1 Introduction

Research on perovskite compounds began in the 1990s, nevertheless it was not until 2009 that perovskite solar cells were first reported. Since then, their power conversion efficiency has increased rapidly from 3.8% 2009 to 25.5% in 2023 (Green et al. 2021; Dahbi et al. 2022a). Metal perovskites have been studied and gained significant attention for over an extended period due to their unique properties (Qaid et al. 2023; Bawazir et al. 2022; Tahiri et al. 2021a, 2021b; Dahbi et al. 2021a). Lately, a novel category of perovskite compounds, the so-called triple perovskites, has become favorable options as compounds for numerous applications (Guo et al. 2020; Saparov et al. 2015a; Wang et al. 2021; Singh et al. 2020). The metal halide triple perovskites have the typical chemical formula of A3B2X9, where A is alkaline earth or rare-earth cations, B is transition metal cations, while X is a halide anion. The Lead-free metal halide triple perovskite materials have numerous benefits over conventional ones, they are more stable leading them to be less prone to degradation over time in sunlight which is the mean issues related to the organic cation of the conventional perovskites solar cells leading to reduce their power conversion efficiency, therefore hinding their commercialization (Dahbi et al. 2022a, b; Li et al. 2022; Ghrib et al. 2021; Liu et al. 2020). Moreover, they have strong defect tolerance, long carrier lifetimes and high carrier mobilities enhancing the efficiency of the solar energy conversion to electrical power which improve of photovoltaic performance (Dahbi et al. 2021b; Saparov et al. 2015b; Lehner et al. 2015a; Harikesh et al. 2016; Hoye et al. 2016; Pazoki et al. 2016; Hebig et al. 2016). The A3B2X9 compounds have crystallographic structures which can undergo a sequence phase transitions; for instance; Cs3Bi2I9, with the P63/mmc symmetry at room temperature was studied by Laue and four-circle neutron diffractometry from room temperature down to 50 K. At T = 220 K, the crystal undergoes a second-order proper ferroelastic phase transition to a polydomain structure with a nonprimitive monoclinic C12/m1 space group (Park et al. 2015). Luo et al. (2023) discovered that the transitioning A3Bi2I9 from a three-dimensional to a two-dimensional structure triggers significant property changes. In 2D, t A3Bi2I9 materials exhibit modified electronic, optical, and mechanical characteristics, along with shifts in thermal conductivity and chemical reactivity. These alterations offer potential for new applications but require careful exploration and understanding (Jorio et al. 2000). Furthermore, tunable electronic structure behavior and optical properties of triple perovskites make them promising compounds for optoelectronic and effective photocatalysts for water splitting for hydrogen production applications (Dahbi et al. 2021b; Saparov et al. 2015b; Lehner et al. 2015a; Harikesh et al. 2016; Hoye et al. 2016; Pazoki et al. 2016; Hebig et al. 2016; Park et al. 2015; Jorio et al. 2000; Luo, et al. 2023; Bai et al. 2022). For instance, antimony-based halide triple perovskites such cesium antimony triiodide (Cs3Sb2I9) has been found to exhibit a high efficient light emission, showing a potential candidate for use in light-emitting diode (LEDs) (Xie et al. 2023). Under a high pressure up to 14 GPa, the forbidden band of Cs3Sb2I9 is efficiently decreased from 2.05 eV to 1.36 eV (Geng et al. 2019). Further, at room temperature intense raman scattering was observed for Cs3Sb2I9, Rb3Sb2I9, Cs3Bi2I9 and Rb3Bi2I9 materials demonstrating strong electron − phonon coupling and high polarizability, high resistivity, and high photo-response at room temperature (Geng et al. 2020). Besides, high quality thin films derivative Cs3Sb2I9 perovskite exhibiting a forbidden band of 2.05 eV and enhancing its stability in ambient air compared to analogous CH3NH3PbI3 films (Saparov et al. 2015a). Experimentally by optical absorption and ultraviolet photoemission spectroscopy and computationally by DFT calculations, the optical properties and electronic structures of A3Bi2I9 (A = K, Rb, or Cs) are investigated, and it was observed that these compounds are easy to prepare, and A3Bi2I9 (A = K, Rb, or Cs) triple perovskites are more chemically stable than the related lead halides (Kyle et al. 2017). The optical measurements indicate these kinds of compounds are semiconductors with the forbidden band value in the [1.89 − 2.06 eV] range and therefore they exhibit high resistivities (1010–1011 Ω.cm) (Harikesh et al. 2016; Geng et al. 2020; Lehner et al. 2015b). Besides, photocatalytic hydrogen production from water splitting is an important area of research and development due to the increasing demand for clean and sustainable energy sources with no greenhouse gas emissions which can be utilized in various applications, including fuel cells for transportation fuel and power generation (Li et al. 2022; Liu et al. 2020). As far as we know, A3B2I9 (A = Rb or Cs; B = Sb or Bi) triple perovskites are insufficiently explored in literature, and there is few researches that studied the optical and electronic properties (Geng et al. 2020; Kyle et al. 2017), and no author studied the ability of the use of these triple perovskites as materials for hydrogen production from water splitting. Therefore, the aim of this work is to explore the first principle calculations of geometrical properties, thermodynamic stability electronic structure behavior, optical spectra, and photocatalytic performance for the clean triple halide perovskites compounds A3B2I9 (A = Rb or Cs, and B = Sb or Bi).

2 Computational details

In an effort to study the clean Iodine-based triple perovskites A3B2I9 (A = Rb or Cs, and B = Sb or Bi), we have used the FP-LAPW method based on the density functional theory (DFT) (Peresh et al. 2014), using ab initio calculations implemented in Wien2k software (Sham and Schlüter 1983), while the exchange–correlation function was determined by the Perdew-Burke-Ernzerhof generalized gradient approach (PBE-GGA) (Blaha et al. 2020) was used for computing the structural properties and the enthalpy of formation, while PBE-GGA coupled with the Tran Blaha-modified Becke Johnson (TB-mBJ) (Wu and Cohen 2006) were used for electronic, optical and photocatalytic performance in order to achieve the accurate results. To accomplish the optimal theoretical results, the Self-consistent calculations were carried out by taking the plane-wave cutoff value RMT × Max as 7.0. Whereas the Gmax presents the density Fourier-coefficient expansion is seted as 12 (a.u). The k-space meshes of 4 × 7 × 3 were used in the first Brillouin zone.

3 Results and discussion

3.1 Structural properties and enthalpy of formation

At room temperature, the iodine-based triple perovskites A3B2I9 (A = Rb and Cs, and B = Sb and Bi) crystalize in monoclinic structure (space group N° 14, P21/n), toms occupy 12 A atom, 8 B atom and 36 I atom, respectively, where the BI6 octahedra undergo a distortion toward a rhombohedral elongation (Geng et al. 2020; Camargo-Martínez and Baquero 2012) (See Fig. 1).

Fig. 1
figure 1

The unit cell of the monoclinic structure of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) triple perovskites

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By optimizing the geometrical structure, we can discover the atoms equilibrium position in the crystal, which provide insight into the physical properties of a given compound, for instance; the geometrical structure affects the electronic structure behavior which is important for understanding the behavior of compounds. Therefore, by using X-ray diffraction, Rb3Sb2I9 unit cell crystal structures are a = 14.591(3) Å, b = 8.1879(16) Å, c = 20.584(4) Å and β = 90.36(3)° (Geng et al. 2020), while unit cell crystal structures are a = 14.537(7) Å, b = 8.385(4) Å, c = 21.11(1) Å and β = 90.09(4)° for Cs3Bi2I9 (Camargo-Martínez and Baquero 2012), and a = 14.6443(19) Å, b = 8.1787(9) Å, c = 20.885(2) Å and β = 90.421(7)° for Rb3Bi2I9 (Kyle et al. 2017). Table 1 the optimized lattice parameters and betta angle (β) of monoclinic structure of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) compounds are aligned with the experimental results (Geng et al. 2020; Kyle et al. 2017; Camargo-Martínez and Baquero 2012).

Table 1 The optimized geometrical constants and β (°) of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) in this study compared with experimental results
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Moreover, to predict the chemical reactions and stability of a material, the enthalpy of formation of all studied compounds is simulated using the following equation (Lehner et al. 2015c; Dahbi et al. 2022c, 2022d):

$${\Delta {\varvec{H}}}_{{\varvec{f}}}=({E}_{total}\left({{A}_{12}B}_{8}{I}_{36}\right)-12{E}_{total}(A)-{8E}_{total}(B)-36{E}_{total}(I))$$

where, Etotal (A12B8I36) shows the total energy each compound, while Etotal (A) is the total energy of Cs or Rb atoms, Etotal (B) is the total energy of Sb or Bi atoms, and Etotal (I) represents the total energy of I atoms. Although, Fig. 2 illustrate that the values of enthalpy formation of all studied structures have negative sign, proving that these structures can be formed spontaneously under standard conditions (Dahbi et al. 2022d, 2022e), and they release energy when formed because they are thermodynamically stable.

Fig. 2
figure 2

The calculated enthalpy of formation of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) compounds

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4 Electronic behavior

The investigation of electronic properties is important due to several reasons because they provide valuable information about the electronic structure and properties at the atomic and molecule level of the material including; the energy levels of the electrons and the nature of the chemical bonds within the material by disclosing numerous solids applications like optoelectronic devices and solar cells. In this section, the Total (TDOS) and Partial Density Of States (PDOS) and the electronic band structure were calculated for A3B2I9 (A = Rb or Cs, and B = Sb or Bi) compounds along the high symmetry point of the Brillouin zone (A → Y → Γ → Z → A) are plotted in Fig. 3. It can be observed that the Fermi level of A3B2I9 compounds are lies above the valence Highest Occupied Molecular Orbital (HOMO), proving the p-type semiconductor behavior of A3B2I9 perovskites. On one hand, the Valence Band (VB) of all investigated compounds is principally composed by I-5p5 states with some admixture of Sb-5p3 and Sb-5s2 orbits for A3Sb2I9, Bi-6p3 and Bi-6s2 for A3Bi2I9 compounds, respectively. On the other hand, the Conduction Band (CB) is predominantly composed by Sb-5p3 and I-5p5 orbits, and by Bi-6p3 and I-5p5 orbits for A3Sb2I9 and A3Bi2I9, respectively. Additionally, the band structure of all studied compounds confirms that the highest occupied molecular orbital is positioned between Γ (0.0, 0.0, 0.0) and Z (0.5, 0.0, 0.0) high-symmetry point, while the lowest unoccupied Molecular Orbital (LUMO) is situated at Γ high-symmetry point, showing an indirect semiconductor behavior of all studied compounds. These outcomes are in complete agreement with the other simulated results (Kyle et al. 2017). Besides, the forbidden band values of these compounds are in the range of [1.8 eV–2.369 eV] which is aligned with the experimental data (Geng et al. 2020; Kyle et al. 2017) (Table 2).

Fig. 3
figure 3figure 3

The calculated band structure and partial density of states of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) compounds

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Table 2 The calculated forbidden band of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) in this study compared with theoretical and experimental results
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5 Optical spectra

The ability of a compound to efficiently absorb sunlight is essential for photocatalyts devices and for solar cells, because it design their performance (Lehner et al. 2015c; Dahbi et al. 2022c, 2022d, 2020; Adhikari et al. 2022; Mouhib et al. 2022). The absorption coefficient, reflectivity, and transmittance of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) perovskites in percentage are plotted in Fig. 4. It can be seen that all studied compounds have high visible light absorption due to their suitable forbidden band values [1.8 eV–2.369 eV] which determine the light wavelengths that can they absorb are facilitate efficient electron–hole pairs (excitons) generation. Further, Fig. 4 shows low transmittance and reflectivity of A3B2I9 triple perovskites contribute to efficient visible light harvesting that contribute to the electrical current generation, because maximizing a material’s absorption leads to minimize the transmittance through it, as well as minimize the incident light reflection off the materials surface. These advantages facilitate effective carrier transport, minimizing recombination and maximizing the conversion of light into electrical energy and maintain its performance and durability over an extended period. Thus, the optical properties advantages of A3B2I9 triple perovskites are desirable in various optoelectronic applications, including solar cells and photocatalytic.

Fig. 4
figure 4figure 4

The reflectivity, absorption and the transmittance of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) perovskites

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6 Photocatalytic performance

Electrolysis, also known as water splitting, is a procedure that utilizes electricity to isolate dihydrogen monoxide molecules (H2O) into oxygen (O2) and hydrogen (H2) gases, respectively. Furthermore, the energy levels of HOMO and LUMO of all studied triple perovskites are determined using the following formula (Li et al. 2022; Liu et al. 2020; Lehner et al. 2015c):

$${E}_{LUMO }=\upchi {+ E}_{0}- \frac{{E}_{g}}{2}$$
(1)
$${E}_{HOMO }=\upchi +{E}_{0}+\frac{{E}_{g}}{2}$$
(2)

Where \({{\varvec{E}}}_{{\varvec{L}}{\varvec{U}}{\varvec{M}}{\varvec{O}}}\) and \({{\varvec{E}}}_{{\varvec{H}}{\varvec{O}}{\varvec{M}}{\varvec{O}}}\) are the LUMO and HOMO energy level positions, respectively, χ represents the Mulliken electronegativity of A3B2I9 compounds, E0 is the free electron the energy in the hydrogen Normal Hydrogen Electrode (NHE) potential (− 4.5 eV), while Eg is its forbidden energy (Lehner et al. 2015c). Moreover, Fig. 5 highlights that the two fundamental conditions must be met to achieve the desired outcome are respected for all studies triple perovskites, because, the HOMO and LUMO of all A3B2I9 (A = Rb or Cs, and B = Sb or Bi) perovskites are satisfied the necessary conditions to split water, where HOMO are below the dihydrogen monoxide oxidation potential (1.23 eV) while HUMO are greater than the proton reduction potential (0 eV) (Li et al. 2022; Liu et al. 2020; Lehner et al. 2015c), as well as all studied compounds exhibit high visible light absorption which assess the viability materials for water splitting devices. Therefore, these compounds are most likely to be used for hydrogen production from mater splitting.

Fig. 5
figure 5

The calculated HOMO and LUMO positons of A3B2I9 (A = Rb or Cs, and B = Sb or Bi) perovskites relative to the NHE potential

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7 Conclusions

In summary, the first principle calculations are explored to study the geometrical structure, thermodynamic stability, electronic structure behavior, optical spectra and photocatalytic performance A3B2I9 (A = Rb or Cs, and B = Sb or Bi) were performed using ab-initio calculations. It was found that all studied structures are thermodynamically stable. Moreover, VB of A3B2I9 compounds is principally composed by I-5p5 states with some admixture of Sb-5p3 and Sb-5s2 orbits (Bi-6p3 and Bi-6s2 orbits) for A3Sb2I9 (A3Bi2I9) compounds. Besides, the calculated band structure of all studied compounds confirms that HOMO is positioned between Γ (0.0, 0.0, 0.0) and Z (0.5, 0.0, 0.0) high-symmetry point, while the LUMO)is situated at Γ high-symmetry point, confirming that A3B2I9 compounds are indirect semiconductor perovskites. Further, the optical spectra shows low transmittance and reflectivity of A3B2I9 triple perovskites contribute to efficient visible light harvesting that contribute to the electrical current generation. Finally, all studied compounds can split water to produce hydrogen. Thus, A3B2I9 triple perovskites can be used as potential candidate for photocatalytic and photovoltaic applications.