A comparative study of the mechanical stability, electronic, optical and photocatalytic properties of CsPbX3 (X = Cl, Br, I) by DFT calculations for optoelectronic applications

Organic free Cs-based perovskite materials are potential candidates for electronic and optoelectronic applications. A systematic comparative study of the mechanical, electronic, optical, and photocatalytic properties of CsPbX3 (X = Cl, Br, I) was conducted using density functional theory to compare the applicability of these materials in optoelectronic, photocatalytic, and photovoltaic (PV) devices. We calculated structural and elastic properties to determine the better agreement of damage-tolerance and electronic and optical responses for suitable device applications. Optimized lattice parameters and elastic constants showed excellent agreement with the experimental data whereas some properties were found to be much better than other theoretical reports. CsPbBr3 is thermodynamically more stable and more ductile compared to the other two perovskites. The hydrostatic pressure dependent mechanical stability showed that CsPbCl3 and CsPbBr3 sustained stability under low applied pressure, whereas the stability of CsPbI3 was very high. The electronic band gap calculations showed that CsPbCl3, CsPbBr3, and CsPbI3 are suitable for green, orange, and red emissions of optical spectra owing to the proper electronic band gaps. CsPbI3 can be shown as the best photocatalyst for the hydrogen evolution reaction and CsPbBr3 is the most stable photocatalyst due to its nearly balanced oxidation and reduction potentials, but CaPbCl3 is better for O2 production. The density of states and other optical properties have been reported in this study. Thus, our findings would be beneficial for experimental studies and can open a new window for efficient electronic, optoelectronic, and hydrogen production along with the biodegradation of polluted and waste materials.


Introduction
The demand for more efficient PV cells, optoelectronic and electronic devices is of great concern with the increasing world population under the worse conditions of insufficient energy crisis. 1 With this increasing demand, researchers are extremely careful on a healthy ecosystem. A new kind of effective, ecofriendly, and renewable energy capturing technology has achieved much more interest among the world scientic community. [2][3][4][5][6][7][8][9][10][11] The present photovoltaic market is dominated by Sibased solar cells 12,13 but they do not work for long due to low efficiency and maintenance of the expensive purication processes. 1 Besides, their less optical absorption, less carrier mobility, and indirect band type 1 have made this rethinkable in the competitive race for the production of more functioning device, and the amorphous Si thin lm technology is costeffective and the fabrication process is simple. However, its low stability as well as lower photo conversion efficiency (PCE) are of great concern. 14,15 Thus, researchers are eagerly concerned to nd alternative low-cost, earth-abundant, and solution-processable solar cell materials. To this end, organicinorganic halide perovskites meet these demands and are of great interest. In the 1990s, perovskite materials started their research journey extensively for the replacement of Si and multifunctional solar cell devices.
The perovskite solar cell was rst reported by Miyasaka and co-workers in 2006 and they reported a PCE of $2.2% 16,17 that reached 3.8% in 2009. 18 In 2018, a research report on a PCE of 27.6% was published, which mentioned that a 30% plus PCE was possible by the end of 2020, but in 2020, the US National Renewable Energy Laboratory certied a perovskite solar cell with a max. PCE of 25.5%. 19 Researchers found hope for mixed halide perovskites from a comparative study of different structures. Thus organic-inorganic lead halide perovskites solar cells have drawn incredible attention in the scientic community as alternative competitors to some inorganic photovoltaic materials, such as copper indium gallium sulde and selenide (CIGS), cadmium telluride (CdTe), amorphous or single crystal silicon (a-Si or c-Si), iron disulphide (FeS 2 ), and gallium arsenide (GaAs). Though multi-junction AlGaInP, AlGaAs, GaAs, GaInAs cells are certied as 47.1% efficient in the present research, 20 all of these compounds are expensive due to the presence of scarcity elements, In, and Ga, and they are also toxic as they contain As and P. Hence, metal halide perovskites [21][22][23][24][25][26][27][28][29][30][31] solar cells have a great possibility to replace the dominating Sibased solar cells by proper selection of atoms in a right place. Organic-inorganic halide perovskites with a formula of AMX 3 (where, organic-inorganic cation A ¼ CH 3 NH 3 + or Cs + , etc.; inorganic cation M ¼ Pb 2+ or Sn 2+ , etc.; halide X ¼ Cl À , Br À , I À ) 1,32 are highly 33-36 efficient due to excellent absorption coef-cient, [37][38][39] carrier mobility, lengthy carrier life, and a suitable band gap. [40][41][42][43][44][45] Due to low physical and chemical stabilities of organic-inorganic perovskites, 1 inorganic perovskites have achieved tremendous research interest. Among them, Cs-based inorganic perovskites CsPbX 3 (X ¼ Cl, Br, I) are promising materials for next-generation advanced electronic, optoelectronic and photonic devices, and they possess temperaturedependent phases. 46 The properties of CsPbX 3 can be tuned by metal or mixing halides to enhance optoelectronic device applications such as LEDs, photo-detectors, and lasers. 52 CsPbI 3 is a highly efficient thermally stable solar cell due to its relatively high light absorption coefficient, and carrier mobility in the visible region. 85 Organic-inorganic perovskites have a great tendency to dissolve under humidity at high temperature 86 and are greatly sensitive to light and heat 49 as well as the presence of toxic lead in these perovskites, which causes huge health issues to live creatures. It can be seen that CsPbX 3 (X ¼ Cl, Br, I) are direct band gap semiconductors that absorb visible and ultraviolet light. Hence, these compounds are used in photovoltaic and optoelectronic devices. It should be remembered that pressure plays an important role in tuning the physical properties of any materials. [87][88][89] It treats phase transitions and is oen reversible if the external conditions are the same in the complete cycle. 90,91 In this sense the high-pressure studies oen offer fundamental insight into the optoelectronic properties of perovskite materials. [92][93][94] Perovskites are an advanced class of materials that have exhibited great potential in optoelectronic technologies thus all-inorganic perovskites have an extremely versatile crystal structure. Thus far, there are no such theoretical reports on the pressure-dependent comparative studies of the elastic, mechanical, electronic, optical, and photocatalytic properties of CsPbX 3 . In this work, for the rst time, a pressure-dependent comparative study of the mechanical, elastic properties and electronic, optical, and photocatalytic properties has been performed through rst-principles calculations based on the density functional theory (DFT). In this study, we tried to nd out more stable and efficient materials among them to make a prediction for the proper selection of perovskite materials for electronic, photocatalytic, and optoelectronic applications.

Methodology
The bulk perovskites of CsPbX 3 (X ¼ Cl, Br, I) exhibit cubic structure of space group Pmm (221), and the lattice constants are 5.734, 6.017, and 6.38, respectively (Table 1). To compare and analyze the data of the structural, mechanical, electronic, optical and photocatalytic properties, DFT calculations were performed using the CASTEP code in Materials Studio simulation soware. [95][96][97][98][99][100] Valance shell and ion core electrostatic interactions of ingredient atoms were investigated under Generalized Gradient Approximation (GGA) of Perdew-Burke-Ernzerhof (PBE) with norm-conserving pseudo-potentials treatment but the mechanical properties were calculated using ultraso pseudopotentials for the better agreement with experimental data. The photocatalytic properties were also calculated from the electronic band structure calculations. Initially, we chose the cubic structure to carry out the numerical operations.
A primitive cell of CsPbCl 3 consisting 5 atoms was formed with 1 Cs atom that occupied the Wyckoff site (0, 0, 0), 3 Pb atoms at the site of (0.5, 0.5, 0.5) and 1 Cl atom at (0, 0.5, 0.5) fractional coordinates 101 as depicted in Fig. 1. The sets of valence shall are interacted as Cs: 5s 2 5p 6 6s 1 , Pb: 5s 2 5p 6 5d 10 6s 2 6p 2 , Cl: 3s 2 3p 5 , Br: 4s 2 4p 5 and I: 5s 2 5p 5 . All the crystals were optimized using the same soware functional treatments. CsPbCl 3 was simulated rst by providing a lattice parameter as a ¼ 5.734 (ref. 101) and the optimized structure with minimum formation enthalpy was conrmed with plane wave basic set kpoints of 6 Â 6 Â 6 and cut-off energy of 520 eV with SCF tolerance 2 Â 10 À6 eV per atom, convergence tolerance energy of 2 Â 10 À5 eV per atom as well as maximum force and stress 0.05 eVÅ À1 and 0.10 GPa, respectively. The maximum atomic displacement was restricted up to 0.002Å. We calculated the elastic, electronic, and optical properties for CsPbBr 3 and CsPbI 3 aer replacing the Cl atom (100%) with Br and I atoms under the same conditions.

Structural properties
The three phases (cubic, tetragonal and orthorhombic) of CsPbCl 3 were primarily chosen as the highest temperature phases of the cubic structure to carry out the numerical operations for high-temperature device applications. The optimizedcell structure of CsPbCl 3 was determined and then the Cl atom was replaced by Br and I atoms, which were then optimized for CsPbBr 3 and CsPbI 3 perovskite structures. Fig. 1(a)-(c) represent the optimized crystal structures of CsPbCl 3 , CsPbBr 3 and CsPbI 3. The optimized cell parameters for the corresponding perovskites are represented in Table 1. From Table 1, it can be seen that aer several k-points tests the optimized lattice parameter a ¼ b ¼ c of CsPbCl 3 was 5.785Å, which was elongated about 3.9% and 11.2% aer the replacement of halide Cl atom by Br and I atoms and the obtained values were in a great agreement with other theoretical and experimental values. 32,82,83,[102][103][104][105][106][107][108][109][110]123 From the cell parameters and volumes of CsPbX 3 (X¼ Cl, Br, I) results, a relation can be expressed as CsPbCl 3 < CsPbBr 3 < CsPbI 3 (Table 1) with volume increments of 12.4% and 37.8% for CsPbBr 3 and CsPbI 3, respectively.

Mechanical properties
The mechanical properties of the cubic crystals of CsPbX 3 were explicitly and implicitly calculated using three independent elastic tensors C 11 , C 12 and C 44 . The calculated values are represented in Table 2 and shown graphically in Fig. 2(a) for the isostructural of CsPbCl 3 , CsPbBr 3, and CsPbI 3 . Mechanical stability was justied under Born criteria for these crystals 111 and it is clearly seen that all are mechanically stable because they satisfy the condition C 11 + 2C 12 > 0, C 44 > 0 and C 11 À C 44 > 0 as well as another stability condition of C 12 < B < C 11 . 106 All of these in the bulk form are elastically anisotropic, conrmed by the relation 2C 44 ¼ C 11 À C 12 (ref. 112) and reconrmed by nonzero Zener's anisotropy factor A. 113,114 The C 11 > C 12 > C 44 conditions show that the materials resist longitudinal deformation of more than shape deformation, where the largest value of C 11 for CsPbBr 3 offers more resistance to longitudinal deformation. Young's modulus (E) is an indication of the degree of resistance offered by a material to longitudinal tension. 106 A comparative data set of E's ( Table 2) could be an inspiration for Table 2 Calculated pressure independent (at 0 GPa) elastic constants C ij (GPa), elastic moduli B, G, E (GPa), Pugh's ratio B/G, Poisson's ratio s, and machinability index m M ¼ B/C 44 and elastic anisotropy factor A, melting temperature T m for CsPbCl 3 , CsPbBr 3 and CsPbI 3  conducting further research on CsPbBr 3 for band gap tailoring and other purposes due to the comparatively high value of E. Pressure responses of CsPbX 3 are depicted in Fig. 2(b) with B, G, E data. A comparative study of Cauchy pressure C 12 À C 44 (ref. 115) of the tabulated data shown in Table 1 conrms the brittlelike nature of CsPbCl 3 > CsPbBr 3 > CsPbI 3 , which can be reconrmed from the values of Pugh's ratio B/G < 1.75 for all structures, 116 which is shown in Fig. 2(c). It offers a completely new result from other researchers' ndings, 117,118 which may open a new opportunity to observe the material insight. CsPbBr 3 offers a larger value of bulk modulus, whereas CsPbCl 3 offers the least value, thus the compressibility of these perovskites can be ordered as CsPbBr 3 < CsPbI 3 < CsPbCl 3 . The elastic and universal anisotropy factors A and A U were calculated using the following relations 115,116 as The values of Zener's anisotropy factor, A, for all structures were less than unity. Any deviation from unity conrms the elastic anisotropic property. 117 For these materials, the order of anisotropy can be obtained as CsPbBr 3 > CsPbI 3 > CsPbCl 3 ( Table 2). The melting point temperatures (T m ) were calculated using the following empirical formula proposed by Fine et al. 118 T m ¼ 553 + 5.91C 11 From Table 2, it is obvious that CsPbBr 3 possesses the highest melting temperature due to the highest C 11 and the comparison suggests that CsPbBr 3 is a better choice for hightemperature efficiency and potential applications in comparison to the other two. The value of the machinability index indicates the suitability of the materials for industrial applications, whereas CsPbBr 3 shows dominating nature over CsPbCl 3 and CsPbI 3 ( Table 2) though its H v value is the lowest one.
The calculated elastic constants are tabulated in Table 3. The values of the calculated elastic constants are positive and satisfy the Born stability criteria, which implies that the compounds are mechanically stable. The calculated elastic constants for CsPbCl 3 are in good agreement with the available theoretical results reported in the literature. 115 It should be noted that the mechanical instability is responsible for the negative values of C 44 and B/C 44 , whereas stability can be satised by the value of C 44 > 0. From Table 3 and Fig. 3(a), we observed that CsPbCl 3 and CsPbBr 3 lose mechanical stability at an applied pressure above 20 GPa and 25 Gpa, respectively, while CsPbI 3 can tolerate more pressure and shows stability up to the hydrostatic pressure of about 75 GPa. The mechanical instability was conrmed from the negative value of C 44 corresponding to the threshold pressures for individual perovskites. From the above discussion and the obtained results, the stability order of the three compounds under applied pressure can be followed as CsPbI 3 > CsPbBr 3 > CsPbCl 3 , but CsPbI 3 remains stable under hydrostatic pressure approximately three times more than that of CsPbCl 3 (Table 3 and Fig. 3(c)). The Poisson's ratio of the system was calculated using the following formula.
The calculated values are also included in Table 3. It is obvious that with the increase in hydrostatic pressure, the value of the Poisson's ratio s increases for CsPbX 3 . It is well known that s can separate crystalline solids as brittle and ductile at the borderline value of 0.26. From Table 3, it can be clearly evident that all the structures possessed values greater than 0.26, indicating that they must be quite ductile in nature. Among them, CsPbI 3 is more ductile as it has more pressure tolerance. Bulk to shear modulus ratio (B/G) with the critical value of ductility of 1.75 served as the borderline between the ductile and brittle behaviors of crystalline solids. It also predicted a more ductile behavior of CsPbI 3 .
Young's modulus, E measures the stiffness against longitudinal deformation as well as thermal shock resistance of the materials. A larger value of E indicates a smaller thermal resistance. The thermal shock resistance order under different pressure conditions followed the order CsPbCl 3 > CsPbBr 3 > CsPbI 3 (Fig. 3(b)).

Electronic properties
The energy band diagram with k-points in Brillouin zone sampling represents the energy band gap of a material. Fig. 4(a)-(c) represents the electronic band structures of CsPbX 3 . The energy differences between the top of the valence band (VB) and the bottom of the conduction band (CB) along the same point of momentum space (at the R point) for all structures provides evidence for the existence of a direct band gap. Electronic transition in the direct band gap material offers less momentum loss for carrier propagation as the phonon contributions are negligible for pair creation. From Fig. 4, it is clearly seen that the valence shells are extended from À5 eV up to 0 eV, where 0 eV energy levels (green lines) represent the Fermi levels (E F ). The electronic shells above the E F form conduction bands, which have been extended from 0 eV up to 5 eV. From Fig. 4(a)-(c), it is seen that CsPbCl 3 , CsPbBr 3 and CsPbI 3 have direct band gaps with values of 2.385 eV, 2.061 eV and 1.784 eV, respectively, where CsPbCl 3 , CsPbBr 3 and CsPbI 3 show the carrier transitions for green, orange and red emissions of visible spectra, respectively. Solar irradiance on earth's surface is of maximum photon ux density for green wavelength and appreciably high enough for orange as well as red spectra of the visible region. 105 The obtained values of the band gap are listed in Table 1. By comparing the band gaps shown in Table 1, it is evident that the value of CsPbCl 3 is closest to the theoretical reported values of 2.168 eV, 102 119,122 From Table 1 it is clearly seen that the calculated band gap of CsPbBr 3 is 2.061 eV, whereas the band gaps of CsPbBr 3 are reported as 1.796 eV, 103 1.74 eV, 106 (Table 1). 83,102,103,109 It should be noted that the theoretical band gap obtained using PBE-GGA is a little bit underestimated compared to the experimental value, which could be due to the error in GGA. [119][120][121][122][123] It can be seen that when Cl is partially replaced by Br and I atoms, the band gap decreases because of an increase in the atomic size. In all cases, the origin of some discrepancies with experimental values may arise from the drawbacks of the calculative process of the rst principal calculations. From Fig. 4(a)-(c), it is explicitly clear that the top of the VB is well dispersive than the bottom of the CB, which indicates that the photo-generated holes possess lower effective mass. A lower carrier effective mass corresponds to higher carrier mobility. As such, the photogenerated holes in the VB can transfer more rapidly to the surface of CsPbX 3 to participate in conduction and in photocatalytic reactions. This nature of the charge carriers for CsPbX 3 systems supports the p-type conduction of CsPbCl 3 , CsPbBr 3, and CsPbI 3 . The curvature of the valence band maxima shows a decrement with the replacement of Cl by Br and I. The hole mobility decreases with the insertion of Br and I in the place of Cl in CsPbCl 3 .
Atomic contributions to the band structure formation are shown in terms of density of states (DOS) for individual atoms and the total densities of states (TDOS) for all atoms are shown in Fig. 3(d-f) for CsPbX 3 perovskites. From Fig. 4(d), it is evident that the DOS of CsPbCl 3 can be divided into six major regions. The rst region (Fig. 3(d)) À21.14 eV to À19.54 eV is mainly arising due to the Cs-6s orbital state, the second region À15.08 eV to À13.54 eV is due to the Pb-5d state, the third region À13.38 eV to À12.23 eV is due to Cl-3s, the fourth region À7.33 eV to À5.82 eV is due to the hybridization of Cs-5p and Pb-5d states and the h region lies between À3.16 eV to 0 eV below the E F level, which is called the top of the valence band and is originated from the 3p orbital of Cl atom. Whereas the conduction band that lies between 2.38 eV and13.24 eV, above the E F level, originated from the hybridization of the 6p orbital of Cs and 6p orbital of Pb and 3p orbital of Cl atoms. In a similar way, for CsPbBr 3 the core VB originated from the mixing of Cs-3p, Pb-5d, Br-3s, Cs-5p, and Pb-5d and the top of the valence band originated from the 4p state of Br atom and the CB band arise from the hybridization of the 6p orbital of Cs and the 6p orbital of Pb and the 4p orbital of Br atoms (Fig. 4(e)). For the CsPbI 3 system, the core VB originated from Cs-3p, Pb-5d, I-3s, Cs-5p, and Pb-5d and the top of the valence band originated from the 5p state of the I atom and CB occurred from the predominant hybridization of Cs-6p, Pb-6p and I-5p orbitals of Cs, Pb, I atoms ( Fig. 4(f)). From the atomic contribution plots, it is clear that Pb and halogen atoms have a major contribution to the valence and conduction bands, which reduces the band gap energy. The s and p states of Pb and the p state of the halogens play a major role in the reduction of band gap energy as shown in Fig. 4(d)-(f). The order of decrement can be assigned as CsPbCl 3 > CsPbBr 3 > CsPbI 3 (Fig. 5).

Optical properties
Many application elds, such as absorbers, reectors, optical coatings, and different optoelectronic devices of materials are examined from their optical responses. In the presence of an external electromagnetic wave, the photonic interactions of the material can provide information on the properties and application predictions as a function of energy. These properties are analyzed for electronic transitions between occupied and empty states, band structures, bond types as well as internal structures of the materials according to their optical spectra. The frequency-dependent complex dielectric function is followed by the Kramers-Kronig transformation as 3(u) ¼ 3 1 (u) + i3 2 (u), which is also related to the representation of relative permittivity. The imaginary part of this complex function is, where u ¼ 2pv is the frequency of the incident photon and e,û,r are the electronic charge, polarization vector of the incident eld, and radius vector, respectively. Whereas, J k c and J k v are the wave functions of the conduction and valence bands at K, respectively. Using 3 1 and 3 2 , other optical properties such as absorption coefficient a(u), optical conductivity s(u), loss function L(u), reectivity R(u) and refractive index n(u) can be calculated 118 using the following expressions.
The dielectric function is a fundamental parameter that is related to the charge-carrier regeneration rate of certain materials used in the solar cell. 124,125 It gives a clear idea of the performance of optoelectronic devices. 126 Higher dielectric constant values of the perovskite solar cells can lead to lower recombination rates. Fig. 6(a) shows the imaginary parts of the dielectric function of CsPbX 3 perovskites. The real part of the dielectric function shows a higher value at low photon energy and then decreases rapidly with the increase of photon energy. It is well known that a perovskite material with such a higher value of the real part of the dielectric function exhibits a lower band gap, 127 which is also seen in the electronic band structure. On the other hand, the values of the imaginary part of the dielectric function decrease to zero at a higher photon energy region. It should be noted that there are few peaks arising at 3.9, 7.8, 11.0 and 14.1 eV for CsPbCl 3 ; 3.5, 7.3, 10.3 and 13.9 eV for CsPbBr 3 ; and 3.0, 6.3, 8.5 and 13.9 eV for CsPbI 3 . The rst peak is due to the generation of the electron-hole pairs for conduction. The 2 nd and 3 rd peaks are due to the interband optical transitions from the valence bands to the conduction bands. The fourth peak around 14.0 eV is due to the collecting excitons from the free carriers, which is the so-called plasma frequency and the peak is called the plasmon peak. These irregular photo responses of the materials cause the difference in band gaps among them.
It is well known that the performance of solar cells is determined by various optical properties, among them the absorption coefficient (a) is the crucial property. The variation of optical absorption of CsPbX 3 perovskites can be seen in Fig. 6(b). The value of a of the I-based perovskite demonstrates its maximum intensity in the ultraviolet region compared to that of Br and Cl-based perovskites. The rst peak of a offers an optical transition of electrons from Cl-3p of the valence band to Pb-6p of the conduction band at higher energy compared to that of the interband transitions of electrons in the case of CsPbBr 3 and CsPbI 3 . The optical band gaps can be seen from the absorption peaks of corresponding materials as E g (CsPbCl 3 )> E g (CsPbBr 3 ) > E g (CsPbI 3 ), which is coherent with the calculated values of E g of CsPbX 3 perovskites ( Table 1). The highest absorption peaks for all materials occurred at the same energy of 14.6 eV ( Fig. 6(b)). Fig. 6(c) shows the real part of photoconductivity. From the gure, it is evident that if the absorption of photons enhances, the rate of photoconductivity tends to increase. Thereby, greater absorption and more photoconductivity are observed in the I-based perovskite compound relative to the Br and Cl-based perovskite compounds. The photoconductivity comparison of these materials shows some peaks over a wide range of energy spectra. The conductivity initiatives and the rst peaks are ordered in terms of the energy as s (CsPbI 3 ) > s (CsPbBr 3 ) > s (CsPbCl 3 ). Photoconductivity increases at the energy edges 4.2, 7.8, 11.3 and 14.1 eV for CsPbCl 3 , 3.8, 7.3, 10.2 and 14.1 eV for CsPbBr 3 and 3.0, 6.4, 8.3 and 14.1 eV for CsPbI 3 as a result of photonic energy absorption, which is shown in Fig. 6(c).
Reectivity is an important optical property that determines the surface nature of the materials for optoelectronic and solar cell applications. 128 Fig. 6(d) shows the reectivity spectra of CsPbX 3 perovskites. From these data, it can be seen that the reectivity is very low for all the studied cubic perovskite compounds; however, the reectivity shows maximum for CsPbI 3 and minimum for CsPbCl 3 perovskites, at the optical range. Some peaks arise in each spectrum, which are the responses still true for infra-red and visible regions. In the visible region, the rst peaks are observed at 4.2, 3.8 and 3.3 eV for CsPbCl 3 , CsPbBr 3 and CsPbI 3 , respectively. Some other peaks are observed at 7.8, 11.5, 15.6, 20.4 eV for CsPbCl 3 , at 7.3, 10.9, 15.4 eV for CsPbBr 3 and at 6.3, 9.0, 11.3, 15.8 eV for CsPbI 3 . From the comparison of reectivity, it is clearly seen that CsPbI 3 shows the most homogeneous response over a wide energy range in the ultraviolet region.

Redox potentials: photocatalytic activity
The photocatalytic activity of material depends highly on the suitable band gap, the recombination rate of carriers, and proper redox potentials. An idealization arises from a narrow band gap, low recombination rate with long-life carriers, and proper redox potentials of the compounds irradiated under visible light. The redox ability for visible light exposure can be calculated theoretically by aligning the CBM and VBM compared to the water reduction/oxidation potential level (Fig. 7). The positions of CBM and VBM can theoretically be predicted by employing the following equations, 129 where E CB and E VB are the CB and VB edge potentials, X is the absolute electronegativity of CsPbX 3 . Absolute or Mulliken electronegativity is numerically equal to the geometric mean of electronegativities of ingredient elements where the rst ionization energy and the atomic electron affinity are well employed. 130 E g is the electronic band gap value and E e is the energy of free electrons on the hydrogen scale (4.5 eV).
The calculated electronegativities, X are 5.56 eV, 5.17 eV, and 4.83 eV, whereas the electronic band gaps E g are observed (in Fig. 4) as 2.385 eV, 2.061 eV and 1.784 eV for CsPbCl 3 , CsPbBr 3 and CsPbI 3 respectively. The CBM potentials occurred at À0.24 eV, À0.36 eV, À0.57 eV versus NHE and the VBM potentials were at 2.15 eV, 1.70 eV and 1.22 eV for CsPbCl 3 , CsPbBr 3 and CsPbI 3, respectively. By comparing these values, it is seen that the CBM-negative responses can be ordered as CsPbCl 3 < CsPbBr 3 < CsPbI 3 to the H + /H 2 level and the VBM can be ordered as CsPbCl 3 > CsPbBr 3 > CsPbI 3 with positive to O 2 /H 2 O (1.23 eV). Analysis of these results provides explicit evidence that CsPbCl 3 is one of the best candidates for its strong ability of water oxidation from the thermodynamics aspect generating O 2 , whereas CsPbI 3 is the best candidate as an H 2 producing agent due to its strong redox potential. In contrast, CsPbBr 3 was found to be the best performer for the photocatalytic process in the visible region due to nearly equal effectiveness to both the oxidation and reduction processes.

Conclusions
The above mentioned properties investigation compares the applicability of these materials in optoelectronic, photocatalytic, and photovoltaic (PV) devices. We calculated structural, and elastic properties to determine the better agreement of damage-tolerance and electronic and optical responses for suitable device applications. The optimized lattice constant and elastic constant showed excellent agreement with the experimental data whereas some properties were found to be much better when compared to other theoretical reports. CsPbBr 3 is thermally more stable but more brittle than the other two perovskites. From a comparative study, it is seen that CsPbCl 3 , CsPbBr 3, and CsPbI 3 are suitable for green, orange, and red emissions, respectively, of the optical spectra, owing to the proper electronic band gap. Theoretically, it was observed that CsPbI 3 is the best photocatalyst for the hydrogen evolution reaction and CsPbBr 3 is the most stable photocatalyst due to its nearly balanced oxidation and reduction potentials, but CaPbCl 3 is better for O 2 production. Thus, pressure can be employed to tune the properties of materials by adjusting their lattice parameters, electronic orbitals, crystal structure interatomic distances, and bonding patterns for efficient electronic and optoelectronic applications.

Author contributions
M. Aktary performed conceptualization, designed the study, interpreted the data, and wrote the manuscript. M. Kamruzzaman helped study, data analysis, and wrote the manuscript. R. Afrose Helped us to understand soware, DFT calculations, data curation, writing-review, writing and editing the manuscript.

Conflicts of interest
The authors declare no competing nancial interests.