Effect of mono-halogen-substitution on the electron transporting properties of perylene diimides: A density functional theory study

Journal of Molecular Liquids 287 (2019) 110968

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Effect of mono-halogen-substitution on the electron transporting properties of perylene diimides: A density functional theory study Keke Wen, Songyan Feng, Xugeng Guo ⁎, Junfeng Li ⁎, Jinglai Zhang ⁎ Institute of Upconversion Nanoscale Materials, Henan Provincial Engineering Research Center of Green Anticorrosion Technology for Magnesium Alloy, College of Chemistry and Chemical Engineering, Henan University, Kaifeng 475004, China

a r t i c l e

i n f o

Article history: Received 28 February 2019 Received in revised form 16 April 2019 Accepted 12 May 2019 Available online 17 May 2019 Keywords: Electron transporting material Mono-halogen-substitution Electron mobility Adsorption mechanism Density functional theory

a b s t r a c t Density functional theory and Marcus electron transfer theory were used to explore the electron transporting properties of a series of mono-halogenated perylene diimides X-PDI (X = F, Cl, Br), as well as their parent compound H-PDI. The electronic structures, absorption spectra, electron mobility, and adsorption properties were investigated. It is found that the theoretically simulated absorption spectra reproduce very well the experimentally available data. The predicted electron mobilities follow the order of F-PDI b H-PDI b Cl-PDI ≈ Br-PDI, which is in accordance with the experimental trend. Furthermore, our theoretically designed molecule Cl-PDI exhibits good hydrophobicity, stability and solubility. Importantly, the electron mobility of Cl-PDI is very similar as that of BrPDI. Considering that mono-bromine-substituted perylene diimide Br-PDI has been observed to be an excellent electron transporting material in inverted perovskite solar cell, mono-chlorine-substitution Cl-PDI is also expected to be a potential ETM. © 2019 Elsevier B.V. All rights reserved.

1. Introduction In recent years, considerable attention has been focused on the field of perovskite solar cells (PSCs), due to their advantages in low cost, simple fabrication and high efficiency [1–4]. It is known that based on either mesoscopic or planar device architectures with normal (n-i-p) or inverted (p-i-n) structures, PSCs usually consist of a light harvesting perovskite layer sandwiched between a hole transporting layer and electron transporting layer. In sharp contrast to the multitude of papers reporting hole transporting materials (HTMs), only a few reports have dealt with ETMs [5–20]. For inverted PSC devices, an ETM is located upon perovskite layer and a metal electrode is deposited on top of the ETM layer. Therefore, ETMs have a remarkable influence on the efficiency and stability of inverted PSCs. So far, the C60 fullerene derivative, [6,6]-phenyl C61 butyric acid methyl ester (PC61BM), has been widely used as an ETM in the inverted PSCs, owing to the high conductivity [21], decent electron mobility [22], and suitable energy level alignment [23]. However, its high cost, poor solubility and photochemical instability limit its further commercial applications [24,25]. To overcome such drawbacks, non-fullerene ETMs have recently been prepared for use in inverted PSCs. The perylene diimide (PDI) derivatives are attracting great interest as ETMs in PSCs due to their fascinating properties, such as good ⁎ Corresponding authors. E-mail addresses: [email protected] (X. Guo), [email protected] (J. Li), [email protected] (J. Zhang).

https://doi.org/10.1016/j.molliq.2019.110968 0167-7322/© 2019 Elsevier B.V. All rights reserved.

photochemical stability, high electron affinity, easy functionalization and high conductivity [26–30]. Recently, Jo and co-workers used a new perylene diimide dimer (diPDI) as an ETM for inverted PSCs and acquired power conversion efficiency (PCE) of 10% [29]. More recently, Wu et al. synthesized two simple mono-halogen-substituted PDI derivatives, F-PDI and Br-PDI, as well as the parent H-PDI, and explored the feasibility of replacing PC61BM using the three compounds as ETMs for inverted PSCs [30]. They observed that compared with PSCs based on HPDI, the mono-fluorine substituted F-PDI PSCs showed virtually no photovoltaic effect, while the mono-bromine substituted Br-PDI PSCs exhibited better performance, with a notable PCE of 10.50% in the presence of ZnO nanoparticles [30]. Importantly, owing to the highest solubility, conductivity, and electron mobility among the three compounds, the PCE of Br-PDI-based PSCs is comparable to that of PC61BM-based PSCs (10.50% vs. 11.07%) [30]. Despite such contributions, theoretical investigations on the electron transporting properties of the small organic ETMs for PSCs are still scarce [31,32]. To understand the effect of simple mono-halogen substitution on their properties, we employed density functional theory (DFT) and Marcus electron transfer theory to determine the geometries and electron transporting properties of four perylene diimides X-PDI (X = H, F, Cl, Br), as shown in Fig. 1. The DFT theory has been proven to be the most popular approach in the last 30 years [33–35], and the Marcus electron transfer theory has been found to be suitable for estimating the electron hopping rate [36,37]. It is expected that the present calculations can provide a theoretical guide for understanding the intrinsic transporting properties of organic small molecules.

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revised to include inter alia statistical aspects and quantum effects [56,57]; however, the more simplified method that is still applied extensively in the literature [32,58,59] and in the present work, is adequate for a priori studies on novel molecules. To better understand the interfacial interaction between the ETMs and CH3NH3PbI3, it is necessary to study the adsorption process of ETM molecules on the CH3NH3PbI3 (110) facet. Taking Br-PDI as a representative example, we explored its adsorption properties on the 3 × 4 × 4 CH3NH3PbI3 cell (110) surface. For the Br-PDI-CH3NH3PbI3 system, molecular dynamics (MD) simulation was performed in NVT ensemble with the timestep of 1 fs to get an initial guess. The bare CH3NH3PbI3, isolated Br-PDI molecule and Br-PDI-CH3NH3PbI3 system were optimized by using the projector-augmented wave (PAW) [60,61] method, as performed in the Vienna Ab initio Simulation Package (VASP) program [62–65]. The Perdew-Burke-Ernzerhof (PBE) of GeneralizedGradient Approximation [66] was employed. It should be emphasized that the bottom two layers of atoms were fixed, while the upper two layers of atoms closer to the Br-PDI molecule were optimized. The kpoint sampling (2 × 2 × 1 grid) was applied and a cutoff energy of 400 eV was adopted consistently on the basis of Monkhorst and Pack scheme in our calculations. Moreover, the total energy was converged to 1.0 × 10−4 eV/atom. Van der Waals interactions were considered by performing DFT-D3 calculations. The density of states (DOS) and projected density of states (PDOS) were obtained to further analyze the interfacial properties. The Visualization for Electronic and Structural Analysis (VESTA) code [67] was used to visualize the crystal structures.

Fig. 1. Chemical structures of the molecules investigated in this work.

2. Theoretical method and computational details In order to gain insights into the geometrical configuration of the investigated compounds, density functional theory (DFT) calculations were carried out using B3LYP [38–40] hybrid functional along with a 6-31G(d,p) basis set. Harmonic vibrational frequencies of the four molecules were also calculated at the same theoretical level. There are no imaginary frequencies in all geometric structures, indicating that the optimized geometries are stable minima in the potential energy surfaces. According to the optimized structures, their UV–vis absorption spectra were simulated by the time-dependent DFT (TD-DFT) calculations. Five functionals B3LYP, CAM-B3LYP [41], LC-BLYP [42,43], PBE0 [44] and M06-2X [45] were employed in combination with a polarizable continuum model (PCM) [46,47] using chloroform as solvent. All the calculations are implemented in the Gaussian 09 package [48]. The hopping transport model was used to describe the carrier motion process. According to the Einstein relation, the drift mobility, μ, is expressed as [49,50]: μ¼

e 1 X 2 r kP kB T 2n i i i i

ð1Þ

where kB represents the Boltzmann constant; T, the temperature (298 K); ri, the intermolecular center-to-center distance; n, the dimensionality (here, we consider the charge motion as a random walk in three dimensions, that is, n = 3); ki and Pi, the hopping rate and the relX ki) for the charge transfer to the ith neighative probability (P i ¼ ki = i

bor, respectively. The self-exchange electron hopping rate k can be evaluated by using the Marcus theory [51]: k¼

 4π2 v2 1 λ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi exp −  h 4kB T 4πλkB T

ð2Þ

where λ denotes the reorganization energy; h, the Planck constant; v, the electronic transfer integral. It should be pointed out that limitations of Marcus theory comprise the lack of configurational entropy, nuclear tunneling, and electronic coupling over a broad temperature range, which have been further developed using the McConnell equation [52] and Marcus-Levich-Jortner theory [53,54]. Despite available other charge transfer theories [55], Marcus theory has been commonly

3. Results and discussion 3.1. Frontier molecular orbitals It is known that the primary condition of an ideal ETM is the energy level matching in an inverted PSC, that is, the energy levels of the highest-occupied molecular orbital (HOMO) and the lowestunoccupied molecular orbital (LUMO) for an ETM molecule are lower than those of the valence band top (VBT) and conduction band bottom (CBB) of perovskite, respectively. In general, the HOMO and LUMO of frontier orbitals are closely related to the gain and loss of electrons, both of which play a vital role in the hole and electron transport processes [32]. Therefore, we optimized the ground-state structures of four targeted molecules by employing the B3LYP/6-31G(d,p) calculations, and the corresponding geometries are provided in Fig. S1 of the Supporting Information. Then, we explored the energy levels of HOMO and LUMO using the B3LYP functional along with a larger 6311++G(d,p) basis set. Their frontier molecular orbitals, together with the calculated and experimental energy levels, are depicted in Fig. 2. It is apparent that the electron density distributions of HOMOs and LUMOs of the studied molecules have similar characteristics. The HOMOs and LUMOs are mainly delocalized on the central perylene diimide cores, and the influence of mono-halogen-substitution on the HOMO and LUMO energy levels is negligible. For mono-halogenated X-PDI (X = F, Cl, Br), the electron distributions of LUMOs are slightly extended to fluorine, chlorine and bromine atoms, respectively. Moreover, the electron distributions of LUMOs for Br-PDI and Cl-PDI are larger than that of F-PDI, which may be the decisive factor for the different volumes of halogen atoms. As shown in Fig. 2, the LUMO energy levels of the four molecules are in the range from −3.80 to −3.90 eV, all of which are lower than the CBB energy level of perovskite. This guarantees that the electrons are transferred from the perovskite to the ETM, and the ETM can serve as a hole blocking layer to suppress charge recombination. It is important to highlight that the theoretical calculations of the LUMO energy levels agree well with the available experimental data, with the deviation of less than 0.2 eV. As for the HOMO energy levels, the predicted results are much lower than the VBT of the perovskite. The calculated HOMO energy levels of H-PDI, F-PDI and Br-PDI

K. Wen et al. / Journal of Molecular Liquids 287 (2019) 110968

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Fig. 2. Contour plots of frontier molecular orbitals for the investigated molecules, and their theoretical and experimental energy levels are also presented.

are decreased by 0.35, 0.51 and 0.37 eV, respectively, with respect to their experimental values [30]. It appears that all four molecules obey the energy level matching principle. However, we note that the F-PDI-based PSCs were observed to exhibit virtually no photovoltaic effect, whereas the Br-PDI-based PSCs showed better performance, in comparison with PSCs based on H-PDI. Accordingly, the energy level matching is only an essential condition of an effective ETMs. As can be seen below, electron mobility plays a more important role for determining the performance of ETMs.

3.2. Electronic absorption spectrum In general, the absorption of the ETMs locates the UV region, thus ensuring a small overlap with the light absorption of the perovskite. Recent literatures have demonstrated that the absorptions of some ETM molecules are in the visible light region, and the related PCE of PSCs reaches about 17.1% [68,69]. Hence, it is necessary to simulate the UV– vis absorption spectrum of the ETM molecules. The absorption spectra of all molecules were simulated at five different functional levels in combination with the PCM model using chloroform as solvent, and the corresponding data are shown in Table 1. It is evident that the PBE0 functional yields the best agreement with the experimental findings [30], with the maximum deviation of 6 nm. Therefore, the curves of absorption spectra obtained by TD-PBE0 are plotted in Fig. S2 of the Supporting Information. Compared with H-PDI, the predicted maximum absorption wavelengths of F-PDI and Cl-PDI are blue-shifted by 2 and 1 nm, respectively, while the bromine atom induces a slight red-shifting of the absorption (4 nm). Overall, the simple monohalogen-substitutions have no significant effect on the maximum absorption wavelengths.

Table 1 The value of the maximum absorption peak for the investigated molecules by means of B3LYP, CAM-B3LYP, LC-BLYP, PBE0 and M06-2X methods in chloroform with the 6-31G (d,p) basis set along with the experimental result. Mol. H-PDI F-PDI Br-PDI Cl-PDI a

B3LYP 534 532 539 –

CAM-B3LYP 474 471 473 –

LC-BLYP 508 506 509 –

PBE0 519 517 523 518

M06-2X

3.3. Electron transporting properties Electron mobility is another important indicator for measuring the performance of ETMs, which can regulate the short-circuit current density, further leading to the change in the PCE of device [70]. In general, a larger short-circuit current density must rely on a higher electron mobility, in turn, resulting in a higher PCE of the device. Additionally, carrier transfers are also very important in many physical and chemical processes. The intermolecular electronic coupling significantly affects the carrier mobility. In the previous study, crystal prediction was generally performed by using Materials Studio package [71]. In these predicted crystal structures, a molecule was selected as the center to diffuse charge, and eight or nine nearest neighboring intermolecular hopping pathways were recognized. Given that the expensive computational cost and the accuracy of calculation results, the above method is markedly unsuitable for our current research. It has been verified that the transfer path between the most stable dimer is preferred in other possible transfer routes [72]. Consequently, the electron transporting mobility can be approximately estimated by means of the most stable dimer according to Eqs. (1) and (2). The initial guess structure of the dimer is the primary condition for the accuracy of the final calculation. Molecular dynamics (MD) simulations of the dimer were completed for 30 ps at 298 K in NVT ensemble with the FORCITE module of Materials Studio 7.0 package. To achieve a better understanding of the circumstance of thermodynamic equilibrium, the energy versus time curve of the four molecules during the kinetic simulation is plotted in Fig. S3 of the Supporting Information. As can be seen in Fig. S3, the MD simulations for the investigated molecules reach the thermal equilibrium after 18 ps. The equilibrium structure with lower energy is randomly selected as the initial guess of dimer. Afterwards, the optimization is carried out at the M06-2X/6-31G(d,p)

Table 2 The centroid to centroid distances (r, Å), the electron transfer integrals (v, meV), reorganization energies (λ, eV), electron hopping rate (k, s−1) and electron mobilities (μ, cm2·V−1·s−1) of the optimized dimer. Molecule

Expt.a

471 468 471 –

Experimental absorption wavelengths measured in chloroform solution [30].

525 520 524 –

r H-PDI F-PDI Br-PDI Cl-PDI a

Experimental dataa

Calculated data

8.09 9.98 8.30 7.38

v −18.10 6.13 53.30 55.90

λ 0.28 0.31 0.30 0.30

Experimental data from Ref. [30].

μ

k 11

6.52 × 10 5.81 × 1010 4.75 × 1012 4.98 × 1012

μ −2

2.77 × 10 3.75 × 10−3 2.13 × 10−1 1.76 × 10−1

1.12 × 10−4 8.31 × 10−6 1.08 × 10−3

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K. Wen et al. / Journal of Molecular Liquids 287 (2019) 110968

Fig. 3. Electron density distributions for LUMOs of the dimers.

level. The stable structures of the obtained dimers are depicted in Fig. S4 of the Supporting Information. Based on the optimized dimer, the centroid to centroid distance (r), electron transfer integral (v), reorganization energy (λ), electron hopping rate (k), and electron mobility (μ) are listed in Table 2. Among these molecules considered here, the λ and r values of F-PDI are the largest, while the v and k results are the smallest, thus resulting in the smallest μ. The μ of F-PDI is estimated to be 3.75 × 10−3 cm2·V−1·s−1. The μ of H-PDI is one-order-of-magnitude larger than that of F-PDI, mainly owing to the larger k of the former. The μ of Br-PDI is largest among the four molecules investigated in the present work, and the calculated value is 2.13 × 10−1 cm2·V−1·s−1. It is noteworthy that the predicted μ values of H-PDI, F-PDI, and Br-PDI are in the order of F-PDI b H-PDI b Br-PDI, which is consistent with the experimental findings, although the theoretically estimated results are 2–3 orders of magnitude lager than the experimentally available data [30]. Such an overestimation has also been found in a recent theoretical study that the predicted μ value of the TDTP molecule (2.3 × 10−2 cm2·V−1·s−1) is about 2 orders of magnitude lager than the experimental observation (2.8 × 10−4 cm2·V−1·s−1) [17,32]. Generally, if the deviation between the theory and experiment is within three orders of magnitude and their relative order is consistent, the theoretical method should be reliable. As for Cl-PDI, the μ is calculated to be 1.76 × 10−1 cm2·V−1·s−1, which is very close to that of Br-PDI. Considering that mono-bromine-substituted perylene diimide Br-PDI has observed to be a good ETM material, the mono-chlorine-substitution Cl-PDI is also expected to be potential ETM, which need to further experimental verification. To visually gain a better understanding of the abnormal phenomenon, the electron density distribution for the LUMO of the four dimers

where η is the resistance of the chemical potential to change in the number of electrons, and IPa and EAa are adiabatic ionization potential and adiabatic electron affinity potential, respectively. The calculated η values are listed in Table 3. From Table 3, one can notice that the η values of the four molecules are in the range of 2.36–2.39 eV, indicating that all molecules are provided with competitive stability.

Table 3 The adiabatic ionization potential (IPa, eV), electron affinities (EAa, eV), and absolute hardness (η, eV), the value of lgPn-octanol/water measures the hydrophilic and hydrophobic properties of the molecule.

Table 4 The calculated solvation Gibbs free energies (ΔGsolv, kcal/mol) of the studied compounds in chloroform.

Compounds

IPa

EAa

η

H-PDI F-PDI Br-PDI Cl-PDI

7.13 7.16 7.19 7.20

2.36 2.39 2.47 2.46

2.39 2.39 2.36 2.37

lgPn-octanol/water 8.74 9.04 9.42 9.43

is plotted in Fig. 3. It can be seen from Fig. 3 that the electron densities of LUMOs for H-PDI and F-PDI are mainly located in the one molecule of each dimer. Nevertheless, The LUMOs of Br-PDI and Cl-PDI are distributed over two molecules of the dimer. It is certain that there is a significant charge transfer between the two molecules for Br-PDI and ClPDI, while there is only intramolecular charge transfer for H-PDI and F-PDI. Consequently, the electron transfer integrals of Br-PDI and ClPDI is very large (more than 50 meV), thereby giving rise to the relatively larger electron mobility. 3.4. Hydrophobicity, stability, and solubility In a typical architecture of the inverted PSCs, the electron transporting layer is located between the metal electrode and the perovskite, protecting the perovskite layer against oxygen and humidity [20]. As a result, one of the most important criteria for determining the nature of the devices is the stability of the ETM compound, which can be evaluated by absolute hardness (η) [73–75]:

η¼

!   2 1 ∂μ 1 ∂ E IP a −EAa ¼ ¼ 2 2 ∂N 2 ∂N2

ð3Þ

Compounds

ΔGsolv

H-PDI F-PDI Br-PDI Cl-PDI

−26.61 −24.98 −25.37 −27.05

K. Wen et al. / Journal of Molecular Liquids 287 (2019) 110968

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Fig. 4. Temperature and energy of a Br-PDI molecule on 3 × 4 × 4 CH3NH3PbI3 (110) surface in MD simulation.

At the same time, it is also equally necessary to consider the hydrophobic property of the ETM molecules in the humid environment except the stability of individual molecule. As we all know, the multiple factors affecting device performance play critical roles in achieving the large-scale applications of the devices. In the present work, the noctanol/water partition coefficient P was primarily used to describe the hydrophobic property of the compounds [76]. It can be expressed by the following formula:

lgP n−octanol=water ¼

−ðEn−octanol −Ewater Þ 2:303RT

ð4Þ

With the help of the SMD model [77], the single-point energy of a molecule in n-octanol and water is easily obtained. According to the formula (4), the values of lgPn-octanol/water can be evaluated, which are incorporated into Table 3. Generally speaking, the larger the lgPn-octanol/water, the less easily the ETM molecule deliquesces in a humid environment, which is beneficial to improve the stability of the PSCs. As displayed in Table 3, the lgPn-octanol/water values of four targeted molecules are in the range 8.7–9.5. Evidently, Br-PDI and Cl-PDI with relatively larger lgPn-octanol/water exhibit excellent hydrophobicity, which is helpful for facilitating the resistance of CH 3 NH3 PbI 3 to water in environment, thereby enhancing the stability of the PSCs. The ultimate goal for preparing the PSCs is to achieve its large-scale application. When the device is fabricated via solution processing, the previously formed layer should not be dissolved in the following solution so as to form uniform thin-film. In general, the perovskite materials are soluble in aprotic polar solvents, and have hydrophilicity with high surface energy to accelerate the formation of a uniform perovskite thinfilm. Consequently, ETMs in inverted PSCs should be soluble in the nonpolar organic solvents. The solubility of the ETMs in the non-polar organic solvents is another important parameter for the property of the device. The solvation free energy (ΔGsolv) indicates the solubility of the ETMs in the given solvent, which is defined as the difference in free energy between the solute in the solvent and gas phase [78]. As we all know, the more negative the solvation free energy, the easier the material dissolves. In the present system, the solubility of the investigated molecules in chloroform was evaluated, and the corresponding data are presented in Table 4. It is seen that among the four molecules the ΔGsolv of F-PDI is the largest, which indicates that it could dissolve in chloroform spontaneously and presents worse solubility. This is consistent with the experimental results [30]. It is worthy to note that ClPDI has the most negative ΔGsolv, suggesting that the solubility in chloroform is enhanced by the mono chlorine substitution.

3.5. ETM-CH3NH3PbI3 system In the structure of inverted PSCs, the perovskite layer is in the middle of the ETM and HTM. Accordingly, the interfacial interaction between the ETM and the perovskite layer plays a significant role in the overall performance of the device. In the above discussion, the properties of the individual ETM molecule were only explored, and the interfacial interaction between the ETM and the perovskite layer was not investigated in depth. Therefore, in this section, we mainly studied the adsorption of ETMs on the CH3NH3PbI3 (110) surface. First of all, the dynamic simulation was carried out under the NVT ensemble to obtain a reasonable relative position. Then, the structure was optimized to obtain a stable configuration. Considering that the absorption calculation is a very expensive work, it is very difficult to determine the adsorption processes of all the molecules. To save the computational cost, the absorption of Br-PDI on the CH3NH3PbI3 (110) surface, as a representative, was only calculated, owing to the largest electron mobility among the molecules investigated in the work. The obtained temperature and energy curves with time during MD simulations are shown in Fig. 4, and the optimized configuration of the Br-PDI molecule adsorbed on the CH3NH3PbI3 (110) surface is plotted in Fig. 5. We note that the

Fig. 5. Optimized configuration of Br-PDI adsorbed on CH3NH3PbI3 (110) surface.

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K. Wen et al. / Journal of Molecular Liquids 287 (2019) 110968

Fig. 6. Calculated total density of states (DOS) and projected density of states (PDOS) for interfaces of CH3NH3PbI3 (110) adsorbed by Br-PDI.

vertical distance between the bromine atom and the CH3NH3PbI3 (110) facet is estimated to be 3.65 Å, and there is no chemical bond formation between Br-PDI and the CH3NH3PbI3 (110) surface. This clearly indicates that the adsorption between Br-PDI and the CH3NH3PbI3 (110) surface is weak physical adsorption rather than chemisorption. In addition, the DOS and PDOS for the Br-PDI, CH3NH3PbI3 (110) surface and Br-PDI-CH3NH3PbI3 system are displayed in Fig. 6. It can be seen that the band gap of CH3NH3PbI3 is almost unchanged before and after adsorption (about 1.00–1.01 eV). When the Br-PDI molecule is adsorbed onto CH3NH3PbI3 (110) surface, the LUMO and HOMO energy levels of Br-PDI are lower than those of CBB and VBT of perovskite,

respectively. Only in this way can electron transfer from perovskite to ETM be effectively ensured and holes can be further blocked. After adsorption, the CBB of CH3NH3PbI3 shifts to a more positive value, and the LUMO energy level of Br-PDI moves to a more negative value. The difference between the CBB of CH3NH3PbI3 and LUMO of Br-PDI is 0.05 eV before adsorption. However, after adsorption, the value is dramatically increased to 0.98 eV, which promotes the injection of electrons from CH3NH3PbI3 to ETM. In order to better describe the changes of interface properties for the ETM-CH3NH3PbI3 system, the three-dimensional charge density difference of Br-PDI showing charge transfer and interface recombination is shown in Fig. 7. The charge depletion (in blue) and charge accumulation (in yellow) are obviously displayed. After adsorption, it can be clearly seen that the charge density accumulates toward the CH3NH3PbI3 surface, which further promotes the electron transfer from the perovskite to the ETM. Alternatively, On the basis of the Bader method, the number of transferred electrons from perovskite to ETM can be calculated, which can roughly explain the progress of the transfer. The number of transferred electrons for Br-PDI adsorbed to CH3NH3PbI3 (110) surface was 0.07. Therefore, one can conclude that the mono-brominesubstituted perylene diimide exhibits good charge transport capability. 4. Conclusions The electron transporting properties of four perylene diimide derivatives X-PDI (X = H, F, Cl, Br) have been determined by the density functional theory coupled with semi-classical Marcus electron transfer theory. The effect of mono-halogen-substitution on their properties such as electronic structures, absorption spectra and electron mobility were estimated. The main conclusions are as follows. (1) A good agreement is found between the calculated absorption spectra and the experimental findings. (2) The estimated electron mobilities are in the order of F-PDI b HPDI b Cl-PDI ≈ Br-PDI, which is consistent with the experimental trend. (3) Our theoretically designed molecule Cl-PDI shows excellent hydrophobicity, stability and solubility.

In summary, our newly designed Cl-PDI may have a potential application in inverted perovskite solar cell as a non-fullerene electron transporting material. Acknowledgements This work was supported by the National Natural Science Foundation of China (NSFC) (Grant Nos. 21503069 and 21676071). We thank the State Key Laboratory of Physical Chemistry of Solid Surfaces (Xiamen University) and National Supercomputing Center in Shenzhen (Shenzhen Cloud Computing Center) for providing computational resource and software. Appendix A. Supplementary data Supplementary data to this article can be found online at https://doi. org/10.1016/j.molliq.2019.110968. References

Fig. 7. Three-dimensional representations of charge density differences of Br-PDI (defined as Δρ = ρtotal − ρCH 3NH 3PbI 3 − ρETM, ρtotal is the total charge density, and ρCH 3NH 3PbI 3, ρETM, represent the charge density of the individual parts, respectively).

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