The Role of Methylammonium Rotation in Hybrid Halide MAPbX3 (X=I

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

The Role of Methylammonium Rotation in Hybrid Halide MAPbX3 (X=I, Br, and Cl) Perovskites by a Density Functional Approach: Optical and Electronic Properties Ali Mehdizadeh, Seyed Farshad Akhtarianfar, and Saeid Shojaei J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11422 • Publication Date (Web): 26 Feb 2019 Downloaded from http://pubs.acs.org on February 26, 2019

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The Journal of Physical Chemistry

The Role of Methylammonium Rotation in Hybrid Halide MAPbX3 (X=I, Br, and Cl) Perovskites by a Density Functional Approach: Optical and Electronic Properties Ali Mehdizadeh, Seyed Farshad Akhtarianfar*, and Saeid Shojaei* Research Institute for Applied Physics & Astronomy (RIAPA), University of Tabriz, Tabriz, 51665-163 Iran *Correspondence should be addressed to Saeid Shojaei (email: [email protected]) and Seyed Farshad Akhatarianfar (email: [email protected])

Abstract: As a revolutionary material, hybrid halide perovskites can greatly improve the solar-conversion efficiency of solar cells. In this work, a first-principle theoretical study is performed to investigate the role of Methylammonium (MA) rotation in the MAPbX3 (X=I, Br, and Cl) perovskites. To provide a full understanding of the MA rotation, we report electronic and optical properties in different rotational angels and modes. Our results evidence that rotation of MA with Rz and Rx modes causes substantial changes in band structure, density of states (DOS), partial density of states (PDOS), electron density, dielectric function, and absorption spectra. We also showed that these changes are deeply affected by cation-cation (MA-Pb) and cation-anion (MA-X) interactions. Furthermore, the halogens of MAPbX3 were changed to iodide, bromide, and chloride anions to study the inorganic-organic interactions inside the MAPbX3 in detail. Interestingly, we conclude that the rotational modes, location, and orientation of organic cation can be used as an efficient tool to control the band gap, static dielectric constant and absorption edge of the optical spectra. Our results providing useful and accurate insight into the behavior of MA embedded in inorganic octahedra are in good agreement with experimental data being used in photovoltaic applications.

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Introduction: Organic-inorganic 3D-metal halide perovskite materials are of great interest since they can be useful in optoelectronic devices such as highly-efficient solar cells, lasers, and photo-detectors.1-6 These materials are transforming the solar cell research area, having reached photovoltaic power conversion efficiency of above 20 % after only about five years since the first pioneering report.7 These compounds are formed in the standard ABX3 perovskite structure where A is an organic cation (e. g. CH3NH3+: Methylammonium: MA), X is a halogen anion (e.g. X=Iˉ, Brˉ, Clˉ) and B is a divalent metal cation (e.g. Pb+2). Perovskites can adopt a wide variety range of phases that typically involve small promote symmetrybreaking of the aristotype8 and different types of octahedral titling transitions demonstrated by Glazer’s notation.9 From the crystallographic point of view, at low temperatures, Hybrid Organic Perovskites (HOPs) are found in an orthorhombic phase (space group: Pnma). Additionally, they undergo successive phase transitions by increasing temperature. The orthorhombic phase transforms into a tetragonal structure (space group: I4/m) at temperatures more than 161.4 K. Above 330.4 K, tetragonal structure evolves into the cubic symmetry phase with space group of Pm3m.10-11 A very intriguing issue of these materials deals with the orientation and the dynamics of the organic MA cations inside the inorganic structure.12 According to the relatively large size of the PbX6 octahedral compared to the general perovskite-type crystals the embedded MA+ ions can move freely inside the cage at high temperatures.13 Moreover, it has been previously shown that CH3NH3+ has no covalent bonding with the Pb-X framework which makes CH3NH3+ more dynamic for various types of rotations.14 The significant rotation of organic molecule inside the HOPs at finite temperatures which arises from the low dipole-dipole interactions


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of energy barriers is very interesting feature compared to traditional semiconductors.15 In this regard, the orientational dynamics disorder of the MA cations was investigated to elucidate the effect of rotational motion on the structural and electronic properties of HOP system. It was proposed that the MA cations rotate within the inorganic framework on the timescale of a few picoseconds.12 Chen et al discussed the motion of CH3NH3+ as a function of temperature as well as crystal symmetry. This suggests that the photovoltaic performance of hybrid perovskites can be tuned by changing the dynamics of organic cations and also the structure of the organic cation such as size and dipole moment.7, 15-16 Furthermore, experimentally synthesized MAPbI3 was systematically studied using quasi-elastic neutron scattering and group theory to understand the rotational modes of CH3NH3+ cation embedded in the HOP framework.7 Additionally, it has been shown that the rotation of organic cations with low energy barrier can possibly affect the optical and band gap properties of hybrid perovskites.17 Therefore, understanding the motions of organic cations in the HOP framework is highly favorable in order to progress toward photovoltaic device performance optimization as well as development of novel hybrid perovskites. In this work, we study the interaction of MA with PbX6 (X=I, Br, and Cl) octahedra using Density Functional Theory (DFT) in two different rotational axes. The DFT investigations of these halide perovskites provide useful insight into their optical and electronic structure as a function of MA rotation with specific angles. Our work provides a guideline for designing new materials with desired properties in the family of HOPs.



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2. Computational details All the calculations were performed using the PWSCF code as implemented in the Quantum-Espresso package.18 Perdew–Burke–Ernzerhof (PBE) was used as an exchange correlation functional19 within a generalized gradient approximation (GGA). We focused on the pseudo-cubic phase of halide materials with the chemical structure of MAPbI3, MAPbBr3, MAPbCl3 and rotation of organic cation (MA+) within the perovskite structure. Moreover, scalar relativistic ultra-soft and planewave basis sets pseudo-potentials were used to represent density of valence electrons and wave functions. Energy cutoffs of 32 Ry and 288 Ry were used in representation of wave functions and electron density, respectively. A 6×6×6 Monkhorst–Pack grid20 was chosen for sampling the Brillouin zone (BZ) of the cubic systems. The structure was fully relaxed until the force on each atom was smaller than 0.003 ev 𝐴 ―1. For evaluating the optical properties, we have first calculated the frequency dependent complex dielectric function.21 8𝜋 𝜀(𝜔) = 1 + 𝛺𝑁𝑘

∑ (𝐸 𝑘,𝑣,𝑐

|〈𝜑𝑘𝑣|𝑣|𝜑𝑘𝑐〉|2

2 𝑘𝑐 ― 𝐸𝑘𝑣) (𝐸𝑘𝑐 ― 𝐸𝑘𝑣 ― 𝜔 ― 𝑖ƞ)

(1)

where Ω is the volume of the cell, 𝑁𝑘 is the total number of k-points in the BZ, 𝑣 is the operator of velocity, η is an opportune broadening factor, and the indices v and c show the occupied and unoccupied states, respectively. The frequency dependent absorption coefficient, α(ω) is then given by: 𝛼(𝜔) = 𝜔

―𝑅𝑒𝜀(𝜔) + 𝑅𝑒2𝜀(𝜔) + 𝐼𝑚2𝜀(𝜔) 2

3. Results and discussion


(2)

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3.1 Rotation-dependent electronic properties Figure 1 (a) displays rotational pathways for MA+ ions within a Pb-X framework considered in this work: (i) rotation of axis which is perpendicular to the C-N (CH3NH3) ions denoted as Rz, (ii) rotation of whole molecule of MA+ (CH3-NH3) via C– N axis itself (x) denoted as Rx. Moreover, the location and layout of MA and PbX6 octahedral in the HOP bulk has been shown schematically in Figure 1 (b). The different rotational modes of MA have been recently showed in an experimental procedure with tuning the synthesizing temperature 7. They discussed the effect of temperature on orientation and rotation of MA within CH3NH3PbI3 in four-fold rotational symmetry of the C-N axis. Here, we considered seven distinct angles (i. e. 0°, 15°, 30°, 45°, 60°, 75°, and 90°) regarding Rz mode in order to get a clear vision from the MA behavior inside the octahedra. However, we confined the calculations to 45° due to the symmetric similarities involved in Rx mode. All of the three structures MAPbX3 considering Rz and Rx rotations were fully optimized before the main calculations using the 0° (non-rotated) experimental-based lattice constants14, 22 (red solid square in Figure 2). The optimization energies as a function of rotational angels provided in Figure 1S in supplementary information (SI). According to the Rz mode in Figure 1S (a), the total optimization energy of the structures is maximized at 45° relative to the nonrotated one. Notably, at the angle of 30° for either bromide or chloride-based structures, we see a slight decrease (less than 0.1 Rydberg) attributed to the reduction of structure size which will be discussed using electron density maps below. The calculated band gaps and lattice parameters in various rotational conditions are provided in Table 1 and Figure 2. The obtained results demonstrate that the lattice parameter of iodide structure (MAPbI3) in Rz mode displays a peak-like behavior from 0° to 45° (dashed blue line) being maximized at 25°. Approximately, the same ACS Paragon Plus Environment


behavior with a reflectional symmetry is seen from 45° to 90° showing a maximum peak at 75°. The considerably reduced lattice parameter occurred from 25° to 45° implies a drop in volume the of the structure emphasizing that 45°-rotated MA in MAPbI3 has the smallest unite cell among others. Obviously, the lattice parameters of MAPbBr3 and MAPbCl3 structures (Figure 2 (b) and (c)) also show an extremum point at 45° with notable change compared to that of MAPbI3 which is linked to the increased ratio of structure size to the ionic/ Van Der Waals radius (Table 2). In fact, the size of all structures reduces with a steep slope as a consequence of the lattice parameter values from nearly 30° to the angle bisector of stable state axis (X) and perpendicular to the stable state of the organic cation (Y) (i. e. 45°). However, according to the Figure 2 (d), (e), and (f), calculations on Rx-rotated MA reveal that the variation of lattice parameter in this mode is insignificant (less than 0.02 A°) derived from the fixed locations of NH3 and CH3 during Rx rotation. Our results show a good agreement with experimental data in either lattice parameter14, 22 or band gaps.14, 23 On the other hand, based on the calculated band structures and energy band gaps provided in Figure 2, Figure 3, and Table 1, we understand that there is a direct relation between the band gap and the lattice parameter (a & Eg) as a function of rotational angles. Accordingly, the band gap energies of MAPbI3, MAPbBr3, and MAPbCl3 maximally reduce from 1.61 eV, 2.06 eV, and 2.52 eV (non-rotated values) to 1.49 eV, 1.88 eV, and 2.35 eV (45° Rz-rotated values), respectively. Particularly, the energy difference (ΔE) between the band gap of stable state (0°rotated) and 45° Rz-rotated in bromide and chloride-based structures is much higher than that of MAPbI3 because of a noteworthy drop in lattice parameter as discussed earlier. Similar to the lattice parameter, the behavior of the band gap energies from 45° to 90° is roughly symmetrical due to a pseudo-cubic symmetry involved in the


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system. As a result, we can specifically report that decreasing the structure size (calculated from lattice parameter) leads to the increase in interaction radius of organic cation and inorganic octahedral shifting the conduction band to the lower energies. Evidently, the experimentally measured band gaps are embedded in plots of Figure 2 (green solid star symbol) being witness to our findings.14, 23 Fitted results for lattice parameter and band gaps are provided in SI. Furthermore, the band structure of MAPbX3 perovskite materials with detailed zoomed area are shown in Figure 3 based on non-rotated and 45° rotated MA in both Rx and Rz modes. The other considered rotational angels are provided in Figure 2S, 3S, 4S and 5S in SI. The panels of a1, b1, and c1 in Figure 3 depict the band structure corresponding to the stable 0°-rotated MA for MAPbI3, MAPbBr3, and MAPbCl3, respectively. It was found that the direct band gap is located at R and M points of BZ (shown with red and blue dots). The inset zoomed area confirms the formations of degeneracy at R and M points for MAPbI3 and MAPbBr3 in contrast to that chloride structure which show a single degeneracy at R point. Moreover, panels a2, b2, and c2 in Figure 3 represent the band structure of the materials which the organic cation (CH3NH3+) rotates in Rz mode with the tilt angle of 45°. Interestingly, despite the rotation of MA+, the bands still remain direct at high-symmetry R and M points. By giving attention to detail, we come to the conclusion that the 45° Rz rotation of MA+ changes the configuration of CBM at R point with respect to the non-rotated structure in which the third upper band is gradually going downward interacting with two lower bands of CBM owing to the considerable reduction of structure volume (e. g. Figure 3 (a2) left inset image). Additionally, form Figure 2S, 3S, and 4S (SI), we can infer that increase/decrease in the volume of structure affecting the interaction between organic cation and inorganic octahedra make significant alteration to the band structure.



According to Figure 3 (a2) and Figure 2S (SI), the band structure of 15°, 30°, and 45°-rotated MA at the M-point of MAPbI3 Valance Band Maximum (VBM) and Conduction Band Minimum (CBM) are perturbed showing a slight turn from direct to indirect gap. On the contrary, from chloride and bromide-based band structures we observe that only the shape of CBM changes by rotation (Figure 3 (b2) & (c2), Figure 3S, and Figure 4S (SI)). This fact may be rationalized by the relatively large structure of iodide in comparison to that of bromide and chloride during the balancing process through which MA+ and organic octahedra are being stabilized. Due to the specified symmetry of pseudo-cubic system, the behavior of the band structure at 60°, 75°, and 90° rotations is highly similar to that of 15°, 30°, and 0°, respectively. Nevertheless, the value of band gap decreases for all iodide, bromide, and also chloride structures in these cases. Likewise, the panels of a3, b3, and c3 in Figure 3 show the band structures regarding to the rotation of MA in Rx mode indicating a direct band gap located at R and Mpoints of BZ (for more information see Figure 5S (SI)). As seen here, under the influence of Rx rotational mode, the difference between the configuration of band structures (degeneracy, band interactions and shapes) corresponding to the nonrotated and rotated MA is rather negligible. Despite the common semiconductors such as GaAs which show a direct dualdegeneracy at VBM of Г point, MAPbX3 structures display triple degeneracy at CBM of R-point in BZ. This fundamental difference arises from the orientational disorder of organic cation in HOPs.24 It is worth mentioning here that, organic cation does not directly contribute in VBM and CBM. Nevertheless, the size, shape and location of organic cations25-26 within the inorganic (Pb-X) framework plays a significant role in the optoelectronic properties of HOP materials.27 In other words, as presented in Figure 3, Figure 2S to 5S (SI), the rotation of MA in Rz and Rx mode


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alters the value of band structure while keeping its original shape at R point of BZ unchanged. This variation in band structure is related to the interaction of organic cation along with inorganic framework. In this regard, large polarizability of HOPs induces the strong possibility of dispersive interactions which are considered as weak-type interactions e. g. van der Waasls (vdW).11, 15, 28 This will be discussed in the section of electron density and PDOS in detail.

Table1: The band gap and lattice constant values in MAPbX3 and Rz and Rx rotational modes. HOP (MAPbI3)

lattice constant (A°)

Band Gap (ev)

HOP (MAPbBr3)


Band Gap (ev)

HOP (MAPbCl3)


Band Gap (ev)

0° X

6.34

1.61

0° X

5.958

2.06

0° X

5.716

2.52

15° 𝑍

6.351

1.8

15° 𝑍

5.948

1.97

15° 𝑍

5.71

2.55

30° 𝑍

6.356

1.76

30° 𝑍

5.946

2.10

30° 𝑍

5.696

2.60

45° 𝑍

6.31

1.49

45° 𝑍

5.92

1.88

45° 𝑍

5.66

2.35

60° Z

6.354

1.75

60° Z

5.947

2.09

60° Z

5.697

2.58

75° 𝑍

6.349

1.78

75° 𝑍

5.95

2

75° 𝑍

5.704

2.57

90° 𝑍

6.34

1.61

90° 𝑍

5.958

2.06

90° 𝑍

5.716

2.52

45°X(CH3)

6.345

1.72

45°X(CH3)

5.957

2.12

45°X(CH3)

5.70

2.49

45°X(NH3)

6.347

1.73

45°X(NH3)

5.599

2.16

45°X(NH3)

5.699

2.48

45° X

6.355

1.78

45° X

5.952

1.94

45° X

5.694

2.36

Figure 4 shows simulation of electron density of MAPbX3 structures in both 2D and 3D depictions from the view of (001) crystallographic plane. According to the nonrotated structures (MA-0°x) in panels a1, b1, and c1 of Figure 4, the interaction of (CH3NH3+) with PbX6 octahedron leads to a considerable disorder which changes its volume (total volume of the structure as well) (refer to Table 1 & Figure 5). Furthermore, as seen from 2D counter plots of (001) plane in Figure 4, Figure (6S to 9S) (SI), the interaction of NH3 is much higher than that of CH3 due to the



relatively large ionic radius of NH3 (Table 2). To see how the mechanism of organic cation and inorganic octahedra interaction works, the average distortion index (bond length) and volume of octahedra calculations is performed as a function of rotational angles shown in Figure 5 and Figure 10S. It is observed from (001) plane in Figure 4 (a1) (and also Figure 6S (SI)) that the rotation of MA from 0° to 30°-Rz intensely decreases the interaction between components of MA molecule (i. e. CH3/NH3) and PbX6. In consequence, as seen in Figure 5 (a), the average volume of octahedra is lowered leading to a substantial growth in band gap energy (refer to Figure 2). However, increasing the angle of rotation from 30°-Rz to 45°-Rz, position the MA molecule at high symmetry level creating strong connection between CH3/NH3 and Pb+2 cation. This process directly reduces the band gap and interaction disorders by shifting the VBM and CBM band to higher energies (Figure 4 (a2)). The symmetrical interactions in 45°-Rz plane uniformly inflate the volume of PbX6 resulting a reduced disorder in octahedra bonds compared to the other angles (Figure 5 (a), inset image: zoomed area). Next, we study the bromide-based structures in non-rotated, Rz, and Rx modes. By increasing the rotational angle from stable state (0°) to 15°, the interactions between MA molecule and PbX6 become stronger at (001) plane leading to a decreased level of band gap (Figure 4 (b1) & Figure 7S (a)). Nonetheless, the correlation is weakened at 30°-Rz. This major difference in the behavior of iodide and bromidebased structures at 15° and 30° is may be attributed to the reduction of structure volume (Table 2) affecting the MA interactions with neighboring PbX6. Here, from the evidence, we can infer that the crucial effect of rotations is oriented towards the CH3 molecule rather than NH3. In other words, CH3 is highly affected by the rotations while NH3 molecule shows more stability to change of locations. The reason is based on the relatively small ionic radius (and larger van der Waals radius)


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of carbon atom compared to that of nitrogen atom.

However, at 45°-Rz the

interactions become considerably large due in part to the big movement of MA from its non-rotated state at this angle. As seen in Figure 5 (b), the average volume of octahedra in MAPbBr3 perovskite decreases while the average distortion index (bond length) uniformly increases from 0° to 30°-Rz. The reduction in distortion of bond length is also observable from inset zoomed image in Figure 5 (b). Similar to MAPbI3, by locating MA at 45°-Rz, a symmetrical configuration is created which strengthen the correlation between organic and Pb cations and reduce the band gap energy. According to Figure 4 (c1) and Figure 8S (a & b) corresponding to chloride structure, the interaction between organic cation and inorganic octahedra from 0° to 30°-Rz fade into insignificance resulted from reduction of octahedra volume (Figure 5 (c)). Further increase in rotational angle to 45°-Rz leads to significant ordered interactions shown in electron density distribution map of Figure 4 (c2). From the viewpoint of structural volume, MAPbCl3 is smaller than both MAPbI3 and MAPbBr3 confirming highly-ordered interactions in this sample. Because of the symmetry involved in our pseudo-cubic system, the rest of angles, i. e. 75°, 60°, and 90° act similarly like 30°, 15°, and 0° (shown in Figure 6S, 7S, 8S (SI)), respectively. Here, we can conclude that the distance and radius of interaction established between inorganic octahedron and organic cation (MA-Pb/MA-I, Br, Cl) are effective tools for tuning the electron density as well as band gap energies. Additionally, the electron density of the perovskite materials has been calculated regarding the rotational mode of Rx-45° on the (001) plane (Figure 4, a3, b3, and c3) implying no significant variations in comparison to the MA-0°x (Figure 4, a1, b1, c1). The reason is may be due to the fixed locations of the N and C atoms and only displacement of hydrogens in Rx rotational mode. Supplementary figures regarding ACS Paragon Plus Environment


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Rx mode are provided in Figure 9S (SI). The average distortion bond length is also shown in Figure 10S (SI) displaying Rx data. Thus, the structural disorder in the MAPbX3 perovskites rely directly on the presence of MA organic cation formed from two different ionic radii (CH3 and NH3). The interaction level of each molecule with PbX6 octahedra is not necessarily identical. Particularly, the interaction level and disorder in the vicinity of NH3 is larger than that of CH3 because of its relatively large ionic radius (Table 2). Hence, MA plays a remarkable role in cation-cation or cation-onion molecular interactions in HOP structures with respect to the ionic radius of CH3 and NH3. It has been experimentally reported that interactions of the organic cation with the inorganic PbX6 octahedra framework are formed mainly via the end of NH3+ through N+–H· · ·X hydrogen bonding indicating a tunable strength of interactions by the composition of halides.29

Table 2: Ionic, atomic, Van Der Waals radius and lattice constants of I, Br, Cl, N, and C. Atom Name

Ionic radius (A°)

atomic radius (A°)

I Br Cl N C

2.06 1.82 1.67 1.46 0.16

1.15 0.94 0.79 0.56 0.67

van der Waals Radius (A°) 1.98 1.85 1.75 1.55 1.7

To understand the bonding mechanisms between the atoms, we implemented both total DOS and PDOS calculations shown in Figure 6. It shows the contribution of valence orbitals of atoms in the materials for non-rotated and 45°-rotated MA in Rx and Rz mode (see other angles in SI section, Figure 11S to 14S). Panels a1, b1, and


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c1 in Figure 6 corresponds to the PDOS of MA-0°x showing that the valence band maximum (VBM) for each system is mainly contributed by I 5p, Br 4p, and Cl 3p orbitals and partly contributed by Pb 6s orbital, while the conduction band minimum (CBM) is dominated by 6p orbitals of Pb atoms. As seen, the rotation of MA from 0° to 15° in Rz mode increases the role of I 5p, Br 4p, Cl 3p and Pb 6p in valance and conduction bands, respectively. Moreover, total DOS visibly grow in the range of 4 to 9 eV which is directly related to the organic MA molecule. According to the electron density data we discussed above, at this angle the energy level of organic cation in (001) plane increases in comparison to non-rotated states. This is maybe due to the electron interactions of p orbitals of Pb/halogens with those of CH3/NH3 which is called ionic and van der Waals interactions. Additionally, changing the angle from 15° to 30°-Rz decreases the interactions between p orbitals of inorganic and organic components showing a reduced DOS as a result. In this regard, approximately a same symmetrical behavior is observable for 90°, 75°, and 60°, respectively. Notably, we can see a blue shift in DOS of conduction band at the angels of 15°, 30°, 60°, and 75° compared to that of non-rotated states. Furthermore, according to the panels of second row in Figure 6 (a2, b2, and c2), by rotation of MA with 45° Rz mode, the interactions of cation-cation (MA+–Pb+) and cation-anion (MA+ - Iˉ, Brˉ, Clˉ) changes I 5p, Br 4p, Cl 3p, and Pb 6s orbitals in uppermost valence band and shifts the VBM edge to higher energies. Here, the variation of energy states in 45°-Rz is more remarkable than those of 15°, 30°, 60°, and 75° which also affects the Pb 6s and 6p orbital at VBM. In fact, CBM is shifted to higher energies as a result of reduced volume structure and increased interactions among inorganic octahedra (p orbitals of Pb+2 and CH3/NH3) at this 45° rotational angle. Nevertheless, there is also a VBM shift to higher energies which is more than



that of CBM leading to the reduction of band gap at 45°-Rz due to the ∆𝐸𝐶𝑉 = 𝐸𝐶 ― 𝐸𝑉. Most notably, we can say that MA molecule highly affects the energy states when its orientation and rotation is considered in interaction with inorganic octahedra. As shown in right panels of Figure 6 (a3, b3, and c3), by rotating MA with 45°-Rx, energy states of I 5p, Br 4p, Cl 3p, and Pb 6s do not undergo substantial changes which is attributed to the fixed nature of N and C atoms in this rotational mode. Here, the maximum variation of total DOS and PDOS (blue shift) occurs at conduction band states while the VBM states are nearly unchanged. Overall, the rotation of MA cation within the Pb-X framework changes p orbitals of Pb/Halogens and shifts the conduction band to the high energies. This is true for all structures (i. e. MAPbI3, MAPbBr3, and MAPbCl3) and rotational modes (i. e. Rx & Rz). It has been previously reported that location, orientation, and rotational dynamics of MA within the Pb-X framework crucially affects the electronic properties of the system because of a permanent dipole feature of organic cation.30

3.2 Rotation-dependent optical properties Besides the special electronic structure, CH3NH3PbX3 also have excellent ability of light absorption in the visible zone used in solar cell technology. Many of MAPbX3 features such as low exciton binding energy and high charge mobility can be related to the high dielectric constant of the material.31 As discussed in previous sections, the orientation, positioning, and rotational dynamics32 of the CH3NH3+ within the inorganic lattice can have a strong effect on the electronic system.30 The reorientation of the organic cation with its associated dipole moment contributes to the dielectric response, and applies a crystal field to the material; both will affect the


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photovoltaic action. In order to study the solar energy harvesting property of MAPbX3 structures, we have calculated the dielectric function and absorption spectrum for each of them in MA-0°x, Rx, and Rz rotational modes shown in Figure 7, Figure 8, and Table 3. Panels of a, c, and e in Figure 7 present dielectric function regarding the rotation of organic cation with Rz mode. Accordingly, static dielectric constant which is the real part of dielectric function (shown in solid lines in Figure 7) at E=0 is calculated 8.69, 6.57, and 5.17 for non-rotated MA of MAPbI3, MAPbBr3, and MAPbCl3, respectively. Nevertheless, the rotation of MA with Rz mode causes static dielectric constant of materials to decrease in every considered angle (inset zoomed figures). In this rotational mode, the height of peaks at maximum/minimum of real and imaginary parts of dielectric function curves has been shortened in comparison with MA-0°x. Also, because of the reverse relationship between the optical conductivity and the real part of dielectric function, it can be concluded that in regions which the real part of dielectric function has an intense peak, the optical conductivity is weak. 33 The dashed curves in Figure 7, a, c, and e show imaginary parts of dielectric function which the first peak represents the direct optical transition known as optical gap (R transition point in BZ). These peaks are located at 1.61, 2.06, 2.52 for MAPbI3, MAPbBr3, and MAPbCl3 which the MA is along x direction MA 0°-Rx, respectively. However, rotating the MA organic cation with the angle of 45° leads to the red shift of peak energy (other rotational angles induce blue shift to the imaginary part of dielectric function). As seen, by rotating the MA molecule from X-directed orientation to the 90°-Rx, Y axis properties of the system are kept unchanged and behave like dielectric function of 0°-Rx. Furthermore, the effect of MA rotation with Rx mode is shown in panels of b, d, and f of Figure 7 presenting a different outcome from that of Rz with a considerable



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change in static dielectric constant. Also, imaginary part of dielectric function in these panels of Figure 7 (dashed curves) shows blue/red shift according to the increase/decrease of band gap value. As a result, we can conclude here that, rotation of MA with Rz mode leads to the increase of cation-cation (MA-Pb) and also cation-anion (MA-X) interactions due to the significant variations in the locations of NH3 and CH3 molecules. Thus, maximum/minimum of real and imaginary parts of dielectric function curves along with static dielectric constant undergo a change with respect to the MA-0°x structure. Therefore, it can be concluded that the increase/reduction of structure size and band gap value at all rotational modes and angles and its relationship with interaction of organic molecule and the inorganic framework can effectively change the dielectric function of the system.

Table 3: Static dielectric constants and wavelength of absorption edge provided for MAPbX3 and Rz and Rx rotational modes.

𝐇𝐎𝐏(𝐌𝐀𝐏𝐛𝐈𝟑)

𝛆𝟎

α (nm)

𝐇𝐎𝐏(𝐌𝐀𝐏𝐛𝐁𝐫𝟑)

𝛆𝟎

0° X

8.69

751

0° X

6.57

15° Z

6.98

688

15° Z

30° Z

6.78

690

45° Z

6.94

60° Z

α

α

𝐇𝐎𝐏(𝐌𝐀𝐏𝐛𝐂𝐥𝟑)

𝛆𝟎

590

0° X

5.17

488

6.60

629

15° Z

4.79

484

30° Z

4.50

585

30° Z

4.51

473

820

45° Z

6.22

659

45° Z

4.66

530

6.86

700

60° Z

5.70

582

60° Z

4.57

478

75° Z

6.89

696

75° Z

5.85

619

75° Z

4.62

480

90° Z

8.68

749

90° Z

6.56

587

90° Z

5.16

486

45° X(CH3)

7.90

738

45° X(CH3)

6.32

585

45° X(CH3)

5.18

497

45° X(NH3)

7.78

729

45° X(NH3)

4.50

571

45° X(NH3)

5.12

503

45° X

7.56

688

45° X

5.67

635

45° X

5.37

539

(nm)


(nm)

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Figure 8 (a, b, and c) show optical absorption spectrum of HOP materials regarding MA-0°x and Rx and Rz rotated organic cation. It is clear that edge of adsorption starts from 751, 590, and 488 nm for MAPbI3, MAPbBr3, MAPbCl3 when MA is located along x axis, respectively. Table 3 provides optical absorption data corresponding to Rx and Rz in detail, presenting both red and blue-shifted edge of adsorption in rotational modes. The maximum change in wavelength of absorption edge corresponds to the rotation of 45°-Rz which is ~65 nm red-shift indicating 820, 659, and 530 nm for MAPbI3, MAPbBr3, MAPbCl3, respectively. The red shift in imaginary part of dielectric function at 45°-Rz (lowering the edge of electron transition) results from the reduced volume of structure and increased interactions between CH3/NH3 and Pb+2. However, we show that using rotational modes of MA inside the inorganic PbX6 octahedra in the pseudo-cubic structure the improved absorption spectra is obtainable in the visible region. Notably, the calculated absorption spectra for iodide, bromide and chloride structures are reproducing the experimentally reported behavior.34 Therefore, location and orientation of organic cation and its interaction with inorganic octahedra in different angles and directions can possibly increase/decrease wavelength of absorption edge providing a tunable absorption spectrum for HOP perovskites which reveals the importance of organic cation embedded in the inorganic framework.



Conclusion In summary, we presented DFT-based calculations to reveal the effect of MA rotation on electronic and optical properties of hybrid halide MAPbX3 Perovskites. By selecting some specific rotational modes (i. e. Rz and Rx) and angles (i.e. 0°, 15°, 30°, 45°, 60°, 75°, and 90°), we demonstrate the critical impact of MA movement within the Pb-X framework on band structure, electron density, DOS, dielectric function, and absorption spectra of HOP perovskites. Our results showed that, organic cation of MA does not directly contribute to electronic band structure. Nevertheless, its rotation with Rz and Rx modes leads to profound changes in structural, electronic, and optical characteristics of hybrid halide materials. The origin of these changes mostly results from cation-cation (MA+ -Pb2+ ) and cation-anion (MA+ -X- ) interactions. Moreover, we found that band gap, static dielectric constant, and absorption edge of optical spectra can highly be tuned through manipulating the rotational modes, location, and orientation of organic cation. Most notably, the effect of iodide, bromide, and chloride halogens on the inorganic-organic interaction inside the MAPbX3 was thoroughly investigated. Overall, this work provides insights into the mechanism of MA rotation and its effects on structural properties of HOP perovskite materials and show a possible way for engineering the photovoltaic performance which is prerequisite for progress toward device optimization.

Supporting Information The supporting information is available free of charge on the ACS Publication website.


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Figure 1: (a) Rotational pathways for MA+ ions within a Pb-X framework: (i) rotation of axis which is perpendicular to the C-N (CH3-NH3) ions denoted as Rz, (ii) rotation of whole molecule of MA+ (CH3-NH3) via C–N axis itself (𝑒𝑥) denoted as Rx. (b) location and layout of MA within the Pb-X framework in the HOP configuration.



Figure 2: The calculated band gaps and lattice parameters of MAPbX3 perovskite materials rotated MA with Rz mode (a) MAPbI3, (b) MAPbBr3, (c) MAPbCl3 and rotated MA with Rx mode (d) MAPbI3, (e) MAPbBr3, (f) MAPbCl3. Experimental witnesses are provided from Refs. [18, 26, 27] shown in green and red solid shapes. Blue and black arrows indicate lattice parameter and band gap vertical axes, respectively.


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Figure 3: The calculated band structure of MAPbX3 perovskite materials nonrotated (along the x direction) (a1) MAPbI3, (b1) MAPbBr3, (c1) MAPbCl3 and 45°-rotated MA with Rz mode (a2) MAPbI3, (b2) MAPbBr3, (c2) MAPbCl3 and also 45°-rotated MA with Rx mode (a3) MAPbI3, (b3) MAPbBr3, (c3) MAPbCl3. Direct band gap located at R and M points of Brillouin zone (BZ) are shown with dashed line. Inset zoomed images show band degeneracies at R and M points. Fermi level is set to 0 eV.



Figure 4: 2D and 3D depiction of electron density of MAPbX3 perovskite materials non-rotated (MA-0°x) in crystallographic plane of (001) (a1) MAPbI3, (b1) MAPbBr3, (c1) MAPbCl3 and 45°-rotated MA with Rz mode (a2) MAPbI3, (b2) MAPbBr3, (c2) MAPbCl3 and also 45°-rotated MA with Rx mode (a3) MAPbI3, (b3) MAPbBr3, (c3) MAPbCl3. Location of CH3, NH3, and octahedral are shown with dashed line in both 2D and 3D graphs.


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Figure 5: The calculated average distortion index (bond length) and average octahedra volume of MAPbX3 perovskite materials rotated MA with Rz mode (a) MAPbI3, (b) MAPbBr3, and (c) MAPbCl3. Zoomed inset images show distortion bond length at the angle of 45°-rotated MA with Rz mode.



Figure 6: The calculated DOS and PDOS for each single orbital of MAPbX3 hybrid perovskite non-rotated MA-0°x (a1) MAPbI3, (b1) MAPbBr3, (c1) MAPbCl3, and 45°-rotated MA with Rz mode (a2) MAPbI3, (b2) MAPbBr3, (c2) MAPbCl3, and also 45°-rotated MA with Rx mode (a3) MAPbI3, (b3) MAPbBr3, (c3) MAPbCl3. The molecular interactions with rotation of MA leads to the changes in the levels of valence and conduction bands relative to that of the non-rotated MA (MA-0°x) shown in dashed black lines. The configuration of each structure with non-rotated and rotated MA is also depicted as inset image.


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Figure 7: The dielectric functional of MAPbX3 hybrid perovskite regarding Rz rotational mode (a) MAPbI3, (c) MAPbBr3, and (e) MAPbCl3. The effect of Rx rotation of MA, CH3 and NH3 on dielectric function is shown with panels of (b) MAPbI3, (d) MAPbBr3, and (f) MAPbCl3. Static dielectric constant at E=0 is demonstrated in detail with zoomed inset image.



Figure 8: Optical adsorption spectrum of perovskite structures in non-rotated and 15°,30°, 45°, 60°,75°and 90° for Rz and 45° for Rx-rotated organic cation within the PbX6 octahedra framework (a) MAPbI3, (b) MAPbBr3, and (c) MAPbCl3. Absorption spectrum of 0° and 90° are approximately overlap.


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TOC Graphic


The Role of Methylammonium Rotation in Hybrid Halide MAPbX3 (X=I

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