Theoretical Study on Rotational Controllability of Organic Cations in

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX-XXX

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Theoretical Study on Rotational Controllability of Organic Cations in Organic−Inorganic Hybrid Perovskites: Hydrogen Bonds and Halogen Substitution Shohei Kanno, Yutaka Imamura,* and Masahiko Hada Department of Chemistry, Tokyo Metropolitan University, 192-0364 Hachioji, Tokyo, Japan S Supporting Information *

ABSTRACT: The organic cation dynamics in organic−inorganic hybrid perovskites strongly affect the power energy conversion and unique physical properties of these materials. To date, the first-principles rotational potential energy surface (PES) of formamidinium (FA) has not been reported. Thus, we examined the rotational energy barriers for FA in cubic-phase perovskites (FABX3 (B = Sn/Pb; X = Cl/Br/I)) by density functional theory and compared these with those of methylammonium. The calculated rotational PES of FAPbI3 indicates that FA rotates around the N−N bond axis (φ) with a low energy barrier, whereas the energy barrier for FA rotation around the axis penetrating the C atom and the center of gravity of FA (θ) is high. Moreover, the φ and θ rotational barriers of FA increase with halogen substitution. Thus, we reveal important design rules for controlling the rotational barrier and orientation by forming hydrogen bonds and halogen substitution.

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INTRODUCTION Organic−inorganic hybrid perovskites have attracted significant attention as photovoltaic materials for next-generation solar cells. Recently, the power conversion efficiency (PCE) of perovskite solar cells has skyrocketed from 3.8% to more than 20%.1,2 The high photovoltaic performance can be ascribed to the remarkable optoelectronic properties of methylammonium lead iodide (MAPbI3): (1) its band gap of approximately 1.6 eV, which matches the visible to near-infrared regions of solar light,3,4 (2) its small exciton binding energy of a few millielectronvolts,5 and (3) its extended electron and hole diffusion lengths and lifetimes.6,7 Regarding the carrier mobility and the lifetime in MAPbI3, Zhu et al. reported that a liquid-like reorientational motion of the organic cation provides protection for energetic charge carriers in hybrid perovskites with screening on a sufficiently fast time scale to compete with carrier cooling by optical phonon scattering.8 To probe the reorientational dynamics of MA in hybrid perovskites, experimental measurements and theoretical calculations have been performed.9−18 In our previous study, we reported the rotational energy barriers and the rotational relaxation times of MA in cubic-phase MAPbI3 as well as alternative perovskites MAPbX3 (X = Cl or Br) and MASnX3 (X = Cl, Br, or I) using first-principles calculations.19 Recently, formamidinium (FA) has gathered attention as an organic cation in hybrid perovskites20,21 instead of MA because the PCE of the FA lead iodide (FAPbI3) perovskite solar cell is high, and in fact, the Seok group reported that it has the highest certified PCE of 22.1%.2,22 However, previous studies of the rotational dynamics of FA in hybrid perovskites are limited in comparison with those of the rotation dynamics of MA. Recently, © XXXX American Chemical Society

Carignano et al. examined the rotational dynamics of FA in FAPbI3 using first-principles molecular dynamics (MD) simulations.23 In their study, they found that the rotational motion of FA is reducible to those around two rotation axes, which are defined by the N−N bond axis (φ) and the sum of the two vectors of the C−N bond axes (θ), from group theory. They also found that only rotation around the φ axis is possible at room temperature. So far, a detailed potential energy surface (PES) for FA rotation in hybrid perovskites has never been obtained from experimental or theoretical studies. In this study, we examined the detailed PES for the above two rotational motions of FA in cubic-phase FAPbI3 (Figure 1) with full inorganic framework relaxation using density functional theory (DFT). This approach is based on our previous study and can reproduce the experimental MA rotational barriers in cubicphase MAPbI3.19 From the PES, we calculated the rotational energy barriers for the φ and θ rotations. Furthermore, we also examined the FA rotational barriers in the cubic-phase alternative perovskites FAPbX3 (X = Cl or Br) and FASnX3 (X = Cl, Br, or I) because the search for novel hybrid perovskite compounds is of great importance in the design of eco-friendly solar cells and stable ferroelectric materials.24−37 However, a comprehensive study of the FA rotations in alternative perovskites has not been reported. In this paper, we comprehensively discuss the FA rotational dynamics in cubic-phase FAPbI3 and the alternative Received: August 3, 2017 Revised: October 31, 2017 Published: November 7, 2017 A

DOI: 10.1021/acs.jpcc.7b07721 J. Phys. Chem. C XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry C

penetrating C atom and center of gravity in FA, respectively. In the calculation of the PES for the φ and θ rotations, the orientation of FA in FAPbI3 was varied by changing φ and θ from 0 to 360° in 20° steps, where the structure at φ = 0 and θ = 0 corresponds to the optimized geometry. During the PES calculation, the N and C atoms in FA were fixed for each φ and θ. The structural relaxation of the H atoms in FA, the PbI6 inorganic framework, and the lattice constants was considered to reproduce the symmetry lowering associated with the FA rotation and the coupling between the dynamic motions of the PbI6 framework and FA. In these calculations, vdW-DF246 was used as the exchange-correlation functional with ultrasoft pseudopotentials.47 The convergence threshold for the change in the total energy during structural relaxation following the FA reorientation was 10−4 Ry. The calculations for evaluating the PES were performed using the Quantum ESPRESSO code48 with 80 and 960 Ry plane-wave and charge density cut-offs, respectively, and reciprocal space sampling of 63 k-points reduced from 5 × 5 × 5 grid points. For the alternative perovskites FAPbX3 (X = Cl or Br) and FASnX3 (X = Cl, Br, or I), the PESs for FA rotational motion were estimated in a similar way.

Figure 1. Orientation of FA in cubic-phase perovskite. The orientation of FA is described by φ and θ. White, gray, blue, purple, and black spheres represent H, C, N, I, and Pb atoms, respectively.

perovskites and compare them with those of MA in hybrid perovskites.

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COMPUTATIONAL DETAILS First, we performed structural optimization of the ions and the cell parameters and phonon analysis in cubic-phase FAPbI3 using DFT and density functional perturbation theory (DFPT). For the structural optimization, we set the convergence threshold for changes in the total energy to 10−6 eV and reiterated the optimization until the imaginary frequencies corresponding to translational modes were less than 1 cm−1 at the Γ-point. We used the Perdew−Burke−Ernzerhof (PBE)38,39 exchangecorrelation functional with projector augmented wave (PAW) pseudopotentials.40,41 During the geometry optimization and self-consistent field calculations for the phonon analysis, 504 kpoints were reduced from 10 × 10 × 10 grid points by the tetrahedron method and employed for reciprocal space sampling in the first Brillouin zone. The above calculations for the geometry optimization of the initial structures and the frequency analyses were performed using the Vienna ab initio simulation package (VASP) code42−45 with plane-wave and charge density cutoffs of 1800 and 644.9 eV, respectively. Next, to obtain the rotational energy barriers for the two modes around the N−N bond and the sum of the two C−N bond vectors of FA in cubic-phase FAPbI3, the calculation of the PES by DFT was carried out. As shown in Figure 1, we defined φ and θ as rotational angles around the N−N bond axis and an axis

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RESULTS AND DISCUSSION Potential Energy Surface and Barrier for FA rotation in Cubic-Phase FAPbI3. Figure 2a shows the optimized structure of cubic-phase FAPbI3, and the cell parameters are listed in Table S1. We examined the functional dependence of the PBE and vdW-DF2 functionals by evaluating the cell parameters of FAPbI3 in the optimized structure at φ = 0° and θ = 0°. As shown in Table S1, the Bravais lattice vectors were well-reproduced by the vdW-DF2 and PBE functionals. In this study, vdW-DF2 was adopted for optimization and evaluation of the rotational PES. FA is approximately oriented on the (111̅) plane with six iodine ions to form N−H···I hydrogen bonds in a cage of the PbI6 inorganic framework, which is slightly distorted by the displacements of the iodide ions because of the formation of hydrogen bonds. The hydrogen bond lengths are 2.77−2.90 Å and are consistent with those of a previous report (2.75−3.00 Å).49 The number of N−H···I hydrogen bonds in the unit cell is 4, greater than the number in MAPbI3, and the hydrogen bond lengths are shorter than those in MAPbI3 (2.88−2.98 Å).19 This result suggests that the rotational energy barrier of FA in FAPbI3 will be greater than that of MA in cubic-phase MAPbI3, which is

Figure 2. PbI6 inorganic framework and N−H···I hydrogen bonds in (a) the optimized structure as φ = 0° and θ = 0° and (b) the structure at φ = 0° and θ = 80°. White, gray, blue, purple, and black spheres represent H, C, N, I, and Pb atoms, respectively. B


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The Journal of Physical Chemistry C 9.1 kJ mol−1 from experiment and 9 kJ ml−1 from our previous DFT calculations.13,19 To examine the structural relaxation of the PbI6 inorganic framework with cooperative FA motion, we calculated the normal frequencies of cubic-phase FAPbI3 sampled at the Γpoint, and the details are summarized in Table S2. The imaginary modes related to translational motions had negligible frequencies of less than 1 cm−1. The soft phonon modes of the PbI6 inorganic framework appear in the low-frequency region from 8.8 to 53.6 cm−1. In addition, in the high-frequency region from 517.0 to 3476.4 cm−1, the FA vibrational modes appear, which are the characteristic motions of organic molecules in the infrared region. In particular, a remarkable coupling between the soft phonon modes of the PbI6 inorganic framework and the translational and the rotational motions of FA appears in the low-frequency region (see Supporting Information, Table S2), which is also seen in MAPbI3.19 These results suggest that the FA rotational barrier height decreases because of the structural relaxation of the PbI6 inorganic framework via soft phonon modes on a time scale of 0.6−3.8 ps (53.6−8.8 cm−1), as in the case of MA rotation in MAPbI3. Next, we examined the φ and θ rotational PES of FA in cubicphase FAPbI3. First, we also examined how to evaluate the energy barrier for φ rotation from the rotational PES and nudged elastic band (NEB) method (see Supporting Information, Figure S1).50,51 The rotational PES slightly underestimates the rotational barrier in comparison with the NEB method. However, the shapes of potential energy curves are reasonably consistent between the two methods, and therefore, the rotational PES was used for estimating the energy barrier. Figure 3 shows the φ and θ rotational PESs of FA in cubic-phase FAPbI3,

The above results suggest that FA can rotate around φ-axis relatively freely, but the rotation around the θ-axis is restricted by potential walls. This trend is consistent with previous MD simulations.23 A definite difference between the MA and FA rotations in cubic-phase lead iodide perovskites is the existence of anisotropic rotational directions: For the MA rotation in MAPbI3, there is no anisotropy, and MA can rotate around both axes with barrier heights of 6−11 kJ mol−1.19 To investigate the origin of the potential walls with respect to the θ rotation, we analyzed the structure of FAPbI3 at φ = 0° and θ = 80°, which is a geometry located on the potential wall. As shown in Figure 2b, the number of N−H···I hydrogen bonds less than 3.00 Å is two at an FA orientation of φ = 0° and θ = 80°, which is approximately located on a (1̅10) plane with two iodine ions. In comparison with a stable FA orientation with four hydrogen bonds at the φ = 0° and θ = 0° shown in Figure 2a, the number of hydrogen bonds for stabilizing FA is decreased by the reorientation of FA in the cage of the PbI6 inorganic framework. As a result, two potential walls originating in hydrogen bond cleavages appear around θ = 80° and θ = 260° on the PES. In contrast to the θ rotation, during φ rotation, FA is basically surrounded by four iodine ions and relatively freely rotated with the remaining hydrogen bonds except for specific geometries φ = 60° and φ = 240° (see Supporting Information, Figure S2). From the above results, in terms of hydrogen bonds, we can explain the rotational anisotropy, which was identified by the previous first-principles MD.23 We examined an effect of the next cell on the rotational PES using a 1 × 1 × 2 super cell model of cubic-phase FAPbI3. In this model, we rotated an FA in the super cell, and the other ions including the next FA can relax freely. As a result, the height of rotational energy barriers in the super cell decreases from that of the single cell for both φ and θ rotations, because the structural relaxation degree of freedom of the inorganic framework in the super cell, which is cooperative with FA rotation, is larger than that of the single cell. The heights of the two potential walls on θ rotation at φ = 0° were 14 and 9 kJ mol−1 in the single and super cells. Also, the heights of the rotational barriers for φ rotation at θ = 0° were 10 and 6 kJ mol−1 in the single and super cells (see Supporting Information, Figure S3). For 1 × 2 × 1 and 2 × 1 × 1 super cell models, we obtained a similar tendency of the decreased rotational barrier. Even though the barriers become lower, the tendency that the θ rotational barrier is higher than the φ rotational barrier is confirmed in the single and super cells, and therefore, the essence of the discussion in the single cell does not change even for the super cell. From the results on the FA rotational energy barriers, we think that the MA and FA rotations have different effects on the anisotropic screening of carrier dynamics.8 Furthermore, the above result indicates that molecular design for the organic cation can control the rotational directions and barriers in hybrid perovskites toward designing solar cell materials and ferroelectric materials. Potential Energy Surface and Barrier for FA Rotation in Alternative Cubic-Phase Perovskites. Here, we discuss the FA rotational motions in the alternative cubic-phase perovskites FAPbX3 (X = Cl or Br) and FASnX3 (X = Cl, Br, or I). First, the optimized structures of each alternative perovskite are shown in Figure S4, and the cell parameters are listed in Table S3. In all optimized structures, FA is oriented to form four N−H···X (X = Cl, Br, or I) hydrogen bonds in the inorganic framework, which is also seen in FAPbI3. On the other hand, the hydrogen bond lengths become shorter in the following order: Cl-based

Figure 3. Potential energy surface for the φ and θ rotations of FA in cubic-phase FAPbI3. The plotted energies are relative to the energy of the most stable orientation (φ = 300° and θ = 340°).

which were obtained from DFT calculations. The rotational PES of FA shows a strong anisotropy, which does not appear in the PES for MA rotation reported by us previously.19 For example, when FA rotates around the θ-axis by 360° at all φ angles, the rotation is hindered by two potential walls located at θ = 80° and 260°, and the heights of the two potential walls are 10−16 kJ mol−1. On the other hand, when FA rotates around the φ-axis by 360° at all θ angles, the energy barrier height is 4−10 kJ mol−1, and these values are lower than the barrier heights for θ rotation. C


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FAPbBr3, the φ and θ rotational barriers are 7−17 and 18−27 kJ mol−1, which are higher than those of FAPbI3. Furthermore, for FAPbCl3, the rotational barriers increase relative to those of FAPbI3, becoming 10−21 kJ mol−1 for φ rotation and 26−38 kJ mol−1 for θ rotation. This trend is consistent with the rigidities of the PbX6 inorganic frameworks estimated from the soft phonon frequencies. In addition, a similar trend in the rotational barriers, which increase with lighter halogens, is also seen in the Sn-based perovskites. From these rotational barriers, we can expect that FA in the alternative perovskites can rotate around the φ-axis at room temperature, where the lowest rotational barrier heights are 4−10 kJ mol−1. Because the rotational energy barrier of MA is 9.1 kJ mol−1 in cubic-phase MAPbI3, MA rotates at room temperature relatively freely.13 On the other hand, the θ rotational motions of FA are frozen in the Br- and Cl-based perovskites because of the higher rotational barriers of 14−26 kJ ml−1. The increase of the θ-type FA rotational barrier heights by halogen substitutions is more remarkable than that of the MA rotation.19 For FA-alternative perovskites, a better alignment of the FA dipole moments is easily achieved, and in particular, Clbased perovskites can exhibit greater ferroelectricity than I-based perovskites and Br-based perovskites. Thus, we have found a characteristic of hybrid halide perovskites; that is, the rotational energy barriers of organic cations can be controlled by halogen substitution. In a comparison of the Pb- and Sn-based perovskites, the φ and θ rotational barriers in the Sn-based perovskites decrease or become almost equal to those of the Pb-based perovskites despite the more rigid SnX6 inorganic frameworks. To analyze the difference between the φ and θ rotational barriers of FA and the rigidities of the BX6 inorganic frameworks, we compared the vibrational coupling between the FA rotational motion and the BX6 inorganic framework motion. As shown by the blue lines in Figure 4, for the soft phonon modes in Sn-based perovskites, the φ-type rotational motion of FA is coupled with Sn−X stretching motions, and the vibrational level of the FA motion splits into two levels in FASnI3 and FASnBr3 and three levels in FASnCl3 (see Supporting Information, Tables S4, S6, and S8). Furthermore, as shown by the green lines in Figure 4, the θtype rotational motion of FA is coupled with the Sn−Cl−Sn bending motion in FASnCl3. These couplings between the φ- or θ-type rotational motions of FA and the PbX6 inorganic framework do not appear in Pb-based perovskites and are typical of Sn-based perovskites (see Supporting Information, Table S9). From this analysis, we can expect that the structural relaxation of the SnX6 inorganic framework via vibrational motion is more cooperative with the rotation of FA in the cage of the inorganic framework than that of the Pb-based perovskites. As a result, the rotational energy barriers of FA in Sn-based perovskites become relatively small compared with those of the Pb-based perovskites. These results suggest that the coupling between motions of rotations and inorganic framework should be carefully tuned to obtain a desirable rotation barrier.

perovskites (2.29−2.41 Å) < Br-based perovskites (2.47−2.58 Å) < I-based perovskites (2.72−2.88 Å) (see Supporting Information, Figure S4). In addition, the cell volumes are smaller for lighter halogen-based perovskites (see Supporting Information, Table S3). This trend in the bond lengths and cell volumes is consistent with the changes in the halogen ionic radii, which are 1.67, 1.82, and 2.06 Å for Cl−, Br−, and I−, respectively.52 Next, we discuss the phonon analysis and the rotational PES calculations at an FA orientation of φ = 0° and θ = 0° using the optimized structures. The soft phonon frequencies of cubicphase FABX3 (B = Sn or Pb; X = Cl, Br, or I) at the Γ-point are shown in Figure 4, and the details are listed in Tables S4−S8,

Figure 4. Calculated soft phonon frequencies of cubic-phase (a) FAPbI3, (b) FASnI3, (c) FAPbBr3, (d) FASnBr3, (e) FAPbCl3, and (f) FASnCl3. Blue, green, and black lines are the vibrational levels of φ-type FA rotational motion, θ-type FA rotational motion, and the other motions, respectively.

respectively. Overall, the soft phonon frequencies increase in the order Pb-based perovskites < Sn-based perovskites for B-site metals and I-based perovskites < Br-based perovskites < Cl-based perovskites for X-site halogens. The higher frequencies of the Snbased perovskites indicate that the SnX6 inorganic frameworks are more rigid than the PbX 6 inorganic frameworks. Furthermore, the I-based perovskites have relatively soft BI6 inorganic frameworks, whereas the Cl-based perovskites have relatively hard BCl6 inorganic frameworks, as indicated by the increase in the soft phonon frequencies in the order BI6 < BBr6 < BCl6. Previously, we reported that the barriers increase in perovskites with more rigid inorganic frameworks.19 Therefore, we can expect that the energy barriers for the φ and θ rotations of FA increase in the order FAPbI3 < FASnI3 < FAPbBr3 < FASnBr3 < FAPbCl3 < FASnCl3. We estimated the rotational energy barriers of the φ and θ rotations of FA for the cubic-phase alternative perovskites FAPbX3 (X = Cl or Br) and FASnX3 (X = Cl, Br, or I) from the rotational PES. Figure 5 shows the φ and θ rotational PES of FA in cubic-phase alternative perovskites FAPbX3 (X = Cl or Br) and FASnX3 (X = Cl, Br, or I). Table 1 lists the rotational barriers, which were estimated from the total energy differences between the maximum and the minimum potential energies when φ or θ was changed from 0° to 360° for all θ or φ orientations. The rotational energy barriers for MA are also listed.19 Similarly, there are two potential walls located around θ = 80° and 260° on the PES for all alternative perovskites. For FASnI3, the φ and θ rotational barriers are 4−10 and 11−16 kJ mol−1, respectively, which are slightly different from those of FAPbI3 discussed above. This behavior in the rotational PES of FA, similar to that of MA,19 would lead to the liquid-like reorientational motion for screening of energetic charge carriers.8 On the other hand, for

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CONCLUSION In conclusion, we have theoretically examined the rotational energy barriers of FA in cubic-phase FAPbI3 and compared these with the energy barriers of MA rotation. For FAPbI3, the rotational potential energy surface (PES) of FA shows a strong anisotropy, which is not present in the PES of MA in MAPbI3.19 We found that FA can relatively freely rotate around the N−N bond axis (φ), and a rotation around the axis penetrating the C atom and the center of gravity in FA (θ) is restricted by the D


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Figure 5. Potential energy surfaces for φ and θ rotations of FA in cubic-phase (a) FASnI3, (b) FAPbBr3, (c) FASnBr3, (d) FAPbCl3, and (e) FASnCl3. The plotted energies are relative to the energies of the most stable orientations for each perovskite.

axes.19 This difference in the rotational energy barriers originates from the different number of N−H···I hydrogen bonds during each rotational motion. Therefore, the rotational motions of

potential walls on the PES. On the other hand, for MAPbI3, the MA rotation does not show the weak dependence on rotational direction, and MA can rotate freely around various rotational E


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Table 1. Energy Barriers (in kJ mol−1 and meV) for φ and θ Rotations of FA in Cubic-Phase FABX3 and MA in Cubic-Phase MAPbI3 FA rotational energy barrier/kJ mol−1 (meV)

a

BX6 framework

φ rotation

θ rotation

MA rotational energy barrier/kJ mol−1 (meV)a

PbI6 SnI6 PbBr6 SnBr6 PbCl6 SnCl6

4−10 (41−104) 4−10 (41−104) 7−17 (73−176) 8−14 (83−145) 10−21 (104−218) 7−17 (73−176)

10−16 (104−166) 11−16 (114−166) 18−27 (186−280) 14−22 (145−228) 26−38 (269−394) 18−23 (186−238)

6−11 (62−114) 9−11 (93−114) 10−12 (104−124) 10−14 (104−145) 13−18 (135−186) 15−23 (155−238)

Ref 19.

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ACKNOWLEDGMENTS The calculations were performed at the Research Center for Computational Science, Okazaki, Japan. This study was supported in part by competitive funding for team-based basic research of “Creation of Innovative Functions of Intelligent Materials on the Basis of the Element Strategy” from CREST, the Japan Science and Technology (JST) Agency, a Grant-in-Aid for Scientific Research on Innovative Areas “Coordination Asymmetry” KAKENHI JP17H05380 from the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.

organic cations are controllable by the rational design of hydrogen bond networks; for example, the introduction/removal of polarized bonds, such as N−H and O−H, could be used to tune the rotational motion. Furthermore, the controlled rotational motions play a unique role in the carrier dynamics and electric properties, such as ferroelectricity. We also examined the rotational barriers for FA reorientation corresponding to the φ and θ rotational motions in the cubicphase alternative perovskites FAPbX3 (X = Cl or Br) and FASnX3 (X = Cl, Br, or I). From the calculated rotational PES, we found that the rotational barrier heights for the φ and θ motions increase in the order I-based perovskites < Br-based perovskites < Cl-based perovskites. In particular, the halogen substitution strongly affected the θ rotational barrier heights. This trend is consistent with the MA rotations in the alternative perovskites.19 However, the substitution of the B-site metals Pb and Sn affected the rotational energy barrier of FA in a different manner. We found that the φ and θ rotational barrier heights of FA decreased in the Sn-based perovskites compared to those of Pb-based perovskites because the vibrational motions were more cooperative with the FA rotations than those of PbX6. Through the investigation on alternative perovskites, halogen substitution for FA perovskites enhances the rotational barrier over MA perovskites and is effective for controlling the cation rotation. The above study demonstrates design rules for controlling the rotational barrier by modifying the number of hydrogen bonds and halogen substitutions, that is, increasing/decreasing the number of hydrogen bonds and the coupling between the motion of the rotations and halogen-containing inorganic framework. We expect that the current research offers design rules by hydrogen bonds and halogen substitution, which will lead to the development of more efficient solar cells and other functional materials.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b07721. Optimized structures and phonon analysis (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Yutaka Imamura: 0000-0002-9527-6813 Masahiko Hada: 0000-0003-2752-2442 Notes

The authors declare no competing financial interest. F


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