A theoretical study on photophysical properties of triphenylamine-cored molecules with naphthalimide arms and different π-conjugated bridges as organic solar cell materials.

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Cite this: DOI: 10.1039/c4cp04394d

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A theoretical study on photophysical properties of triphenylamine-cored molecules with naphthalimide arms and different p-conjugated bridges as organic solar cell materials† R. F. Jin*a and Y. F. Changb A series of D–p–A star-shaped molecules with triphenylamine (TPA) as a core, 1,8-naphthalimide (NI) derivatives as end groups, and different p-bridges have been designed to explore their optical, electronic, and charge transport properties as organic solar cell (OSC) materials. The calculation results showed that the star-shaped molecules can lower the material band gap and extend the absorption spectrum towards longer wavelengths. The designed molecules own the longest wavelength of absorption spectra, oscillator strength, and absorption region values. Our results suggest that the designed molecules are expected to be promising candidates for OSC materials. Additionally, the molecules with ethyne, thiophene, benzo[c][1,2,5]thiadiazole (BTA), and 2,3-dihydrothieno[3,4-b][1,4]dioxine (DTD) as p-bridges and

Received 29th September 2014, Accepted 23rd October 2014 DOI: 10.1039/c4cp04394d

4-pyridne, 4-aniline, and H in NI fragments have better hole- and electron transporting balance and can act as nice ambipolar materials. The values of hole mobility of molecules with ethyne as a p-bridge and NI as an end group for Pna21 and P21/c are 5.30 103 and 1.27 102 cm2 V1 s1, respectively. On the basis of the investigated results, we suggest that molecules under investigation are suitable donors

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of [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) and its derivatives are acceptors of solar cells.

1. Introduction Organic solar cells (OSCs) have become a promising alternative strategy to relieve the global energy crisis due to their advantages of low manufacturing cost, lightweight, compatibility with flexible substrates, and coatings applicable to large areas.1 Since the pioneering work of Tang on donor–acceptor bilayerplanar heterojunction solar cells,2 the power conversion efficiencies (PCEs) of OSCs have been steadily increased by using novel materials and different device structures.3 The PCEs of solution-processed polymer bulk heterojunction (BHJ) solar cells have exceeded 10% recently.4 Unfortunately, the performance of polymeric materials depends on, e.g., their regio-regularity and polydispersity, making their synthesis and purification difficult and scarcely reproducible.5 As another branch of the OSCs, solution-processed small-molecule OSCs have also attracted increasing attention. Compared with polymer solar cells, small molecule based solar cells have advantages in terms of well-defined structures, accurate molecular weights, no end

a

College of Chemistry and Chemical Engineering, Chifeng University, Chifeng 024000, China. E-mail: [email protected] b Faculty of Chemistry, Northeast Normal University, Changchun 130024, China † Electronic supplementary information (ESI) available. See DOI: 10.1039/ c4cp04394d

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group contaminants, relatively simple synthesis and purification, easy mass-scale production, and good batch-to-batch reproducibility.6 Furthermore, small molecule organic materials could exhibit a higher charge carrier mobility, as well as their band structure can be tuned more easily to absorb sunlight efficiently. As a consequence, they are well on their way to outperform polymers in photovoltaic applications.7 Therefore, it is believed that small-molecule OSCs are promising for their commercial application in the future. To date, the highest reported PCE of small-molecule OSCs has been over 8%,8 but their overall performance is still significantly behind that of their polymer counterparts. Accordingly, it is still a big challenge for the research community to develop new high efficiency solutionprocessable small-molecule OSCs.9 Designing and synthesizing new materials with a suitable frontier molecular orbital (FMO) energy alignment with [6,6]-phenyl-C61-butyric acid methyl ester (PCBM, an excellent acceptor of organic solar cells10) and its derivatives, a broad absorption region, high and balance charge transfer properties, and high ambient stability are still a great challenge in the manufacture of solar cell devices. Furthermore, a number of studies demonstrated some guidelines to experiments, where useful insights have been provided to help understand the nature of molecules.11 It is well known that the PCEs are determined by the open circuit voltage (Voc), short circuit current ( Jsc), and the fill factor (FF) of the

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OSCs.12 Thus, to achieve high efficiencies, an ideal donor material should have a low energy gap (to harvest more sunlight, which leads to higher Jsc) and a deep highest occupied molecular orbital energy level (to increase the open circuit voltage Voc). Additionally, the high hole mobility is also crucial for the carrier transport to improve the Jsc and the FF.13 Nowadays, among the soluble organic photovoltaic small molecular materials, the donor–p conjugated bridge-acceptor (D–p–A) structured organic compounds have become the most efficient strategy used in the design and synthesis of donor materials.14 This type of molecular structure can lower the material band gap and extend the absorption spectrum towards longer wavelengths. At the same time, the electronic energy levels and band-gaps can be tuned effectively through adjusting the acceptor and donor units, and p-bridge units or lengths.15 Triphenylamine (TPA) is a representative unit to construct star-shaped small molecules. The TPA unit possesses a three dimensional propeller structure that makes the TPA-containing molecules exhibit good solubility. In addition, the TPA-containing molecules have high hole mobility. It has been regarded as a promising core building block for organic photovoltaic (OPV) materials.16 On the other hand, 1,8-naphthalimide (NI) derivatives are considered as the most important building blocks of OPV materials due to their chemical stability, a large Stokes shift, and high fluorescent quantum yield.17 The emission and absorption spectrum is adjustable with the introduction of variable electron-donating groups at this position, such as N-substituted groups.18 The substitution of TPA at the 4-position of naphthalene-derived imides may be a good method to develop novel small-molecule OSC materials with the balance of electronand hole-transport. With the above considerations, in this work, we investigated a series of D–p–A star-shaped molecules with TPA as a core, NI derivatives as end groups, and different conjugate p-bridges (CB) for photovoltaic applications (Scheme 1). The purpose of this molecular architecture is to investigate the relationship between the topologic structure and optical as well as electronic properties resulting in a broad absorption region and a high charge

Scheme 1

Molecular structures of the investigated molecules.


transfer rate, rendering it a good candidate for small-molecule OSC materials. Moreover, the computational results such as the FMOs including the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) energies, the HOMO–LUMO gaps (Eg), reorganization energies as well as the absorption spectra were investigated here. We selected 1a as a representative of our system and investigated its carrier mobility and charge transport properties according to the Marcus model.19

2. Computational methods All calculations have been performed using the Gaussian 09 code.20 Generally, the B3LYP method appeared notably adapted to TPA and NI derivatives.21 In order to testify the validity of the selected approach, we take a D–p–A star-shaped molecule with TPA as a core and dicyanovinyl (DCN) derivatives as end groups (TPA–DHT–DCN) as an example because it possesses a similar structure to our designed molecules. The sketch map of the structure of TPA–DHT–DCN is shown in Fig. S1 of the ESI.† The geometry optimization of TPA–DHT–DCN was carried out by the B3LYP and PBE0 methods using the 6-31G(d,p) basis set. The main geometrical parameters of TPA–DHT–DCN at the PBE0/ 6-31G(d,p) level are similar to those of at the B3LYP/6-31G(d,p) level. Thus, on the basis of the B3LYP/6-31G(d,p) optimized geometry of TPA–DHT–DCN, the absorption spectrum was predicted using various functionals such as TD-B3LYP, TD-PBE0, TDCAM-BLYP, TD-BLYP, TD-OLYP, TD-BHandH, TD-BHandHLYP, TD-MPWB95, TD-MPWLYP, and TD-SVWN with a 6-31G(d,p) basis set. The longest wavelengths of the absorption spectrum (lmax), the oscillator strength ( f ), along with available experimental data are listed in Table S1 of the ESI.† The results displayed in Table S1 (ESI†) show that the TD-B3LYP/6-31G(d,p) method provided a better agreement with the reported experimental observations22 than those obtained with other methods, with the maximum deviation being 8 nm. Moreover, the reports in the literature suggested that B3LYP appeared notably adapted to D–p–A molecules consisting of a TPA core and different p-bridges and end groups.23 Hence, the geometry optimization of designed molecules including neutral, cationic, and anionic molecules was carried out by the B3LYP method using the 6-31G(d,p) basis set. The harmonic vibrational frequency calculations using the same methods as for the geometry optimizations were used to ascertain the presence of a local minimum. To compare the energies of FMOs for donors and acceptors, the electronic properties of PCBM and its derivatives were calculated at the B3LYP/6-31G(d,p) level based on the optimized structures at the B3LYP/6-31G(d) level. The absorption spectra of all the compounds were predicted using the TD-B3LYP/6-31G(d,p) method based on the optimized geometries. The atomic charges in S0 and S1 were calculated by the natural population analysis (NPA),24 using the built-in NBO-3.1 subroutines of the Gaussian. The stability is a useful criterion to evaluate the nature of devices for solar cells. To predict the stability of molecules under investigation from a viewpoint of conceptual density functional theory, the absolute hardness, Z, of molecules under


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investigation was calculated using operational definitions25 given by: 1 @m 1 @2E IP EA ¼ (1) ¼ Z¼ 2 @N 2 @N 2 2 where m is the chemical potential and N is the total electron number. In this work, the values for IP (adiabatic ionization potential) and EA (adiabatic electron affinity) were determined according to the equation IP = Ecr Ep and EA = Ep Ear, where p, cr, and ar indicate the parent molecule and the corresponding cation and anion radicals generated after electron transfer. The charge transport can be considered as a hopping process in the organic solid, which can be evaluated by the Marcus model.19 The drift mobility of hopping, m, can be evaluated from the Einstein equation: e m¼ D (2) kB T Where D is the diffusion constant. If we assume that the charge motion is a homogeneous random walk, the diffusion constant can be evaluated as:26 D E P 2 2 2 di ki xðtÞ 1 1 X 2 1 i P D ¼ lim di ki pi ¼ (3) t!1 2n 2n i 2n t ki i

ki Pi ¼ P ki

(4)

j

d is the intermolecular center-to-center distance and n = 3 means the spatial dimension of the crystal. The inverse of the rate constant 1/k corresponds to the hopping time between adjacent molecules. Pi is the relative probability for charge transfer to a particular ith neighbor, namely, it is a 3 d averaged diffusion process. One can clearly see that the mobility and the electron transfer rate have a linear proportion. Utilizing this mechanism, one can deduce that the localized electron is only hopping between adjacent molecules. The charge transfer rate can be described by Marcus theory19 via the following equation: K = (V2/h)(p/lkBT)1/2 exp(l/4kBT)

(5)

where T is the temperature, kB is the Boltzmann constant, l represents the reorganization energy due to geometric relaxation accompanying charge transfer, and V is the electronic coupling matrix element (transfer integral) between the two adjacent species dictated largely by the orbital overlap. It is clear that two key parameters are the reorganization energy and the electronic coupling matrix element, which have a dominant impact on the charge transfer rate, especially the former. For the reorganization energy l, they can be divided into two parts, external reorganization energy (lext) and internal reorganization energy (lint). lext represents the effect of polarized medium on charge transfer, which is quite complicated to evaluate at this stage. lint is a measure of structural change between ionic and neutral states.27 Our designed molecules are used as donors of solar cells in the solid film; the dielectric constant


of the medium for the molecules is low.28 The computed values of the external reorganization energy in pure organic condensed phases are not only small but also are much smaller than their internal counterparts.29 Moreover, there is a clear correlation between lint and the charge transfer rate in the literature.30 In addition, lint and the charge transfer rate have a clear correlation as reported in previous studies.27b Therefore, we mainly study lint of the isolated active organic p-conjugated systems, ignoring the environmental changes and relaxation in this work. Hence, the le and lh can be defined by eqn (6) and (7):28 0 0 le = (E 0 E) + (E E0)

(6)

lh = (E+0 E++) + (E0+ E00)

(7)

Where E+0(E 0 ) is the energy of the cation (anion) calculated with the optimized structure of the neutral molecule. Similarly, E++(E ) is the energy of the cation (anion) calculated with the optimized cation (anion) structure, E0+(E0) is the energy of the neutral molecule calculated at the cationic (anionic) state. Finally, E00 is the energy of the neutral molecule in the ground state. For comparing with the interested results reported previously,31 the reorganization energies for electron (le) and hole (lh) of the molecules were calculated at the B3LYP/6-31G(d,p) level on the basis of the single point energy. The charge transfer integral for hole (electron) transfer can be obtained through a direct approach, which can be written as:32 D 0 E Vij ¼ f01 F^ f02 (8) Vij is the transfer integral, f01 represents the unperturbed frontier orbital of molecule 1, f02 corresponds to molecule 2 ˆ0 is the Kohn–Sham–Fock operator of the dimer in the dimer. F ˆ0 is evaluated obtained with the unperturbed density matrix. F by the molecular orbitals and the density matrix of the two individual molecules, which can be studied separately by using the standard self-consistent field procedure. Thus, in order to predict the transfer integral, the single-crystal structures were used to generalize all of the possible nearest neighbouring intermolecular hopping pathways. Through a direct approach evaluating the electronic coupling between the two adjacent molecules, the electronic coupling matrix element is obtained. The pw91pw91/6-31G(d) method is employed to calculate the transfer integral. This method gave a reasonable description of the intermolecular coupling term previously.33 The molecular crystal structure is predicted by the module Polymorph of software package Materials Studio.34 The geometry of the cluster models used in the present study was taken from the B3LYP/ 6-31G(d,p) level. The Compass force field was used for the prediction. van der Waals and Coulomb interactions were evaluated by using the Ewald summation method with a cutoff of 6 Å, and the Ewald accuracy tolerance was set to 0.0001 kcal mol1. For all molecules, the polymorph predictor calculations are restricted to the ten most popular space groups, P21/c, P1% , P212121, C2/c, P21, Pbca, Pna21, Cc, Pbcn, and C2, since many organic structures are found in these space groups according to the statistics of the Cambridge Structural Database.


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3. Results and discussion


3.1.

Frontier molecular orbitals

To characterize the optical and electronic properties, it is useful to examine the FMOs of the compounds under investigation. The qualitative molecular orbital representations of the HOMOs and LUMOs of 1a–1d and 2a–2d are shown in Fig. 1. The distribution patterns of FMOs for 3a–3d and 4a–4d are given in Fig. S2 of the ESI.† The total and partial densities of states (TDOS and PDOS) on each fragment of the investigated molecules around the HOMO–LUMO gaps were calculated based on the current level of theory. The HOMO and LUMO contributions of individual fragments (in %) to the FMOs of the investigated molecules are given in Table S2 in the ESI.† The FMOs of the compounds under investigation show p characteristics as visualized in Fig. 1 and S2 (ESI†). For the investigated molecules, the HOMOs are mainly localized on the TPA and CB fragments with only minor contributions from NI fragments. The sum of contributions of TPA and CB fragments of HOMOs are larger than 76.9%, while the corresponding contributions of NI fragments are within 23.1%, respectively. In contrast, the LUMOs mainly reside at the NI fragments with only minor contributions from

Fig. 1

CB and TPA fragments for 1a–1d, 2a–2d, and 4a–4d. The contributions of NI fragments of LUMOs are larger than 76.6%, while the corresponding sum contributions of CB and TPA fragments are within 23.4%, respectively. For 3a–3d, the LUMOs mainly reside at NI and CB fragments with only contributions from TPA fragments. The sum contributions of NI and CB fragments of LUMOs are about 94%. These results reveal that the different p-bridge units and end groups have obvious effects on the distribution of FMOs for the compounds under investigation. The distribution patterns of the FMOs of the compounds under investigation provide a remarkable signature for the intramolecular charge transfer (ICT) character of the vertical S0 - S1 transition. Analysis of the FMOs indicates that the excitation of the electron from the HOMO to LUMO leads the electronic density to flow mainly from the TPA and CB fragments to NI fragments for 1a–1d, 2a–2d, and 4a–4d. The percentages of charge transfer from TPA and CB fragments to NI fragments are 53.5–80.7%. For 3a–3d, the excitation of the electron from the HOMO to LUMO leads the electronic density to flow mainly from the TPA fragments to CB and NI fragments, the percentages of charge transfer from TPA fragments to CB and NI fragments are about 70%. The results displayed in Table S2 (ESI†) reveal that

Electronic density contours of the frontier molecular orbitals for 1a–1d and 2a–2d at the B3LYP/6-31G(d,p) level.



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the TPA and CB serve as donors and NI serves as acceptors for 1a–1d, 2a–2d, and 4a–4d, while CB and NI fragments serve as acceptors and TPA fragments serve as donors for 3a–3d, respectively. In order to well understand the ICT character of the vertical transition, we select 1a–1d as representatives of the system under investigation. The calculated NPA charge densities are collected in Table S3 (ESI†). It clearly shows that the values of Dq on TPA and CB fragments are positive, while the corresponding values of Dq on NI fragments are negative for 1a–1d. A positive value of Dq indicates that the TPA and CB fragments are electron-donating in nature; on the other hand, a negative value implies the electron-withdrawing nature of the NI fragment. Hence, the charge-transfer character of the vertical S0 - S1 transition and the properties of donors–acceptors are also supported by NPA analysis. Furthermore, the photophysical properties of ICT are well known and highly dependent on the electron donor–acceptor strength.35 Therefore, the ICT transition in the D–p–A molecules becomes much easier after introduction of p-conjugated bridges, resulting in the large bathochromic shift in their absorption and fluorescence spectra. Another way to understand the influence of the optical and electronic properties is to analyze the EHOMO, ELUMO, and Eg. The EHOMO, ELUMO, and Eg of the designed molecules, PCBM and its derivatives bisPCBM and PC70BM are given in Fig. 2. The EHOMO, ELUMO, and Eg of NI and TPA are listed in Table S4 in the ESI.† As shown in Fig. 2 and Fig. S4 (ESI†), the EHOMO values of all molecules are higher than that of NI, while the corresponding values of ELUMO are lower than that of NI except for 4b and 4c. The ELUMO values of 4b and 4c are slightly higher than that of NI. The ELUMO values of all molecules are lower than that of TPA, while the corresponding EHOMO values are lower than that of TPA except that the ELUMO values of 4b and 4c are slightly higher than that of TPA. Thus, the Eg values of all molecules are smaller than those of NI and TPA, respectively. These results indicate that these D–p–A star-shaped molecules can lower the material band gap and extend the absorption spectrum towards longer wavelengths. For 1a–1d, their EHOMO and ELUMO values are in the order 1b 4 1c 4 1a 4 1d. Therefore, the prediction of their Eg values is in the sequence 1b 4 1c 4 1a 4 1d. This shows that molecules with 4-aniline

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and 4-anisole (1b and 1c) electron-donating groups in NI fragments possess higher ELUMO and EHOMO and thus larger Eg in comparison with a molecule with a H atom (1a) in the NI fragment, respectively. The Eg value of 1b is larger than that of 1c. This may be attributed that the ability of electrondonating of 4-aniline is larger than that of 4-anisole. In contrast, the molecule with a 4-pyridne (1d) electron-withdrawing group in the NI fragment has lower ELUMO and EHOMO and thus smaller Eg in comparison with molecule 1a. Similar phenomena are also found for 3a–3d and 4a–4d. The Eg values of 3a–3d and 4a–4d are in the order 3b E 3c 4 3a 4 3d and 4b 4 4c 4 4a 4 4d, respectively. For 2a–2d, their EHOMO values are in the order 2c 4 2b 4 2a 4 2d, and their ELUMO values are in the sequence 2b 4 2c 4 2a 4 2d. Thus, the prediction of their Eg values is in the order 2b 4 2d 4 2c 4 2a. This shows that the molecule with a 4-pyridne (2d) electron-withdrawing group in the NI fragment possess larger Eg in comparison with the H atom (2a) in the NI fragment. The reason is that the 4-pyridne (2d) in the NI fragment results in worse conjugation due to the large dihedral between TPA, NI, and CB fragments. Furthermore, the sequence of EHOMO values for 1a–4a is 4a 4 2a 4 3a 4 1a; the order of their ELUMO values is 4a 4 2a 4 1a 4 3a. As a result, the Eg values are in the sequence 1a 4 2a 4 3a 4 4a. Similar phenomena are also found for 1b–4b, 1c–4c, and 1d–4d. These results suggest that the aromatic groups as p-bridges can reduce the Eg values of the compounds under investigation. The order of the Eg values for different p-bridges is ethyne (1) 4 thiophene (2) 4 BTA (3) 4 DTD (4). This can be explained by the fact that the derivatives with aromatic groups have a strong conjugative effect between TPA, NI, and CB fragments. These results suggest that the different p-bridges and end groups NI fragments have effects on the EHOMO, ELUMO, and Eg for the compounds under investigation. It is well-known that PCBM, bisPCBM, and PC70BM are excellent acceptors for organic solar cells.4,36 Therefore, we choose these three fullerene derivatives as acceptors in our work. As shown in Fig. 2, the ELUMO values of the designed molecules are higher than those of PCBM, bisPCBM, and PC70BM, respectively. The differences between the EHOMO of the designed molecules and the ELUMO of PCBM are larger than 1.71 eV, while the

Fig. 2 Evaluation of calculated FMO energies for investigated molecules as well as FMO energies for PCBM, bisPCBM, and PC70BM at the P3LYP/6-31G(d,p) level.



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corresponding values of bisPCBM and PC70BM are larger than 1.81 and 1.754 eV, respectively. These results imply that the designed molecules can provide better matches of FMOs to PCBM, bisPCBM, and PC70BM. Therefore, different p-bridges and NI derivative end groups can tune the FMOs of derivatives to be more suitable for PCBM, bisPCBM, and PC70BM.


3.2.

Absorption spectra

Table 1 presents the absorption region R, the longest wavelength of the absorption spectrum (lmax), the oscillator strength ( f ), and main configurations of the designed molecules. The absorption wavelengths lmax and the oscillator strength f of the first fifteen excited states for the compounds under investigation are listed in Tables S5 and S6 of the ESI.† As shown in Table 1, for 1a–1d and 2a–2d, the lmax values are in the order of 1d 4 1b 4 1a 4 1c and 2d = 2a 4 2c 4 2b, which is in excellent agreement with the corresponding reverse order of Eg values displayed in Fig. 2 except for 1b and 2d. As mentioned above, this may be attributed that 1b and 2d show worse conjugation due to the large dihedral between TPA, NI, and CB fragments. The oscillator strength for an electronic transition is proportional to the transition moment.37 In general, larger oscillator strength corresponds to a larger experimental absorption coefficient. Thus, the f values of 1b and 2d are smaller than those of other compounds in 1a–1d and 2a–2d, respectively. Their corresponding f values are in the sequence of 1c 4 1d 4 1a 4 1b and 2c 4 2a 4 2b 4 2d, respectively. For 3a–3d and 4a–4d, the lmax and R values are in the order of nd 4 na 4 nc 4 nb (n = 3 and 4), which is in excellent agreement with the corresponding reverse order of Eg values displayed in section 3.1.

Table 1 Predicted absorption region R, the longest wavelength of absorption lmax, corresponding oscillator strength f, and main configurations of the designed molecules at the TD-B3LYP/6-31G(d,p)-31G(d,p) level

Species

lmax (nm)

f

Main configurations

1a 1b

521 520

0.96 0.25

1c 1d 2a 2b

517 527 542 516

1.04 0.99 0.60 0.58

2c

538

0.62

2d

542

0.54

3a 3b 3c 3d

590 588 589 594

0.48 0.50 0.50 0.51

4a 4b 4c 4d

571 564 569 589

0.63 0.67 0.66 0.61

H H H H H H H H H H H H H H H H H H H H H H

a

- L (0.70) - L (0.26) 1 - L + 1 (0.40) - L + 1 (0.29) - L (0.70) - L (0.70) - L (0.70) - L (0.64) - L + 1 (0.27) - L (0.69) 1 - L (0.12) - L (0.64) 1 - L + 1 (0.21) - L (0.70) - L (0.70) - L (0.69) - L (0.69) - L + 1 (0.11) - L (0.70) - L (0.70) - L (0.70) - L (0.70)

Ra (nm) 154 125 129 166 201 122 151 195 210 130 164 212 218 138 164 222

R = the difference of the longest and shortest wavelength values with oscillator strength larger than 0.01 considering the first fifteen excited states.


Their corresponding f values are in the sequence of 3d 4 3b = 3c 4 3a and 4b 4 4c 4 4a 4 4d, respectively. The order of their R values of both 1a–1d and 2a–2d are similar to those of 3a–3d and 4a–4d, respectively. Moreover, the f value of 1c is the greatest among the investigated molecules, corresponding to the most intensive absorption spectra. It indicates that the 4-aniline and 4-anisole substitution in NI fragments results in smaller lmax and R values than those of H- or 4-pyridnesubstitution in NI fragments. However, the f values of molecules with 4-aniline and 4-anisole substitution in NI fragments are larger than those with H- or 4-pyridne-substitution in NI fragments. Furthermore, a careful inspection of the results displayed in Table 1 reveals clearly that the lmax and R values of molecules with BTA and DTD (3 and 4) p-bridges are larger than those of molecules with ethyne and thiophene (1 and 2) p-bridges, respectively. It suggests that molecules with BTA and DTD p-bridges can lower the material band gap and extend the absorption spectrum towards longer wavelengths. As a result, D–p–A star-shaped molecules under investigation own the large lmax, f, and R values. Thus, the molecules under investigation could be used as solar cell materials with intense broad absorption spectra. In addition, most of the transitions correspond to the excitation from the HOMOs to the LUMOs. 3.3.

Reorganization energy and stability properties

Understanding the relationship between the molecular structure and charge transport properties of a material is a key factor for designing good candidates for solar cell devices. It is wellknown that the lower the reorganization energy values, the higher the charge transfer rate.19 The calculated reorganization energies for holes and electrons and absolute hardness are listed in Table 2. The results displayed in Table 2 show that the calculated lh values of all the designed molecules are smaller than that of N,N0 -diphenyl-N,N0 -bis(3-methlphenyl)-(1,10 -biphenyl)4,4 0 -diamine (TPD) which is a typical hole transport material (lh = 0.290 eV).29a This implies that the hole transfer rates of the designed molecules might be higher than that of TPD. Their le values are smaller than that of tris(8-hydroxyquinolinato)aluminum(III) (Alq3) which is a typical electron transport material (le = 0.276 eV),29b indicating that the electron transfer rates of the designed molecules might be higher than that of Alq3. Among these molecules, nc (n = 1–4) own the smallest lh values, implying that they have better properties for hole-transport. A careful inspection of the results displayed in Table 2 reveals clearly that 1a and 1b have the largest lh values, while 3a and 4b own the smallest lh values for 1a–4a and 1b–4b, respectively. For 1c–4c and 1d–4d, 1c and 1d show the smallest lh values, while 4c and 4d own the largest lh values. In contrast, 1a and 1b have the largest le values, while 4a and 4b own the smallest le values for 1a–4a and 1b–4b, respectively. However, the le values of 1c and 4c are larger than those of 2c and 3c for 1c–4c, respectively. Similar phenomena are also found for 1d–4d. These results indicate that the lh and le values are affected by the introduction of different p-bridges and substitution groups to these D–p–A star-shaped molecules. The introduction of an ethyne p-bridge leads to the increase of the hole transfer rates, while


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Table 2 Calculated le, lh, and Z of the designed molecules at the B3LYP/ 6-31G(d,p) level

Species

lh (eV)

le (eV)

Z (eV)

1a 1b 1c 1d 2a 2b 2c 2d 3a 3b 3c 3d 4a 4b 4c 4d NI TPA

0.179 0.230 0.077 0.098 0.159 0.166 0.130 0.160 0.116 0.185 0.084 0.116 0.178 0.148 0.172 0.180 0.196 0.114

0.218 2.133 0.124 0.122 0.161 0.151 0.175 0.138 0.134 0.154 0.152 0.151 0.108 0.136 0.131 0.120 0.278 0.254

2.083 1.966 2.061 2.051 2.017 1.986 1.989 1.987 1.971 1.861 1.951 1.950 1.911 1.909 1.904 1.869 3.650 2.687

DTD p-bridges decrease the hole transfer rates for molecules with 4-anisole- and 4-pyridne-substitution in NI fragments. In contrast, for molecules with H- and 4-aniline-substitution in NI fragments, the introduction of an ethyne p-bridge leads to the increase of the electron transfer rates, while the DTD p-bridge decreases the hole transfer rates. The introduction of thiophene and BTA p-bridges increases the electron transfer rates for molecules with 4-anisole- and 4-pyridne-substitution in NI fragments, while introduction of ethyne and DTD p-bridges leads to the decrease of the hole transfer rates for molecules with H- and 4-anilinesubstitution in NI fragments. In addition, the differences between the le and lh values are less than 0.04 eV except for 1b and nc

Fig. 3

(n = 1–4). It implies that na, nb, and nd (n = 1–4) have better equilibrium properties for hole- and electron-transport except for 1b. Therefore, they may be used as good candidates for ambipolar charge transport materials under the proper operating conditions. It suggests that the designed molecules with ethyne, thiophene, and DTD p-bridges are potential ambipolar charge transport materials under the proper operating conditions. Considering the results obtained above, the lmax, and absorption range, all the designed molecules can be used as promising charge transport materials in small-molecule OSCs from the stand point of the smaller reorganization energy. The absolute hardness Z is the resistance of the chemical potential to change in the number of electrons. As expected, inspection of Table 2 reveals clearly that molecules under investigation have nearly equal values of absolute hardness (about 2.0 eV), being smaller slightly than the values of building blocks NI and TPA (3.650 and 2.687 eV). It indicates that the stabilities of molecules are slightly smaller than that of 1, which may be due to the steric hindrances. These results reveal that the different p-conjugated bridges and end groups do not significantly affect the stability of these bipolar molecules. 3.4.

Calculated crystal structure and transport properties

From the obtained results, one can find out that the compounds under investigation have the suitable FMO energies to match those of PCBM, bisPCBM, and PC70BM, broad absorption regions, and smaller reorganization energies. We calculated the mobility of 1a as representation to study its charge transport property. The calculated crystal structures of 1a predicted by Material Studio are shown in Fig. 3. The calculated crystal structures of 1a with

Herringbone structures of 1a in different space groups.



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Fig. 4 Crystal structures and hopping routes of 1a in different space groups.

two lowest total energies belong to space groups P21/c and Pna21. The total energies and lattice constants of 1a in different space groups are listed in Table S7 of the ESI.† Thus, we predict the mobility of 1a in these two space groups. The transmission paths are selected according to the optimized crystal structures. We arbitrarily choose one molecule in the crystal as the carrier donor and take all its neighboring molecules as paired elements. Each pair is defined as a transmission path. Fig. 4 shows the most important pathways (dimers). Then the charge transfer integral can be calculated according to the transmission path, and the mobility can be estimated from the Einstein relationship. The calculated transfer integrals of 1a for holes and electrons in space groups P21/c and Pna21 are listed in Table 3. The data in Table 3 demonstrate that the electronic coupling is determined by the relative distance and orientations of the interacting molecules.38 Furthermore, 1a possesses the largest absolute electron and hole coupling values in pathways 3, 5, and 6 for space group Pna21 and in pathways 1 and 2 for space group P21/c. It reveals that the orientation of the interacting molecules is the key factor of hole or electron coupling for 1a, because the co-facial stacking structure is expected to provide a more efficient orbital overlap leading to the most efficient charge transfer route.35 The values of hole mobility of 1a for Pna21 and P21/c (5.30 103 and 1.27 102 cm2 V1 s1) are much larger than that of TPD (1.0 103 cm2 V1 s1).39 The value of hole mobility for 1a is larger than that of electron mobility for the P21/c space group, while the corresponding value of electron mobility is slightly smaller than that of hole mobility for the Pna21 space group. 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 properties. The obtained electron mobility of 1a for the Pna21 space group is very close to its hole mobility, while the corresponding electron mobility for the Pna21 space group is slightly less than its hole mobility.


Table 3 Center–center distance and the corresponding hole and electron coupling between the dimer in all of the nearest neighboring pathways for 1a in different space groups [T = 298 K, in cm2 V1 s1]

Space group

Pathway

Distance (Å)

Electron coupling (eV)

Hole coupling (eV)

Pna21

1 2 3 4 5 6 7 8 Drift mobility

10.764 10.764 16.432 12.416 16.432 16.432 12.416 16.432

2.47 2.47 1.90 1.51 1.90 1.90 1.48 1.76 8.54

106 106 103 105 103 103 105 1023 103

4.30 4.30 2.10 2.98 2.10 2.10 2.98 1.15 5.30

108 108 103 104 103 103 104 1023 103

P21/c

1 2 3 4 5 6 7 8 Drift mobility

9.459 9.459 17.125 17.477 22.284 23.682 17.67 15.570

2.63 2.63 1.60 9.01 3.20 0.00 5.48 2.87 1.99

104 104 103 107 1027

1.43 1.43 3.10 8.91 1.65 0.00 3.09 1.66 1.27

104 104 103 108 1028

1016 106 103

1017 106 102

The theoretical prediction shows that 1a can be made as a hole transfer material used for solar cells. Moreover, it also has balanced charge transport characteristics, which agrees with the results of reorganization energy.

4. Conclusions In the present work, we investigated a series of D–p–A starshaped small molecules with TPA as a core, NI derivatives as end groups, and different p-bridges for photovoltaic applications. The FMO analysis has turned out that the star-shaped


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molecules can lower the material band gap and extend the absorption spectrum towards longer wavelengths. For the molecules with ethyne, BTA, and DTD as p-bridges, the Eg values of molecules with 4-aniline and 4-anisole groups are larger than those of with H and 4-pyridne groups in NI fragments. The Eg values of molecules with 4-aniline and 4-pyridne electron-withdrawing groups are larger than those of molecules with H and 4-anisole groups in NI fragments for the molecules with thiophene as p-bridges. For the molecules with different NI derivatives as end groups, the Eg values of molecules with ethyne and thiophene as p-bridges are larger than those of molecules with BTA and DTD as p-bridges. Our results reveal that the molecules under investigation own the largest lmax, f, and R values. Thus, they could be used as solar cell materials with intense broad absorption spectra. The reorganization energies of the derivatives were also investigated. Our results suggest that the lh and le values are affected by the introduction of different p-bridges and substitution groups to these starshaped molecules. The designed molecules are expected to be promising candidates for electron transport materials. Additionally, the derivatives na, nb, and nd (n = 1–4) have better hole- and electron transporting balance and can act as nice ambipolar materials. The values of hole mobility of 1a for Pna21 and P21/c are much larger than that of TPD, respectively. The theoretical prediction shows that 1a can be made as a hole transfer material used for solar cells. Moreover, it also has balanced charge transport characteristics. On the basis of the investigated results, we suggest that molecules under investigation are suitable donors of PCBM, and its derivatives bisPCBM and PC70BM are acceptors of solar cells.

Acknowledgements Financial support from the Inner Mongolia Key Laboratory of Photoelectric Functional Materials and the Science and Research Creative Team of Chifeng University is gratefully acknowledged.

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