Theoretical Investigation on Porphyrin-Based Small Molecules as

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Theoretical Investigation on Porphyrin-Based Small Molecules as Donor Materials for Photovoltaic Applications Xiaorui Liu, Cheng Zhi Huang, and Ming Li J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09437 • Publication Date (Web): 11 Nov 2016 Downloaded from http://pubs.acs.org on November 13, 2016

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The Journal of Physical Chemistry

Theoretical Investigation on Porphyrin-Based Small Molecules as Donor Materials for Photovoltaic Applications

Xiaorui Liu[a,b], Chengzhi Huang[a], Ming Li*[a] a

Key Laboratory of Luminescent and Real-Time Analytical Chemistry (Southwest University), Ministry of

Education, School of Chemistry and Chemical Engineering, Southwest University, Chongqing 400715, China b

College of Pharmaceutical Sciences, Southwest University, Chongqing 400715, China

Corresponding Authors *Prof. M. Li, E-mail: [email protected] Tel: +86-02368254602

Abstract: An effective strategy to improve the efficiency of organic solar cells (OSCs) is to incorporate the porphyrin derivatives as electron-rich units into the acceptor-donor-acceptor molecules. To achieve this goal, starting from the parent molecules DTS(PTTh2)2 and DTS(FBTTh2)2 which are based on dithieno(3,2-b; 2’,3’-d)silole (DTS) electron-rich unit connected to each of two electron-withdrawing units ([1,2,5]thiadiazolo[3,4-c]pyridine (PT) and 5-fluorobenzo[c][1,2,5]thiadiazole (FBT)), we designed two types of porphyrin-based small molecules by replacing DTS unit with the porphyrin derivatives in DTS(PTTh2)2 and DTS(FBTTh2)2, respectively . From the calculated results, the porphyrin-based molecules in OSC applications not only yield an enhanced light absorptions with a redshift and stronger spectra and increased hole mobility which is conducive to enhance the short circuit current and fill factor, but also exhibit smaller exciton binding energy and better electron transfer properties at donor/acceptor (D/A) interface in comparison with the parent molecules. According to the predicted crystal structure for porphyrin-based molecules, the hole mobilities of the porphyrin-based molecules (S1b, S1c, S2b and S2c) are 0.240, 0.166, 0.124, 0.511 cm2V-1s-1, respectively. In view of the excellent properties, the porphyrin-based molecules as donor materials can act as a good candidates for providing a large short-circuit current and fill factor in OSC 1

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applications.

1. Introduction Organic solar cells (OSCs) as promising renewable energy sources have attracted much attention recently due to its advantage such as low cost, lightweight, large-area fabrication, flexible devices, etc.1-5 The power conversion efficiencies (PCEs) of OSCs based polymer as donor materials have been in excess of 11% for single junction devices.6 In comparison with the polymer materials, small molecular materials in OSC applications have many advantages such as well-defined molecular structures, adjustable molecular weights, tunable electronic properties and better batch-to-batch reproducibility.

7-11

To date, a high PCE in exceed of 8% has been reported from

single-junction small molecular OSCs.12-16 However, the overall performance of small-molecular OSCs is still obviously behind that of the polymer-based OSCs.17-20 In view of the advantages of the small-molecular donors, development on high-efficiency solution-processed small-molecular OSCs for the research community is still a very significant. It is still a great challenge to design and synthesize a small-molecular materials with a suitable frontier molecular orbital energy in matching with that of [6,6]-phenyl-C71-butyric acid methylester (PC71BM) and its derivatives, a broad optical absorption, high charge mobility, and high air stability in the manufacture of OSC devices. 20-21 The parameters of short-circuit current (Jsc), open-current voltage (Voc) and fill factor (FF) are used to measure the performances of OSC devices.20 Jsc is a function of the light-absorbing efficiency, exciton-diffusion efficiency, charge-transfer efficiency, and charge-collection 2


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efficiency.3, 22-26 Voc of the OSCs is mainly controlled by the energy offset between the lowest unoccupied molecular orbital (LUMO) of the acceptor and the highest occupied molecular orbital (HOMO) of the donor.

26-28

FF is effected by the morphology of active layer and the charge

mobility.25, 29 The active layer including molecule donors and acceptor materials play a key part in completing the optical absorption, exciton generation, electronic transfer at donor/acceptor (D/A) interface and free charge transport.3, 23-24 Accordingly, more efforts should focus on the design and understanding of the structure-property-function relationships of the small-molecular donor and acceptor materials in active layer of OSC devices. For an OSC device, the most important requirement is that the small-molecular donors should have a strong and wide absorption profile in closely matching with the solar spectrum. To improve the performance of the donors, the main approach to obtain a molecule donor with low band gap (Eg) are based on the strategy which constructs the alternated donor-acceptor structure.20, 30-32 For example, Heeger and co-works33 report a solution-processed small-molecule donor, DTS(PTTh2)2, with a acceptor-donor-acceptor (A-D-A) structure, which consist of the [1,2,5]thiadiazolo[3,4-c]pyridine (PT) unit as an electron-withdrawing acceptor block, the dithieno(3,2-b; 2’,3’-d)silole (DTS) as an electron-rich donor unit. The organic molecule adopt the D-A structure which not only can form strong interchain interactions that is in favor of charge transport, but also can fine-tune the frontier molecular orbital levels of conjugated molecules, resulting in desired optoelectronic properties.30 The DTS(PTTh2)2 as donor material exhibits strong optical absorption, especially from 600~800 nm and good hole mobility (~0.1 cm2 V−1 s−1) in a field-effect.33 The OSC device based on the DTS(PTTh2)2 donor and PC71BM acceptor, a record PCE of 6.7% was achieved.33 On basis of the molecule DTS(PTTh2)2, Su and co-works34 designed 3



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a series of small molecular donors which exhibit good performance with large Voc, stable charge transfer and effective charge transport. In addition, they proposed some efficient strategies to provide a guideline of molecular design for the conjugated organic molecules.35 Bazan et al.36 replaced electron-withdrawing block PT with 5-fluorobenzo[c][1,2,5]thiadiazole (FBT) in DTS(PTTh2)2, and synthesized the molecule p-DTS(FBTTh2)2. The small-molecule OSCs with PCE of 8.9% from p-DTS(FBTTh2)2 donor and PC71BM acceptor was achieved through the optimization of OSC devices.15 However, the limitation of solar absorption for the small-molecular donors in OSC devices still is the first fundamental issue.25 Fortunately, the excellent properties of porphyrins and their derivatives, including strong Soret and moderate Q bands, fast electron injection, good photophysical and thermal stability, make them as building blocks for the construction of light harvesting architectures in OSC applications.37-41 Porphyrins-based sensitizers in dye sensitized solar cells are in record of PCE as high as 13%.42 Herein, starting from the reported excellent A-D-A molecule DTS(PTTh2)2 (S1a)33, we introduced the porphyrin derivatives as electron-rich block to replace the DTS unit, and then built two molecules S1b and S1c, respectively. Similarly, on the basis of the reported A-D-A molecule p-DTS(FBTTh2)2 (S2a)36, another two porphyrin derivative-based molecule S2b and S2c were constructed. The chemical structures of the investigated small-molecular donors (S1a-S1c and S2a-S2c) are presented in Figure 1. In the present contribution, we aimed to provide a molecule models of improving the solar absorption for porphyrin-based molecule as donor materials and further have an insight into the role of porphyrin-based molecule in electron transfer at the D/A interface, charge transport ability and the performance in OSC devices. Thus, the geometric structure, electronic properties and absorption spectrum of all small-molecular donors were first 4


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investigated by density functional theory (DFT) and time-dependent density functional theory (TD-DFT). The charge transport in the small-molecular donors were also investigated. Furthermore, taking the representative PC71BM acceptor material as a reference15, the properties of electron transfer in active layer for the small-molecular donors were investigated in order to inspect the effect on the performance of OSC devices.

2. Computational Details In the present work, the ground-state geometry of the small molecules depicted in Figure 1 was fully optimized in the gas phase employing DFT.43 To save the computational cost and simplify the calculations, the branched alkyl chains in molecular backbone were was repacked by methyl groups because of its no significant influence on the frontier molecular orbitals and optoelectronic properties of molecules.44 The calculated vibrational frequencies in geometry optimization for all investigated molecules show that there were not imaginary frequency, which indicates that all the optimized structures are the global minima on the potential energy surface and stable structures. In order to first validate a computational method in comparison with the experimental data on those properties of the reported donor molecules, a wide class of hybrid functionals including43 B3LYP, PBE045 and HSE0346 at 6-311G(d,p) levels were chose to calculate the HOMO and LUMO energy of the molecules (S1a and S2a) (see Table S1). As shown in Table S1, the calculated results of HOMO energy with HSE03/6-311G(d,p) method and basis set for S1a and S2a are -5.16 eV and -5.03 eV, respectively, in good agreement with these experiment values (S1a: -5.20 eV33, S2a: -5.12 eV36, respectively). Similarly, the calculated results of the LUMO energy levels at HSE03/6-311G(d,p) level for S1a and S2a (-3.72 eV and -3.47 eV, respectively) agree 5



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well with the reported experimental data (-3.60 eV33 and -3.34 eV36 for S1a and S2a, respectively). The calculation on the properties of molecular orbitals for these molecules by other methods obviously deviate from the experimental data (see Table S1). In addition, we calculated the Zn atoms of molecules S1b and S2b with the lanl2dz basis set.43 The calculated results show that the HOMO/LUMO energies of molecules S1b and S2b are -5.23/-3.84 eV and -5.10/-3.63 eV, respectively, in good agreement with the results (-5.22/-3.83 eV and -5.09/-3.63 eV) of 6-311G(d,p) basis set calculations. Hence, the ground-state structure and energy of all donor molecules in this work were calculated at HSE03/6-311G(d,p) levels. The absorption spectra of S1a and S2a were calculated by TD-DFT with different methods of M05, M062X and BMK functional at the 6-31g(d,p) basis set level in chloroform solvent with polarizable continuum model (PCM).43, 47 Table S2 shows that TD-BMK/6-31g(d,p) method and basis set in chloroform solution can give a reliable result on optical absorption (659 nm and 619 nm, respectively) of S1a and S2a in keeping with the experimental results (655 nm for S1a33 and 590 nm for S2a36, respectively). Therefore, the optical absorptions of all molecule donors and the donor-acceptor blends were calculated with TD-BMK/6-31g(d,p) levels in chloroform solvent. The absorption spectra of molecules were calculated using the SWizard program (revision 5.048-49) with the Gaussian model (the half bandwidths were taken to be equal to 2000 cm-1). The distance of the ππ stacking between the small-molecular donors and the PC71BM acceptors in D-A blends were calculated by the M062X/6-31G(d) functional and basis set.50 The molecular crystal structure was predicted by the polymorph predictor module in Materials Studio.51 The geometry of a single molecule was optimized by the DMol3 module and electrostatic potential charges of all atoms were obtained.52-53 Then the crystal structure prediction was carried out by 6


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employing the PBE functional and the Dreiding force field.54 For the investigated molecules, the polymorph calculations are restricted to the six most probable space groups, P21/c, P1, P212121, C2/c, P21 and Pbca. The crystal structures in terms of their total energies were sorted. The obtained crystal structures of the investigated molecules with the lowest energies were selected for further calculations on their charge mobility. The energy calculations on the charge transport of the small molecules were obtained from HSE03/6-311G(d,p) method and basis set. The transfer integral in hole transport were calculated by the PW91/TZP functional and basis set in ADF program.55-58 Su and co-works59 calculated the transfer integral on this levels which can give a reliable result for organic small molecules. In order to ensure the validity of the method for crystal structure prediction, the crystal structures of molecule S1a were predicted using same method. The main hole hopping pathways selected based on the predicted crystal structures with the lowest energy in term of their total energies for each S1a crystal structures are presented in Figure S3. The parameters such as hole transfer integral, hole transport rates, center-of-mass distances and hole mobilities of main hopping pathway selected on basis of the crystal structure for molecule S1a are listed in Table S3. The results indicate that the calculated hole mobility (0.166 cm2V-1s-1) of S1a based on the predicted crystal structure are very agreement with that (0.144 cm2V-1s-1) on basis of the experimental crystal structure. Therefore, the selected methods on crystal structure predictions are feasible. The electron densities of the electron transitions in optical absorptions were given by Multwfn 2.1 program.60 The calculations of ground-state geometry, energy and optical absorptions on DFT and TD-DFT were carried out by the Gaussian 09 program. 61

3. Results and Discussion 7



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3.1 Molecular geometries at ground states Optimized geometry and parameters on basis of HSE03 at 6-311G(d,p) calculations for all small-molecular donors were presented in Figure S1 of the Supporting information (SI) and Table 1, respectively. As shown in Table 1 (The geometrical parameters were defined in Figure 1), the selected bond lengths (L) of carbon-carbon bond (C2-C3) for all molecules (1.40-1.44 Å) are shorter than that of the single C-C bond (1.54 Å) which exhibit the double-bond character. The L of C2-C3 bonds for the porphyrin-based small-molecular donors was shortened. For example, the L of C2-C3 bonds for S1b (1.40 Å) and S1c (1.40 Å) are shorter than that of S1a (1.44 Å). It is attributed the strengthening and shortening of C2-C3 bonds to the π-bonding interaction. These results give us an important information that the π-electrons are distributed on the whole backbones rather than partially localized on a certain unit, especially for the porphyrin-based molecules (S1b, S1c, S2b and S2c). Moreover, Table 1 shows that the dihedral angles (Φ) of all investigated molecules are in the range of 0.001~3.49 degree which they exhibit good planarity. 3.2 Frontier molecular orbitals The frontier molecular orbitals is one of the important factors to illustrate the electronic properties, optical absorptions and carrier transport properties thus that influence on the OSC efficiency.62-64 Moreover, for an OSC devices, one of the important requirements for the ideal donor materials is that they have suitable frontier molecular orbital energy levels in matching with these of the acceptors in order to ensure the photoinduced charge separation and efficient charge transfer at D/A interface.

3, 23-24

The calculated frontier molecular orbitals on HSE03/6-311g(d,p)

level for all investigated molecules are shown in Figure 2. In Figure 2, one can see that both the 8


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HOMOs and LUMOs possess π feather. The HOMOs of all molecules spread over the whole molecular

backbones,

while

the

LUMOs

localized

on

the

middle

porphyrin,

[1,2,5]thiadiazolo[3,4-c]pyridine and 5-fluorobenzo[c][1,2,5]thiadiazole unit. The good HOMO delocalization is in favor of electronic coupling and hole transport. Another way to have an insight into the influence of the electronic and optical properties on the performance of the OSC devices is to analyze the HOMO/LUMO energy and the band gap (Eg). The data of HOMO/LUMO energy and Eg of all investigated molecules on the calculations of HSE03/6-311G(d,p) functional and basis set in conjunction with experimental data were displayed in Figure 2. In the work, the calculated results of the HOMO/LUMO energy (-5.16/-3.72 eV and -5.03/3.47 eV for S1a and S2a, respectively) based on the screened method and basis set (see Table S1 of the SI) are in agreement well with the experimental values (-5.20/-3.60 eV33 and -5.12/-3.34 eV36 for S1a and S2a, respectively). Consequently, the HOMO/LUMO energy of designed molecules was further calculated by the same method (as shown in Figure 2). In Figure 2, one can see that the values of HOMO/LUMO energy for S1a-S1c and S2a-S2c are -5.16/-3.72 eV, -5.22/-3.83 eV, -5.14/-3.79 eV, -5.03/3.47 eV, -5.09/-3.63 eV and -5.00/3.59 eV, respectively. For molecules S1a-S1c and S2a-S2c, the calculated Egs are 1.44 eV, 1.39 eV, 1.35 eV, 1.56eV, 1.46 eV and 1.41 eV, respectively. Compared with S1a, the Egs of these porphyrin-based molecules (S1b and S1c) are decreased by 0.05 eV and 0.09 eV, respectively. The Egs of S2b and S2c are decreased by 0.10 eV and 0.15eV in comparison with that of S2a. The narrow Egs of porphyrin-based molecules mainly drive from the downshifted LUMO contributions. For the porphyrin-based molecules, a stronger degree of hybridization and π-conjugation in the LUMO than these of S1a and S2a (Figure 1) should be related to the significant downshift of the LUMO 9



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level which results in reducing the band gap. In OSC device, conventional architecture of indium tino xide(ITO)/ molyb-denum oxide (MoOx)/donor: acceptor/aluminum (Al) is most commonly used.65-66 It very important factors that the energy levels of donor molecules are in matching with these of the anode and the acceptor PC71BM in order to ensure efficient electron transfer from the donor molecules to the acceptor PC71BM.67-68 Here, we assume the ITO/MoOx were anode in OSC device. The HOMOs (-5.22, -5.14, -5.09 and 5.00 eV) of the porphyrin-based molecules (S1b, S1c, S2b and S2c) are deeper than the Fermi energy levels of ITO (-4.7), 65-66 and the LUMOs (-3.83, -3.79, -3.63 and -3.59 eV) higher than that of PC71BM (-4.3 eV15), which indicated the energy levels of the porphyrin-based molecules as donor are good in matching with corresponding Fermi energies of ITO electrodes and LUMO energy level of PC71BM very well. In addition, the LUMO energy of the donor molecules must be higher than the LUMO energy of the acceptor (i.e. PC71BM) by at least 0.3 eV to guarantee efficient electron transfer at D/A interface.67-68 As shown in Table 2, the energetic driving force ∆(LUMOD-LUMOA) between the molecule donors and PC71BM are 0.58, 0.47, 0.51, 0.83, 0.67 and 0.71 eV, respectively, which can ensure electron transfer at D/A interface from the donor molecules to the acceptor PC71BM.

3.3 Electronic absorption spectra To

characterize

the

optical

absorptions

of

all

molecule

donors,

we

performed

TD-BMK/6-31g(d,p) calculations in chloroform solvent on basis of the ground-state structure optimized the BMK/6-31g(d,p) in chloroform. The absorption spectra of molecules from the Gaussian model are reported in Figure 4, while Table 3 reports the maxima in simulated 10


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absorption (λmax), oscillator strength (f), major configurations together with the experimental data. As shown in Table 3, the calculated λmaxs (659 nm for S1a and 619 nm for S2a) are in good agreement in their experimental results (655 nm for S1a33 and 590 nm for S2a36) very well. In Figure 4 and Table 3, one can see that the maxima absorption of the porphyrin-based molecules (S1b and S1c) are red shift and more intensity in comparison with those of corresponding molecule S1a. The S2 series are the same trend with S1 series. The order of the λmax for S1 series is S1a (659 nm) < S1b (721 nm) < S1c (738 nm). The trend of the λmax for S2 series is S2a (619 nm) < S2b (691 nm) < S2c (707 nm). As shown in Table 3, the major transitions in the maxima absorption for all molecule donors come from HOMO→LUMO transitions. Figure 4 and Table S4 shows that the second absorption peaks for S1a-S1c and S2a-S2c are 554 nm (f =0.42), 506 nm (f =0.78), 504 nm (f =0.70), 523 nm (f =0.32), 495 nm (f =1.04) and 495 nm (f =0.84), respectively. Obviously, in the second absorption bands, the porphyrin-based molecules (S1a, S1c, S2b and S2c) have an enhanced absorption spectra than those of corresponding S1a and S2a, respectively. The values of f for S1a-S1c and S2a-PS2c are 2.03, 2.83, 2.85, 2.23, 2.73 and 2.76, respectively. It’s clear that the porphyrin-based molecules (S1b, S1c, S2b and S2c) in the maxima absorption exhibit much better light-absorbing efficiency (nλ) than that of corresponding molecule S1a and S2a, respectively. The ηλ of an optical material in a given spectral rang is associated with the f, ηλ=1-10- f. 26 The f of a transition is proportional to the squared transition dipole moment.69 Those results indicated that the porphyrin-based molecules have a much broader and a more enhancing absorption within the visible and infrared regions thus that provide more efficient sunlight absorption for increasing the Jsc, making the porphyrin-based molecules good candidates as donors in OSC applications. 11



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3.4 Performance of donors in active layers In OSC devices, the active layer with the structure of the donor-acceptor blends is a key component to achieve the light-to-electricity conversion. 23-26On basis of the working mechanism in OSC devices, after electron excitation in molecule donor when absorbs sunlight, the generated excitons will move to the D/A interface to take place the charge dissociating (hole and electron). With the enough energetic driving force as the precondition, the electron will transfer from donor molecule to acceptor PC71BM. The energetic driving force for the exciton dissociation come from the energy offset of the LUMO between the molecule donor and PC71BM acceptor to overcome the exciton binding energy (Eb). The Eb is an important fundamental parameter that determines the optoelectronic properties in OSC devices.70 The parameter of Eb can be taken as the energy difference between the electronic and optical band gap.26 From the Table 2, the molecule donors exhibit smaller Eb (0.24 eV for S1a, 0.22 eV for S1b, 0.21 eV for S1c, 0.27 eV for S2a, 0.24 eV for S2b, 0.22 eV for S2c, respectively). This reveals that the small-molecular donors can guarantee efficient exciton-dissociation at the D/A interface. In order to evaluate the performance of the small-molecular donors in active layer, taking the representative acceptor material PC71BM as a reference which blended together the small-molecular donors, one firstly has to construct their structures on the donor-acceptor blends. It is reported that the morphology of donor-acceptor blends in active layer of OSC devices are very key to effect on the PCE.71 Actually, the active layer consisted of the donor and the acceptor are blended to form an interpenetrating network.3 However, the construction of the theoretical models on donor-acceptor blends is a challenging work. In this work, for paralleled comparison on the performances of the small-molecular donors, we use a favorable arrangement with a large 12


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intermolecular electronic coupling, in which the two plans of six-carbon ring’s of the PC71BM and the small-molecular donor are perpendicular with the line across the mass-centers of the PC71BM and the small-molecular donor (see Figure S2). It must be point out that there are more extended morphology of donor-acceptor blends (except the structure in Figure S2) between the PC71BM acceptor and the small-molecular donor. In order to find the optimized mass-center distances between the PC71BM acceptor and the small-molecular donor, the potential energy curves along the mass-center distance were calculated by functional and basis set of M062X/6-31G(d), and the minimal potentials can be obtained (in Figure S2). On basis of the potential energy curve (In Figure S2), the optimized distance (D) of donor-acceptor blends for small-molecular donor S1a-S1c and S2a-PS2c are 3.2, 3.0, 3.3, 3.3, 3.0 and 2.9 Å, respectively. The maxima in simulated absorption (λmax), oscillator strength (f), major configurations of the donor-acceptor blends were calculated and listed in Table S5. As shown in Table S5, one can see that the maxima absorption of donor-acceptor blends for the porphyrin-based molecules (S1b-PC71BM and S1c-PC71BM) are red shift and more intensity in comparison with those of corresponding molecule S1a-PC71BM. The donor-acceptor blends for S2 series are the same trend with S1 series. The order of the λmax for the blends of S1 series is S1a-PC71BM (663 nm) < S1b-PC71BM (716 nm) < S1c-PC71BM (734 nm). The trend of the λmax for S2 series is S2a-PC71BM (633 nm) < S2b (688 nm) < S2c (706 nm). The values of f for blends of S1a-S1c and S2a-PS2c are 1.84, 2.59, 2.63, 0.82, 2.46 and 2.46, respectively. It’s clear that the blends of porphyrin-based molecules (S1b, S1c, S2b and S2c) in the maxima absorption exhibit much better light-absorbing efficiency (nλ) than that of corresponding blends of S1a and S2a, respectively. Those results indicated that the donor-acceptor blends of porphyrin-based molecules have a much 13



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broader and a more enhancing absorption within the visible and infrared regions thus that provide more efficient sunlight absorption for increasing the Jsc, making the porphyrin-based molecules good candidates as donors in OSC applications. After exciton-dissociation, we expect more electron move from donor molecule to acceptor PC71BM. Efficient electron transfer from donor to acceptor at D/A interface can increase the external quantum efficiency (EQE) or Jsc.

3, 22-26

Herein, the electron transfer distance (D),

transferred charge amount (∆q), overlaps between the regions of density depletion and increment (w) in the transitions of S0 →S1, S0 →S2 and S0 →S3 for all donor-acceptor blends were calculated and listed in Table S6. The parameters in the lowest excited singlet state ware summarized in Figure 5. As shown in Figure 5, for the lowest singlet excited states of all donor-acceptor blends corresponding transitions come from HOMO→LUMO, HOMO→LUMO+1, HOMO→LUMO+2 and HOMO→LUMO+3, and the electron move from the small-molecular donor to acceptor PC71BM. Compared with S1a and S1b series, the corresponding blends of the porphyrin-based molecules have larger electron transfer distance, more transferred charge amount and smaller overlaps between the regions of density depletion and increment (except the S2c-PC71BM). For example, the Ds of S1b-PC71BM (6.528 Å) and S1c-PC71BM (6.463 Å) are larger than that (5.377 Å) of S1a-PC71BM and the ∆qs of S1b-PC71BM (1.193|e-|) and S1c-PC71BM (1.411|e-|) are more than that of S1a-PC71BM (1.024 |e-|). In addition, the overlap (denotes as w) between the regions of density depletion and increment are calculated. For blends of S1 series, the extents of overlaps are in the order of S1a-PC71BM (0.156) > S1b-PC71BM (0.015) > S1c-PC71BM (0.012). For the S2 series, the overlaps are in the order S2c-PC71BM (0.250) > S2a-PC71BM (0.058) > S2b-PC71BM (0.025). In order to achieve a good charge separation, only a weak overlap should be 14


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evidenced. However, for the blends of S2c-PC71BM, it shows good performances in the excited singlet state S0→S2, in which the parameters of D, w and ∆q are 6.092 Å, 0.031 and 1.399 |e-|, respectively (see Table S6). In a word, either of a lager D, a greater ∆q and smaller w for the donor-acceptor blends are in favor of increasing the electronic transfer efficiency for OSC applications. Through the analysis of transferred charge amount, electron transfer distances, and overlaps involved in the lowest electron transition, the porphyrin-based molecules can act as a good candidates as donors with good electronic transfer efficiency at D/A interface in OSC applications. 3.5 Performance of donors in hole transport After the exciton dissociating in the charge transfer (CT) state at the D/A interface, the generated holes and electrons will transport along the interpenetrating network of small-molecular donors and PC71BM acceptor toward their respective electrodes, respectively. For an OSC device, active layer act as a charge transport layer with high hole and electron mobility in favor of improving the charge transport (to increase JSC and FF).72 Generally, two typical mechanisms, the coherent band model and the hopping model, usually used to describe the properties of the carrier transport in organic materials.63 At the room temperature, it is generally accepted that the properties of charge transport in organic molecules can be estimated as carrier hoping between adjacent fragments on basis of the hopping model.

73-74

Importantly, the charge transport rate (kCT) of the organic

materials can be estimated by Marcus theory.

75-76

Here, the charge transport rate kCT are mainly

influenced by two parameters of the reorganization energy (Λ) and the transfer integral (v). The theoretical details of hole transport are presented in SI. In order to calculate the charge transport rate, the reorganization energy between neutral states 15



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and cationic states is an important parameter. According to the Marcus theory, a low reorganization energy implies a high charge transport rate or hole mobility. The calculated reorganization energy of S1a-S1c and S2a-S2c are 0.215, 0.158, 0.135, 0.215, 0.162 and 0.134 eV, respectively, indicating that the porphyrin-based molecules exhibit smaller reorganization energy than that of corresponding molecule S1a and S2a. Thus, the porphyrin-based molecules (S1b, S1c, S2b and S2c) may have better hole transport ability than corresponding molecule S1a and S2a, respectively. According to the Marcus theory, a good p-type organic conjugated material should have a large charge transfer integral v for increasing charge transport rate or hole mobility. In this work, the hole transfer integral (vh) is mainly investigated because the p-type molecules as donor materials in hole transport play a major role. As we all known, the charge transfer integral is significantly dependent on the distribution patterns of frontier molecular orbitals and the intermolecular arrangement of neighboring molecules.77 Hence, in order to calculate the charge transfer integral for investigated molecules, the relative positions of adjacent fragment must be presented. The crystal structure of molecule S1a belongs to the C2/C space group.77 The experimental crystal structures of molecules S1b-S1c and S2b-S2c are not available presently. Fortunately, the crystal structure for the investigated molecules can be predicted from the polymorph module in Material Studio software. On basis of the calculations in most probable space groups, the obtained crystal structure for the investigated molecules (S1b-S1c and S2b-S2c) belong to the P1, P1, P1 and P21, respectively. We arbitrarily choose one molecule as a center in the crystal donor and take all its neighboring molecule as paired dimers. Each pair between neighboring molecules is defined as a transport pathway. The main pathways were presented in 16


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Figure 6. It’ point out that the parameters of hole transport for molecule S2a were ignored in order to save the computational cost. According to the calculations of hole transport rate in Marcus formula on basis of the calculated hole reorganization energy and the transfer integral in main transport pathway, the hole mobility of the investigated small-molecular donors can be obtained from the Einstein relation. The hole transfer integral (vh), hole transport rates (kh), center-of-mass distances (d) and hole mobility (uh) of main hopping pathway selected on basis of the crystal structure for small-molecular donors (S1a-S1c and S2b-S2c) were listed in Table 4. From the uh of molecule S1a given in Table 4, it is found that the calculated uh (0.144 cm2V-1s-1) is in good agreement with the experimental value (0.12 cm2V-1s-1)33, which demonstrates that it is reliable to have a qualitative comparison between the experimental results and the theoretical data at the present theoretical level. Moreover, Tretiak and co-works predicted the uh of S1a on its crystal structure is 0.2 cm2V-1s-1.77 As shown in Table 4, in comparison with the uh of S1a, the porphyrin-based molecules (S1b, S1c, S2b and S2c) have larger uh. The maxima transfer integral vh among the all pathway for each molecules are in the same magnitudes of 10-2. However, the porphyrin-based molecules exhibit smaller reorganization energy than that of molecule S1a. Thus, in this work, the large hole transport rates kh of the porphyrin-based molecules mainly come from the contributions of hole reorganization energy. Finally, the uhs of the porphyrin-based molecules (S1b, S1c, S2b and S2c) are 0.240, 0.166, 0.124 and 0.511 cm2V-1s-1, respectively. Obviously, the porphyrin-based molecules (except S2b) exhibit better hole transport performances than that of the high-efficient S1a donor. Hence, in view of the hole-transport abilities, the newly porphyrin-based molecules as donors can act as a good candidates for providing a large Jsc and FF in OSC applications. 17



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4. Conclusions In summary, on basis of the reported excellent A-D-A molecule S1a and S2a, we introduced the porphyrin derivatives as electron-rich block to replace the dithieno(3,2-b;2’,3’-d)silole unit, and then built four molecules S1b, S1c, S2b and S2c respectively. According to the working mechanism of the OSC devices, we investigated the electronic properties and optical absorptions of the small-molecular donors and their corresponding performances in OSC applications using DFT, TD-DFT and Marcus theory. The results indicated that the selected methods we used in this works could reproduce the reliable HOMO/LUMO level energy and optical absorptions of S1a and S2a in line with their experimental results. The performances in absorption spectra display that the porphyrin-based molecules (S1b, S1c, S2b and S2c) can enhance the light absorptions with a redshift and stronger spectra in comparison with these of corresponding S1a and S2a, respectively. All investigated molecules exhibit smaller exciton binding energy which can guarantee efficient exciton-dissociation at the D/A interface. Compared with S1a and S2a, the porphyrin-based molecules in active layers exhibit better electronic transfer properties at D/A interface in OSC applications. The present theoretical level can provide a reliable result on the hole mobility for S1a (uh = 0.144 cm2V-1s-1) based on its crystal in good agreement with the experimental value (0.12 cm2V-1s-1). On basis of the predicted crystal structure for porphyrin-based molecules (S1b, S1c, S2b and S2c), the calculated hole mobilities of the porphyrin-based molecules (S1b, S1c, S2b and S2c) are 0.240, 0.166, 0.124, 0.511 cm2V-1s-1, respectively. In view of excellent solar absorption, small exciton binding energy, good electronic transfer properties at D/A interface and high hole mobility, the porphyrin-based molecules (S1b, S1c, S2b and S2c) can act as a good candidates for providing a large short-circuit current and fill 18


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factor in OSC applications. The obtained results are in qualitative and quantitative line with the experimental results and suggest that the current computational model could be further used to obtain valuable insights for the design of new porphyrin-based molecules as donors aiming at developing the performances of presently available OSCs.

Acknowledgements

This work was supported by Fundamental Research Funds for the Central Universities (Grant No. XDJK2016C036) and Project Funded by China Postdoctoral Science Foundation (Grant No. 2016M592618). Moreover, calculations on Materials Studio were provided help of Prof. Hongkuan Yuan who worked at School of Physical Science and Technology in Southwest University.

The Supporting Information is available free of charge on the ACS Publications website at DOI: The calculated potential energy curve of donor-acceptor blends, main hole hopping pathways of molecule S1a, frontier molecular orbital energy, excitation energy of molecules and donor-acceptor blends, transport properties of S1a, electron density difference plots, and the theoretical details of hole transport.

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Figure Captions Figure 1. Chemical structure of the investigated small-molecular donors. Figure 2. Schematic energy levels of the small-molecular donors from the HSE03/6-311G(d,p) level calculations. Figure 3. Illustration of frontier molecule orbitals for the small-molecular donors from HSE03/6-311g(d,p) calculations. Figure 4. Simulated absorption spectra of all small-molecular donors (S1a-S2c) using the TD-BMK/6-31g(d,p) functional and basis set in chloroform. Figure 5. Electron density difference plots and the major configurations of electronic transition in the lowest singlet excited states for donor-acceptor blends. D is the electron transfer distance (Å); ∆q is the transferred charge amount (|e-|), w is overlaps between the regions of density depletion and increment. (Isovalue: 6×10-4e·au-3) 25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 6. Main hole hopping pathways selected based on the crystal structures for all investigated molecules.

Figure 1. Chemical structure of the investigated small-molecular donors.

26


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Figure 2. Schematic energy levels of the small-molecular donors from the HSE03/6-311G(d,p) level calculations.

27



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Figure 3. Illustration of frontier molecule orbitals for the small-molecular donors from HSE03/6-311g(d,p) calculations.

28


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Figure 4. Simulated absorption spectra of all small-molecular donors (S1a-S2c) using the TD-BMK/6-31g(d,p) functional and basis set in chloroform.

29



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Figure 5. Electron density difference plots and the major configurations of electronic transition in the lowest singlet excited states for donor-acceptor blends. D is the electron transfer distance (Å); ∆q is the transferred charge amount (|e-|), w is overlaps between the regions of density depletion and increment. (Isovalue: 6×10-4e·au-3)

30


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Figure 6. Main hole hopping pathways selected based on the crystal structures for all investigated molecules.

31



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Table Captions Table 1 Selected bond lengths L (Å) and dihedral angles Φ (deg) of all moleculesa from the HSE03/6-311G(d,p) level calculations. Table 2 The energetic driving force ∆(LUMOD-LUMOA) and exciton binding energy (Eb). Table 3 Optical absorptions of the simulated molecule donors calculated at the TD-BMK/6-31g(d,p) calculations in chloroform: the maxima absorption (λmax), oscillator strength (f), major configurations together with the experimental data. Table 4 The reorganization energy (eV), hole transfer integral (eV), hole transport rates (s-1), center-of-mass distances (Å) and hole mobilities (cm2V-1s-1) of main hopping pathway selected on basis of the crystal structure for small-molecular donors (S1a-S1c and S2b-S2c).

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Table 1 Selected bond lengths L (Å) and dihedral angles Φ (deg) of all moleculesa from the HSE03/6-311G(d,p) level calculations. S1a

S1b

S1c

S2a

S2b

S2c

L(C2-C3)

1.44

1.40

1.40

1.44

1.40

1.40

Φ(C1−C2−C3−C4)

0.24

1.20

0.72

0.01

5.49

3.49

33



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Table 2 The energetic driving force ∆(LUMOD-LUMOA) and exciton binding energy (Eb). S1a

S1b

S1c

S2a

S2b

S2c

∆(LUMOD-LUMOA) (eV)

0.58

0.47

0.51

0.83

0.67

0.71

Eb (eV)

0.24

0.22

0.21

0.27

0.24

0.22

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Table 3 Optical absorptions of the simulated molecule donors calculated at the TD-BMK/6-31g(d,p) calculations in chloroform: the maxima absorption (λmax), oscillator strength (f), major configurations together with the experimental data. transition

λ(nm)

f

major configurations

Exp. λ (nm)a

S1a

S0 →S1

659

2.03

H→L (90%)

655

S1b

S0 →S1

721

2.83

H→L (89%)

S1c

S0 →S1

738

2.85

H→L (90%)

S2a

S0 →S1

619

2.23

H→L (90%)

S2b

S0 →S1

691

2.73

H→L (89%)

S2c

S0 →S1

707

2.76

H→L (90%)

a

590

From the ref. 33 and 36.

35



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Page 36 of 37

Table 4 The reorganization energy (eV), hole transfer integral (eV), hole transport rates (s-1), center-of-mass distances (Å) and hole mobilities (cm2V-1s-1) of main hopping pathway selected on basis of the crystal structure for small-molecular donors (S1a-S1c and S2b-S2c). Compound

Pathway

Λh/eV

vh

kh

S1a

1

0.215

4.049×10-2

7.40×1012

S1b

S1c

-5

S2c

uexpa

5.498

0.144

0.12

1.000×10

4.51×10

15.207

3

-2.145×10-3

2.08×1010

14.346

4

1.254×10-3

7.09×109

29.198

5

-3

3.064×10

4.24×10

26.133

6

1.000×10-5

4.51×105

17.808

1

-2

0.158

10

3.245×10

12

6.811

9

9.62×10

-4

2

4.530×10

1.87×10

15.585

4

5.249×10-5

2.52×107

29.416

5

-4

9

16.500

6.790×10

4.21×10

-6

4

6

2.522×10

5.81×10

19.915

7

3.684×10-3

1.24×1011

26.776

8

1.813×10-2

3.00×1012

6.958

1

-2

12

2.020×10

5.03×10

7.436

2

-3.422×10-3

1.44×1011

30.113

3

-6.459×10-4

5.15×109

24.822

4

-1.602×10

-2

5

-5.282×10-5

1

0.135

12

-3

1.380×10 0.162

8.478

3.44×107

20.052

10

35.007

12

2.35×10 -2

2.51×10

7.210

1.135×10-4

1.12×108

22.267

3

-5.015×10-5

2.18×107

41.848

4

-1.527×10

-3

2.02×10

18.012

5

-4.661×10-5

1.88×107

36.199

7

-4.785×10

-4

9

16.032

8

-9.186×10

-3

11

7.32×10

23.537

9

-4.094×10-4

1.45×109

29.590

1

-3.131×10

-2

2

-2.790×10

-3

3

-4.525×10-5

4

-6.974×10

-4

5

3.391×10

-5

6 7

0.134

-1.701×10

3.17×10

2

8 a

uh

2

6 S2b

5

D

10

1.99×10

13

8.053

10

9.73×10

17.560

2.56×107

13.367

9

30.622

7

1.44×10

37.305

-1.281×10-4

2.05×108

20.155

7.400×10

-5

7

16.629

-1.281×10

-4

8

20.155

1.23×10

6.08×10

6.85×10 2.05×10

From the ref. 33.

36


0.240

0.166

0.124

0.511

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TOC

37


Theoretical Investigation on Porphyrin-Based Small Molecules as

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