29 −4.31 −2.43 −2.43 5.93

× × × × × × × × ×

10−2 10−2 10−6 10−3 10−6 10−6 10−6 10−6 10−2

structure is expected to provide more efficient orbital overlap leading to the most efficient charge transfer route.48 The value of electron mobility for 1 in Pna21 and the value of hole mobility for 1 in P212121 space group are the largest value in 3229



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ASSOCIATED CONTENT

S Supporting Information *

The schemes and tables not given in the main text. This material is available free of charge via the Internet at http:// pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial supports from the NSFC (No. 21173037 & 21274017) and Science Foundation for Young Teachers of Jilin Agricultural University (No. 201219) are gratefully acknowledged.

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Photophysical Properties of Phenyl- or Thiophene-Cored

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