Material exploration via designing spatial arrangement of octahedral units: a case study of lead halide perovskites

Halide perovskites have attracted tremendous attention as semiconducting materials for various optoelectronic applications. The functional metal-halide octahedral units and their spatial arrangements play a key role in the optoelectronic properties of these materials. At present, most of the efforts for material exploration focus on substituting the constituent elements of functional octahedral units, whereas designing the spatial arrangement of the functional units has received relatively little consideration. In this work, via a global structure search based on density functional theory (DFT), we discovered a metastable three-dimensional honeycomb-like perovskite structure with the functional octahedral units arranged through mixed edge- and corner-sharing. We experimentally confirmed that the honeycomb-like perovskite structure can be stabilized by divalent molecular cations with suitable size and shape, such as 2,2′-bisimidazole (BIM). DFT calculations and experimental characterizations revealed that the honeycomb-like perovskite with the formula of BIMPb2I6, synthesized through a solution process, exhibits high electronic dimensionality, a direct allowed bandgap of 2.1 eV, small effective masses for both electrons and holes, and high optical absorption coefficients, which indicates a significant potential for optoelectronic applications. The employed combination of DFT and experimental study provides an exemplary approach to explore prospective optoelectronic semiconductors via spatially arranging functional units.

Inspired by the success of lead iodide perovskites, substantial efforts have been made to search for various perovskite-based halide materials for optoelectronic applications [35,36]. At present, most efforts focus on material design by partially or completely substituting the constituent elements in the known perovskite structures, mainly the elements comprising the functional octahedral units, whereas relatively few efforts aim to expand the perovskite family by discovering structure motifs with designed arrangements of functional octahedral units. In this work, via a global structure search using CsPbI 3 as a paradigm, we discovered a metastable 3D honeycomb-like perovskite structure with the [PbI 6 ] functional octahedral units arranged by a mixed edge-and corner-sharing means. Experimentally, the honeycomb-like perovskite framework was stabilized by a divalent molecular cation with suitable size and shape, such as dications of 2,2′bisimidazole (BIM). Density functional theory (DFT) calculations and experimental characterizations revealed that the honeycomb-like perovskite with the formula of BIMPb 2 I 6 , synthesized through a solution process, exhibited high electronic dimensionality, a direct allowed bandgap of 2.1 eV, small effective masses for both electrons and holes, and high optical absorption coefficients. A photodetector based on the BIMPb 2 I 6 single crystal showed responsivity and photodetectivity of 0.1 mA/W and 1.1 Â 10 10 Jones, respectively. This work provides an exemplary approach for designing prospective optoelectronic halide perovskites or perovskite derivatives by arranging the functional units.

Results and discussion
To unveil possible frameworks that perovskite-type compounds can form, we predicted energetically stable/ metastable structures using CsPbI 3 as a paradigm. As shown in Fig. S1 in the Supporting Information, all the frameworks of the energetically stable/metastable structures comprised [PbI 6 ] functional octahedral units, which are arranged in different spatial orders. Already-synthesized δ-CsPbI 3 (orthorhombic, Pnma), γ-CsPbI 3 (orthor-hombic, Pnma), and α-CsPbI 3 (cubic, Pm3 m) were involved in the predicted stable/metastable structures ( Fig. 1(a)). Among them, δ-CsPbI 3 , a nonperovskite phase that consists of low-dimensional chains of edgesharing [PbI 6 ] octahedra, is the lowest-energy structure. Associated with low-dimensional structure, δ-CsPbI 3 exhibits a large bandgap ( Fig. 1(b)) and large effective masses (Table S1), and thus is unsuitable for solar cells. The cubic perovskite phase α-CsPbI 3 , which features as a 3D framework of corner-sharing [PbI 6 ] functional octahedral units, is a metastable structure with a formation energy of 30.3 meV/atom, which is higher than that of δ-CsPbI 3 . Owing to the high symmetry and high electronic dimensionality, α-CsPbI 3 exhibits desired electronic properties for solar cells, including a suitable direct allowed bandgap, small effective masses for both electrons and holes, high optical absorption coefficients, and high defect tolerance. However, for use as a solar cell absorber, the intrinsically metastable α-CsPbI 3 could only be stabilized at room temperature in microscale or mesoscale using approaches, such as ligand passivation [37][38][39][40] and ion doping [41]. The orthorhombic γ-CsPbI 3 , a distorted perovskite that is derived from α-CsPbI 3 via octahedral tilting [42], showed enhanced stability compared with the cubic α-CsPbI 3 . The octahedral tilting slightly lowers the electronic dimensionality [22]. As a result, the bandgap and effective masses of the orthorhombic γ-CsPbI 3 are larger than those of the cubic α-CsPbI 3 (Table S1).
As shown in Fig. S1, most newly-predicted metastable structures are low-dimensional, including the face-sharing δ phase that is isostructural to δ-HC(NH 2 ) 2 PbI 3 [23]. Interestingly, we found a 3D honeycomb-like perovskite structure, which holds the potential to provide a high electronic dimensionality for certain optoelectronic applications [22]. The honeycomb-like perovskite consists of Fig. 1 (a) Crystal structures, formation energies, and (b) band structures of newly-predicted honeycomb-like CsPbI 3 perovskite alone with already-synthesized α-, γ-, and δ-CsPbI 3 for comparison. The band structures are aligned by the averaged electrostatic potential, with the valence band maximum of α-CsPbI 3 set to zero pairs of edge-sharing [PbI 6 ] octahedra (i.e., the [Pb 2 I 10 ] units) via conner-sharing, with Cs-Cs cation dimers (even slightly shorter than the Cs-Cs distance in elemental Cs) filled in flattened hexagonal hollow cells. Because of the reduced symmetry and thus reduced degeneracy, the honeycomb-like CsPbI 3 has a bandgap that is slightly larger than those for α-CsPbI 3 and γ-CsPbI 3 perovskites. Nevertheless, the honeycomb-like CsPbI 3 perovskite still exhibits desired electronic properties that are seen in lead halide perovskites, such as high electronic dimensionality, a direct allowed bandgap, small effective masses (Table S1), and high optical absorption coefficients, as shown in Fig. S2. However, like the α-CsPbI 3 and γ-CsPbI 3 perovskites, the honeycomb-like CsPbI 3 is a metastable structure with even higher formation energy (i.e., 9.0 meV/atom, higher than that of α-CsPbI 3 ) and should be easily converted to the δ-CsPbI 3 nonperovskite even if the honeycomb-like CsPbI 3 was successfully synthesized under certain conditions. We supposed substituting Cs-Cs dimer cations with divalent molecular cations with tailored size and shape could suppress phase conversion and stabilize the honeycomb-like perovskite structure, as illustrated in Fig. S3. Besides, to keep the desired high electronic dimensionality, the organic counterions should not cause significant structural distortion in the honeycomb-like perovskite or contribute to band edges with their localized molecular orbitals. Notably, most divalent molecular cations reported in the literature contribute to band edges of related compounds with localized molecular orbitals [43], whereas BIM is one of the few divalent molecular cations that do not contribute to the band edges [44], as confirmed by the DFT calculations (Figs. S4 and S5). Therefore, we focused on synthesizing the predicted 3D honeycomb-like perovskite based on this molecule, and further unveil their unique optoelectronic properties.
In this study, single crystals of BIMPb 2 I 6 were grown by slowly cooling down a diluted HI solution containing stoichiometric BIMI and PbI 2 . The stoichiometric ratio of Pb to I was confirmed to be 1:3 via the energy-dispersive X-ray spectroscopy (EDS) measurement, as shown in Fig. S6. Single-crystal X-ray diffraction (SCXRD) measurement revealed a monoclinic C2/m system, with the detailed crystallographic data listed in Table S2. As shown in Fig. 2(a), the crystal structure of BIMPb 2 I 6 resembles that of a honeycomb-like CsPbI 3 , hence verified the previous expectation that the honeycomb-like perovskite structure could be stabilized by a suitable divalent molecule cation. Owing to the high symmetry, Pb atoms in the inorganic framework are equivalent, and iodine atoms have three different environments (Fig. S7). The bond length of three unique Pb-I bonds are 3.24, 3.20, and 3.15 Å, respectively (Table S3). For each [PbI 6 ] octahedron in BIMPb 2 I 6 , angles of nonaxial I-Pb-I bonds range from 87°to 92° (Table S4). The corner-sharing Pb-I-Pb bonds are linear in the ab-plane and nearly linear (176.4°) along the c-axis. These results indicate that the 3D honeycomb-like inorganic framework exhibits negligible distortion with BIM molecule cations, which is highly desired for high electronic dimensionality, thus the framework has good carrier transport properties. The wellmatched powder X-ray diffraction (PXRD) patterns ( Fig. 2  (b)) further substantiates the solved crystal structure as well as the high phase for the synthesized BIMPb 2 I 6 . Thermogravimetric analysis (Fig. S8) showed that the title compound decomposed at around 280°C, mainly attributed to the sublimation of the organic parts.
To gain insights into the dynamic behavior of the honeycomb-like perovskite framework, Raman measurement was performed at room temperature on a BIMPb 2 I 6 crystal. Low-frequency Raman responses in lead halide perovskites are attributed to stretching or bending vibration modes of the Pb-I bonds [45][46][47]. For BIMPb 2 I 6 , as shown in Fig. 2(c), three peaks in the low-frequency range of 50-200 cm -1 were found and well resolved. Indicated by the DFT results, shown in Fig. S9, the weak and strong peaks at 70 and 91 cm -1 , respectively, were attributed to the bending modes of edge-sharing Pb-I-Pb bonds, whereas the broad peak centered at 99 cm -1 is attributed to the stretching modes of corner-sharing Pb-I-Pb bonds within the (hk0) planes. In addition, Fourier transform infrared (FT-IR) spectroscopy was recorded to reveal the interaction between organic molecules and inorganic framework. We found that the signal at around 3450 cm -1 for BIMPb 2 I 6 was significantly weaker than that of the BIMI 2 precursor, indicative of weak H-bonding interactions between the organic molecular cations and [PbI 6 ] octahedral frameworks of BIMPb 2 I 6 ( Fig. 2(d)). The weak H-bonding (c) Room-temperature lowfrequency Raman spectra of BIMPb 2 I 6 . (d) Fourier transform infrared spectra of BIMPb 2 I 6 , along with the BIMI precursor for comparison interactions in BIMPb 2 I 6 could also be understood from the decreased :N-H-I bonding angle (142°) in the structure model, which was due to the rigid inorganic framework and constrained orientation of organic molecules. (Fig. S10).
DFT calculations were performed for BIMPb 2 I 6 with the experimentally determined crystal structure to understand the electronic properties before experimental characterizations. As shown in Fig. 3(a), BIMPb 2 I 6 exhibits a direct bandgap of 2.10 eV at the M point. The valence band maximum (VBM) comprised antibonding states of the Pb 6s and I 5p orbitals, whereas the conductive band minimum (CBM) is derived mainly from the Pb 6p states (see Figs. 3(b) and S11). By contrast, the BIM molecular cation does not contribute to the band edges due to its relatively high electropositivity. Owing to the 3D connectivity of the band edge-determining [PbI 6 ] octahedra, BIMPb 2 I 6 exhibits a 3D electronic character. Associated with the high electronic dimensionality, the calculated band structure reveals relatively dispersive characters in all directions for the lower conduction and upper valence bands for BIMPb 2 I 6 . The calculated average effective masses for electrons and holes along the directions roughly parallel to the corner-sharing Pb-I-Pb bonds (i.e., the M-Y, M-Γ, and M-A directions) are 0.22m 0 and 0.24m 0 , respectively (Table S1), indicating that both electrons and holes in BIMPb 2 I 6 will be three-dimensionally mobile. Notably, the calculated effective masses for electrons and holes along M-V direction (parallel to edge-sharing octahedra) are 0.59m 0 and 1.38m 0 , respectively. These values are relatively large but far superior to the nearinfinite values for carrier transport across the layers of layered lead iodide perovskites with comparable bandgaps, such as (CH 3 NH 3 ) 2 Pb(SCN) 2 I 2 [48]. The calculated sum of the squares of the dipole transition matrix elements (P 2 ) at various k points revealed high transition probabilities between VBM and CBM. As a result, BIMPb 2 I 6 exhibits high optical absorption coefficients in the order of 10 5 cm -1 (Fig. S12), as in the case with the typical corner-sharing lead halide perovskites.
Experimental characterizations were performed to further evaluate the electronic properties of BIMPb 2 I 6 . As shown in Fig. 4(a), the measured optical absorption spectrum of BIMPb 2 I 6 showed an absorption onset at around 2 eV, which agreed well with the dark-red appearance of the crystals. It is known that the experimental optical absorption edges of metal halide perovskites are attributed to the fundamental band edges and the excitonic bands concurrently [49,50]. In this study, by using the Elliott model, with a Gaussian broadened exciton contribution, the Tauc plot for direct allowed transitions was fitted to yield a direct allowed bandgap of 2.1 eV and an exciton binding energy of~40 meV (Fig. S13). This bandgap is larger than those for lead iodide perovskites but smaller than those for lead bromide perovskites. In addition, a steady-state photoluminescence (PL) spectrum was recorded for the powder sample of BIMPb 2 I 6 under 400 nm excitation. As shown in Fig. 4(a), the PL spectrum showed a sharp and shoulder peak at 627 and around 656 nm, respectively. The sharp peak was ascribed to the exciton emissions. The shoulder peak may be assigned to the recombination of trap states, as indicated by the short PL lifetime (Fig. S14). Based on the calculated and  The rise time (t r ) and fall time (t f ) are intervals that photocurrent rise from 10% to 90% and fall from 90% to 10%, respectively characterized electronic properties, we supposed that BIMPb 2 I 6 could be a prospective semiconductor for photodetection. Therefore, a photodetector based on a single crystal of BIMPb 2 I 6 has been fabricated with a planar electrode configuration. As shown in Fig. 4(b), the current-voltage (I-V) curves exhibited a typical Ohmic contact feature with a low dark current (0.28 nA @ 10 V bias). In addition, the photocurrent increased to 1.3 nA under 5 mW/cm 2 illumination with the same bias, which means the BIMPb 2 I 6 -based photodetector showed a clear photoresponse under a 637 nm light source. The current increased with the enhancement of the power density of the light source and finally saturated under~30 mW/cm 2 . As essential parameters to evaluate the performance of a photoconductor, the responsivity (R) and the specific potodetectivity (D*) of our device were estimated to bẽ 0.10 mA/W and 1.1 Â 10 10 Jones, respectively. To test the device stability, time-dependent photoresponse was measured under 20 mW/cm 2 of 637-nm irradiation controlled by switching on/off cycles at a bias voltage of 10 V. As shown in Fig. 4(c), uniform and repeatable photocurrent responses were observed for each switch-on/off cycle. The rising time (t r ) and fall time (t f ) were determined to be 1.0 and 0.8 ms, respectively (Fig. 4(d)). These preliminary results indicated that honeycomb-like lead halide perovskites represented by BIMPb 2 I 6 could be prospective candidates for highly efficient photodetector materials. Therefore, BIMPb 2 I 6 deserves further experimental optimization.

Conclusions
In summary, we discovered a honeycomb-like perovskite structure that preserves 3D electronic dimensionality by designing the spatial arrangement of the functional octahedral units. Experimentally, the target structure was achieved using a screened divalent molecular cation BIM as a stabilizer. DFT calculations indicated that the synthesized BIMPb 2 I 6 honeycomb-like perovskite possesses high electronic dimensionality and desired optoelectronic properties such as a direct allowed bandgap, small carrier effective masses, and high optical absorption coefficients, whereas experimental characterizations revealed that it exhibited a moderate bandgap of 2.1 eV and PL at 627 nm. The photodetectors fabricated on the basis of BIMPb 2 I 6 single crystals showed responsivity and photodetectivity of 0.1 mA/W and 1.1 Â 10 10 Jones, respectively. The results provided an exemplary approach for designing prospective optoelectric semiconductors via spatially arranging functional units.

Experimental section
DFT calculation: DFT calculations were performed using the projector-augmented wave method as implemented in the Vienna Ab initio Simulation Package (VASP) 5.4 code [51]. The plane-wave cutoff energy was set to 500 eV. The search of crystal structure for CsPbI 3 was conducted using the particle swarm optimization method as implemented in the Crystal Structure Analysis by Particle Swarm Optimization (CALYPSO) code [52,53]. The generalized gradient approximation (GGA) Perdew-Burke-Ernzerhof (PBE) [54] was used as the exchange-correlation functional for structural relaxation and total-energy calculations. Γcentered k-meshes with k-spacing of 0.2 Å -1 were employed for sampling the Brillouin zones. All crystal structures were fully relaxed until the total force on each atom was < 0.01 eV/Å. The vibrational frequencies were obtained using the finite displacement method as implemented in the Phonopy code [55], and the Raman activity was then estimated by calculating the polarizability of the vibrational models using the VASP_RAMAN.PY code [56]. The calculations of electronic properties were performed using the Heyd-Scuseria-Ernzerhof (HSE) [57,58] hybrid functionals with the mixing parameter of 39% and the inclusion of spin-orbit coupling, which provided good bandgap descriptions for γ-CsPbI 3 and BIMPb 2 I 6 . The transition matrix elements were calculated using the VASP_TDM code [59].
Material synthesis: PbI 2 (AR, 99.9%), hydroiodic acid (AR, 45-50 wt.% in water, stabilized by 1.5% H 3 PO 2 ), and hypophosphorous acid (AR, 50 wt.% solution in water) were purchased from Aladdin. All reagents were used as received without further purification. BIM was synthesized with the methodology described in Ref. [60]. The final product was recrystallized in concentrated HI to afford the protonated product, BIMI 2 . An amount of 1 mmol (461 mg) PbI 2 was dissolved in 9-mL HI solution under 120°C to obtain a clear yellow solution, and 2-mL H 2 O was then added to dilute the solution. An amount of 0.5 mmol (148 mg) BIMI 2 was dissolved in 1-mL hypophosphorous acid in another vial. The solution was slowly added to the previous solution under heating. The temperature was lowered to 60°C until dark-red crystals precipitated as the title compound.
Material structure determination: The elemental analysis was conducted using a field-emission scanning electron microscope (FEI Nova NanoSEM 450) equipped with an EDS. A crystal sample with a suitable size was selected for SCXRD on Bruker D8 VENTURE diffractometer, using Mo Kα radiation (l = 0.71073 Å) (50 kV, 30 mA) at 150 K. The collected data were integrated and applied with multiscan absorption corrections using the APEX-III software. The crystal structure was solved and refined by the SHLEXT (intrinsic phasing method) and SHLEXL (full-matrix least-squares on F 2 ) programs, respectively. The VESTA program [61] was used for structure visualization. The Crystallographic Information File (CIF) can be obtained from the Cambridge Crystallographic Data Centre (CCDC) by quoting the deposition number: CCDC 2074690. PXRD measurement was conducted on Brucker D8AA25 diffractometer with Cu Kα radiation (l = 1.54178 Å). The diffractograms were recorded in the range of 2θ = 5°to 65°at 0.02°per step, whereas the integrated time of each step is 0.4 s. Simulated powder diffraction patterns were calculated using the solved crystal structure with VESTA.
Material property characterization: Raman spectra were acquired on LabRAM HR800 using a 732-nm laser as the excitation source. The spectra were collected from 50 to 200 cm -1 . FT-IR spectra were recorded on Bruker VERTEX 70 equipped with an attenuated total reflection accessory. The attenuated signals of solid samples were recorded and solved by FT in the mid-IR ranges (500-4000 cm -1 ). Optical absorption spectroscopy measurements were performed on a Shimadzu 2600i UV-Vis spectrometer. The optical diffuse reflectance was measured in an integrated sphere using BaSO 4 powder as reference. The steady-states PL spectrum was measured on a Horiba-FL3 spectrofluorometer with a 400-nm excitation source. A 425-nm spectra LED was used as the excitation source of time-resolved PL. The emission counts were monitored at the maximum of the emission curve. The lifetime was obtained and calculated via the third-exponential fitting. Thermal stability was estimated by thermogravimetric coupled with differential thermal analysis performed on PerkinElmer Diamond TG/DTA. The powder samples were heated from room temperature to 500°C with a heating rate of 10°C/min. All measurements were conducted under an N 2 flow atmosphere.
Photoresponse characterization: Photoelectric measurements were performed using a planar electrode configuration. The electrode materials were proven not to have any obvious influence on the photoelectric properties. The current-voltage (I-V) and photocurrent-time (I-t) with the light on or off (measured at zero bias) were measured using a high-precision electrometer (Keithley 6517B). A THOR-LABS 637-nm pigtailed laser diode (LP637-MF300) was used for Vis light illumination. The incident light intensity was measured via a light power meter. The temperature during measurements was kept at 298 K using a Linkam TS1500 heating stage.
The responsivity (R) and photodetectivity (D*) of BIMPb 2 I 6 were determined, respectively, as follows: where J ph , L light , and J d represent photocurrent, incident light intensity, and dark current, respectively, and the constant e is the elementary charge (1.6 Â 10 -19 C).