First-Principles Investigation into the Interaction of H₂O with α-CsPbI₃ and the Intrinsic Defects within It

Abstract

CsPbI₃ possesses three photoactive black phases (α, β, and γ) with perovskite structures and a non-photoactive yellow phase (δ) without a perovskite structure. Among these, α-CsPbI₃ exhibits the best performance. However, it only exists at high temperatures and it tends to transform into the δ phase at room temperature, especially in humid environments. Therefore, the phase stability of CsPbI₃, especially in humid environments, is the main obstacle to its further development. In this study, we studied the interaction of H₂O with α-CsPbI₃ and the intrinsic defects within it. It was found that the adsorption energy in the bulk is higher than that on the surface (−1.26 eV in the bulk in comparison with −0.60 eV on the surface); thus, H₂O is expected to have a tendency to diffuse into the bulk once it adsorbs on the surface. Moreover, the intrinsic vacancy of V_Pb⁰ in the bulk phase can greatly promote H₂O insertion due to the rearrangement of two I atoms in the two PbI₆ octahedrons nearest to V_Pb⁰ and the resultant breaking of the Pb–I bond, which could promote the phase transition of α-CsPbI₃ in a humid environment. Moreover, H₂O adsorption onto V_I⁺¹ contributes to a further distortion in the vicinity of V_I⁺¹, which is expected to enhance the effect of V_I⁺¹ on the phase transition of α-CsPbI₃. Clarifying the interaction of H₂O with α-CsPbI₃ and the intrinsic defects within it may provide guidance for further improvements in the stability of α-CsPbI₃, especially in humid environments.

1. Introduction

Over the last decade, the efficiency of organic–inorganic hybrid halide perovskite (HHP) solar cells has improved, and now ranges from 3.8% to 25.2% [1,2,3,4,5,6]. However, HHP solar cells are generally less stable due to the volatility and hygroscopicity of organic cations in the perovskite light-collecting layer [7,8,9]. The low stability of typical HHPs, such as MAPbI₃ (MA⁺: methylammonium) and FAPbI₃ (FA⁺: formamidine), has been noted since the early stages of perovskite solar cell (PSC) research [7,8,9]. In order to address the “vulnerability” of HHP in ambient air, organic components, including MA⁺ and FA⁺, have been partially or even completely replaced by Cs⁺ or Rb⁺ [10,11,12,13]. Completely inorganic halide perovskites (IHPs) show greater prospects for photoelectric applications because of their suitable optical properties and higher stability under external stimuli [14]. Among these, CsPbI₃ is the most typical, with a lower production cost [13,15,16,17,18]. Furthermore, cubic α-CsPbI₃ has a direct band gap [19], a wide absorption spectrum in the solar region, high quantum efficiency, and a long radiation life, meaning that it is expected to be an excellent candidate for use in perovskite solar cells [20]. However, three photoactive “black” perovskite phases (α, β, and γ) of CsPbI₃ can be easily transformed into a more thermodynamically stable “yellow” non-perovskite phase (δ phase) under ambient conditions [21,22], and this polymorphic transformation becomes even more severe when water is present [16,23].

Various theoretical studies have revealed the possible degradation mechanism of CsPbI₃ in a humid environment. The transformation of CsPbI₃ from the α to δ phases has always been attributed to the lower formation enthalpy of the δ phase [16]. Moreover, the instability of the α phase of CsPbI₃ has been well documented to be attributed to the phonon instability of α-CsPbI₃ [24,25]. Kye et al. have further pointed out that the cation vacancy (V_Cs and V_Pb) can weaken the interaction between Cs and PbI₆ and may lower the nucleation barrier, thus promoting phase transformation [26]. On the other hand, Lin et al. have pointed out that I vacancies (V_I) could reduce the surface tension between the α and δ phases and lower the nucleation barrier [23]. It has also been preliminarily determined that H₂O induces a catalytic effect [16]. Jiang et al. [27] studied the effects of several air molecules and found that H₂O may diffuse into and produce a polycrystalline structure and grain boundary, and eventually lead to the phase transformation of CsPbI₃. Li et al. [28] have explored the counterpart system, CsSnI₃, and found that the strong coupling between O and Cs and the hydrogen bond between H and I may lead to the deformation of the (001) surface and, thus, phase instability. Moreover, Lin et al. have also further elaborated that H₂O adsorbed on the surface of α-CsPbI₃ film may introduce V_I, thus effectively catalyzing the transformation from the α to δ phases [23].

However, the exquisite interaction of H₂O with CsPbI₃ and the intrinsic defects within it have not yet been studied. Based on first-principles calculations, we first compared the interaction of H₂O on the (001) surface and in the bulk of α-CsPbI₃. It was found that H₂O binds more strongly in bulk α-CsPbI₃ than on the surface; thus, H₂O tends to diffuse into the bulk. Moreover, we further analyzed the interaction between H₂O and the neutral and charged intrinsic vacancies in α-CsPbI₃. It was found that a neutral Pb vacancy V_Pb⁰ may significantly accelerate the insertion of H₂O. The strong binding between H₂O and V_Pb⁰ induces Pb–I bond breakage and new I–I bond formation, which are expected to promote the phase transition. Moreover, H₂O adsorption onto V_I⁺¹ contributes to a further distortion in the vicinity of V_I⁺¹, which is expected to enhance the phase transition effect of V_I⁺¹. This work may provide guidance for the improved stability of CsPbI₃.

2. Calculation

All the calculations were performed using the code of the Vienna ab initio simulation package (VASP) [29] within the density functional theory (DFT) framework [30]. The Perdew–Burke–Emzerh (PBE) [29] exchange–correlation function within the generalized gradient approximation (GGA) [31] method was used, and the plane wave cutoff energy was 450 eV. The optimized lattice constants of the α-CsPbI₃ structure (pm3m) were a = b = c = 6.414 Å, which are consistent with the previous calculations (6.40 Å) and experimental measurements (6.18 Å) [32,33]. All of the atoms were fully relaxed, until the total energy per atom was less than 1 × 10⁻⁶ eV and the Hellmann–Feynman force per atom was less than 0.01 eV/Å. For adsorption on the α-CsPbI₃ (001) surface systems, we expanded the unit cell into a 2 × 2 supercell in the ab plane and selected a K-mesh size of 3 × 3 × 1; for the insertion of H₂O into the bulk phase of α-CsPbI₃, we constructed a 3 × 3 × 3 supercell and used a 2 × 2 × 2 Monkhorst–Pack K-mesh. We chose the CsI-terminated CsPbI₃ (001) surface because this is the most stable surface with the lowest surface energy, as examined in [34]. A vacuum layer of 18 Å was added in the (001) direction for the surface calculations in order to avoid interactions between the layers. For H₂O adsorption and insertion into α-CsPbI₃, the structures were optimized, the internal coordinates fully relaxed, and the lattice parameters fixed. As far as the van der Waals (vdW) forces are concerned, we conducted D3 dispersion correction [35] for the pristine α-CsPbI₃. The lattice constant was reduced by 0.09 Å, which represents a decrease of around 1.4%. Considering that D3 dispersion correction would increase the binding energy between H and I, which may compensate for the lattice constant reduction, the conclusions drawn in our work are not expected to be affected. Because Cs, Pb, and I are heavy, spin–orbit coupling (SOC) [36] may be significant. As Li et al. [33] have found, SOC mainly decreases the conduction band. Furthermore, it has been found that a GW [37] + SOC calculation can increase the band gap back close to the PBE results. Thus, it seems PBE calculation provides reasonable results for the numerical compensation between GW and SOC.

3. Results and Discussion

The instability of CsPbI₃ with a highly symmetrical perovskite structure is mainly due to the size mismatch between the constituent ions. In order to stabilize the small Cs in the PbI₆ octahedral gap, the PbI₆ octahedron rotates and tilts, resulting in the distortion of the highly symmetrical perovskite structure so as to form less symmetrical non-perovskite structures. Thus, though it possesses better photoelectric properties [19], the cubic structure of CsPbI₃ is very unstable, and recent experiments and calculations have focused on the instability of α-CsPbI₃. Therefore, in this work, we focused mainly on the interaction of H₂O with pristine α-CsPbI₃ and the intrinsic defects within it. The α- and δ-CsPbI₃ structures are shown in Figure 1. PbI₆ extends its three-dimensional framework in an angle-sharing manner along the three coordinate axis directions in α-CsPbI₃, with a Cs atom in the middle of the eight top corners, a Pb atom in the center of the cubic structure, and an I atom in the six faces of the cube center. PbI₆ rotates and breaks into δ-CsPbI₃. As shown, the α-to-δ-CsPbI₃phase transition involves bond breaking and rebonding [38]. However, the bond rearrangement barrier may be high in the pristine lattice and so the intrinsic defects are expected to play a role in phase transformation [23,26]. H₂O, α-CsPbI₃, and the intrinsic defects may also interact.

3.1. Comparison of Adsorption of H₂O on the Surface and in the Bulk of CsPbI₃

Regarding the position of H₂O in CsPbI₃, we first calculated the binding energy E_bind of H₂O on the surface and in the bulk of α-CsPbI₃. Figure 2 shows the structures of the bulk and (001) surface of α-CsPbI₃ with and without H₂O adsorption. For H₂O insertion into the α-CsPbI₃ bulk, the H₂O molecule was placed into three different positions, ensuring that O was close to the Cs and that H was close to the I atoms; however, the optimized structure of the three different initial configurations became similar as a result of O binding with Cs and two H atoms binding with I, as can be seen in Figure 2b. The distance between Cs and O is 2.92 Å, and the distance between the two H and I atoms are around 2.65 Å. The binding energy of the three configurations are also similar, as can be seen in

Table 1. Binding energy of H₂O in the bulk of α-CsPbI₃ at different initial positions.

Initial Position of H2O Insertion	Binding Energy Ebind/eV
near Cs	−1.21
near Pb	−1.25
near I	−1.26

. For H₂O adsorption on the surface, we first generated the possible configurations that could favor Cs–O and I–H bonds, referencing the configurations in [28]. Similar to this study, the energy difference between the different configurations is small, and we show one of the configurations in Figure 2d. The distance between Cs and O is 3.04 Å, which is a little larger than that in the bulk, and the distance between H and I is around 2.60 Å, which is a little smaller than that in the bulk. The strong coupling between O and Cs and the interaction between H and I led to the strong binding of H₂O in CsPbI₃, as in CsSnI₃ [28]. The binding energy of H₂O in the bulk and on the surface of α-CsPbI₃ can be calculated as follows:

$$E_{\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{d}}=E_{\mathrm{a}\mathrm{d}\mathrm{s}}-E_{\mathrm{n}\mathrm{o}{\mathrm{H}}_2\mathrm{O}}-E_{{\mathrm{H}}_2\mathrm{O}}$$

(1)

where $E_{\mathrm{b}\mathrm{i}\mathrm{n}\mathrm{d}}$ represents the binding energy, $E_{\mathrm{a}\mathrm{d}\mathrm{s}}$ and $E_{\mathrm{n}\mathrm{o}{\mathrm{H}}_2\mathrm{O}}$ represent the total energies of the bulk or surface system with and without H₂O adsorbed, respectively, and $E_{{\mathrm{H}}_2\mathrm{O}}$ is the total energy of one H₂O molecule. The energy of the H₂O molecule was calculated within a cell with a vacuum size of 10 Å to ensure the H₂O molecule fully separated from its periodic images. The binding energies of H₂O in the bulk and on the surface of α-CsPbI₃ are both negative, −1.26 eV and −0.60 eV, respectively, indicating that the binding process is exothermic and can proceed spontaneously, in accordance with prior research on CsSnI₃. The binding energy is higher in the bulk than that on the surface, even though H₂O insertion into the bulk may cause a larger distortion, and this could be indicative of the instability of CsPbI₃, and, thus, CsPbI₃ could potentially bond with H₂O. In this regard, H₂O tends to diffuse into the bulk once it adsorbs on the surface. Thus, we focused on the interaction between H₂O and the intrinsic defects in the α-CsPbI₃ bulk in this work.

3.2. Effect of Intrinsic Vacancies within the Bulk Phase on H₂O Insertion

The distribution of the intrinsic defects can usually be estimated with the concentration formula c = N_sitese^−ΔH/kT, where c represents the concentration of the defect, N_sites represents the number of sites for the defect per unit volume, ΔH represents the formation energy of the defect, and k and T represent the Boltzmann constant and temperature, respectively [39]. The formation energies depend on the chemical potentials of the constituent element. As Li et al. [33,40] have calculated, there could be different intrinsic defects within the CsPbI₃ bulk phase, and they found that the formation energies of Pb, the I vacancy V_Pb, and V_I are extremely low, and even negative, under both Pb/Cs-rich and I-rich conditions. The formation energy of Cs vacancy, V_Cs, is also relatively low. Thus, the dominant defects in α-CsPbI₃ are V_Pb, V_Cs, and V_I; moreover, V_Pb and V_Cs tend to be negatively charged V_Cs⁻¹ and V_Pb⁻², respectively, while V_I tends to be positively charged V_I⁺¹. Thus, based on a previous study, we studied the interaction of H₂O with three intrinsic vacancies, V_Cs, V_Pb, and V_I, in α-CsPbI₃ bulk, and the neutral, V_Cs⁰, V_Pb⁰, and V_I⁰, and charged states, V_Cs⁻¹, V_Pb⁻², and V_I⁺¹ [33], were both studied. H₂O was inserted close to the vacancies, and the relative position for H₂O with respect to the vacancies can be seen in Figure 3 and Figure 4. The structures given were optimized. The binding energies for H₂O close to the vacancies can also be calculated with Equation (1), and the results can be seen in

Table 2. Binding energy of H₂O near different vacancies in the bulk of α-CsPbI₃.

Position of H2O Insertion	Binding Energy Ebind/eV
Near VCs−1	−1.29
Near VPb−2	−0.78
Near VI+1	−0.70
Near VCs0	−0.80
Near VPb0	−2.36
Near VI0	−0.48

. The long-range Coulomb interactions converge slowly with the supercell size; thus, charge–charge corrections are sometimes needed [39]. We addressed the energy difference before and after H₂O insertion and, thus, the electrostatic energy from the spuriously repeated charges was expected to be canceled out. Moreover, this process has not been conducted when calculating the 3 × 3 × 3 supercells of α-CsPbI₃ [33]. Therefore, charge–charge correction was neglected in this work. As shown, and compared with that in the pristine lattice, the binding energy of H₂O near the charged vacancies, V_Cs⁻¹, V_I⁺¹, and V_Pb⁻², decreased or was almost unchanged. The binding energy of H₂O near the neutral vacancies, V_I⁰ and V_Cs⁰, further decreased, which could be attributed to the decreased charge on the atoms near V_I⁰ and V_Cs⁰, which in turn reduced the Coulomb attraction between I/Cs and H₂O, which were responsible for the binding between H₂O and CsPbI₃ [28]. However, the introduction of V_Pb⁰ significantly increased the binding energy of H₂O. We then analyzed the changes in the structures in these systems. It must be noted that no matter which vacancy was introduced, the insertion energy was always negative, indicating that the insertion of H₂O is always an exothermic process and can spontaneously occur.

Figure 3 shows the optimized structure of α-CsPbI₃ with V_Cs⁻¹, V_I⁺¹, and V_Pb⁻² with or without H₂O inserted. As shown, when only V_Cs⁻¹ or V_Pb⁻² was introduced, the original cubic structure was not significantly distorted, and the octahedron did not significantly rotate or twist. In the vicinity of the V_Cs⁻¹ vacancy, due to the removal of the attraction of Cs, I slightly moved away from the vacancy, the nearest Pb–I bond was slightly bent, and the remaining I atoms and all of the Pb and Cs atoms are located in their original highly symmetrical position without being offset. For V_Pb⁻², compared with the perfect supercell, the bond length of I–Pb adjacent to V_Pb⁻² was reduced by about 0.1 Å; however, the I–Pb–I bond angle was basically unchanged. Thus, the octahedron framework did not deviate from the perfect supercell, and only adjacent Cs was slightly shifted towards V_Pb⁻². However, when V_I⁺¹ was introduced, the PbI₆ octahedron rotated and twisted to a large extent, and Cs also deviated from the center and moved away from V_I^+1, due to the removal of the attraction or repulsion of the I. The large distortion induced by V_I⁺¹ is consistent with the results of Lin et al. [23], who found that V_I⁺¹ in the crystal lattice can effectively catalyze the transformation from the α to δ phases. However, when H₂O is introduced to V_Cs⁻¹ and V_Pb⁻², the structures in the vicinity of the vacancies become significantly distorted. Moreover, H₂O adsorption onto V_I⁺¹ contributes to further distortion in the vicinity of V_I⁺¹, thus enhancing its effect on phase transformation. To manifest the rotation or twisting of the octahedron, we measured the 2 I–I–I bond angles between the octahedrons close to the vacancies, θ₁ and θ₂, as labeled in Figure 3, and the results are shown in Figure 5. As shown, θ₁ and θ₂ were almost 90° when only V_Cs⁻¹ or V_Pb⁻² was introduced, and they shifted away from 90° when only V_I⁺¹ was introduced. Additionally, θ₁ and θ₂ shifted away from 90° when H₂O was then introduced to V_Cs⁻¹ or V_Pb⁻², even though this shift is still smaller than that for only V_I⁺¹. Another shift occurred on θ₁ and θ₂ when H₂O was further introduced to V_I⁺¹, indicating that H₂O adsorption onto V_I⁺¹ further contributes to the effect of V_I⁺¹ on the phase transition of CsPbI₃.

On the other hand, for the neutral state, the distortion induced by H₂O adsorption onto V_Cs⁰ and V_I⁰ is smaller compared with their charged states, while the distortion induced by H₂O adsorption onto V_Pb⁰ is larger, which is in accordance with the insertion energy trend. Thus, we focused on the effect of H₂O adsorption onto V_Pb⁰. Figure 4 shows the optimized structures of V_Pb⁰ before and after inserting H₂O near V_Pb⁰. As shown, when we introduced only V_Pb⁰ to α-CsPbI₃, the symmetrical structure of α-CsPbI₃ remained basically unchanged. However, when we inserted H₂O near V_Pb⁰, a huge distortion of the structure was induced, and this distortion is even comparable with the distortion induced by V_I⁻. An important feature is that some of the PbI₆ octahedrons actually “disintegrated”, with the measured distances between Pb and I increasing from 3.21 Å to 3.9 Å and 3.1 Å to 4.06 Å, respectively, and the two I atoms actually formed new I–I bonds. The Pb–I bond broke, and a new stable I–I bond formation may be the dominant reason for the significantly high binding energy for H₂O inserted near V_Pb⁰. To absolutely characterize the bonding nature for H₂O near V_Pb⁰, we conducted band structure and charge density calculations, as can be seen in Figure 6. We found that, as shown in Figure 6a, an isolated energy level formed, and that the corresponding charge was indeed located between the I atoms, as seen in Figure 6b,c. The disintegrated PbI₆ octahedrons and new I–I bond formation indicate that the effect of H₂O on V_Pb⁰ could equivalently be recognized as formation of two I vacancies, V_I, close to the one Pb vacancy, V_Pb. The large distortion induced is consistent with the effect of the V_I vacancies and, thus, may also promote α-to-δ-phase transformation. In addition, the binding energy of H₂O near V_Pb⁰ is around 2 eV higher than that of V_Pb²⁻, and the formation energy of V_Pb²⁻ is only nearly 2 eV lower than that of V_Pb⁰ near the Fermi level, as can be found in [33]; thus, V_Pb²⁻ probably causes the transformation from V_Pb²⁻ to V_Pb⁰ and binds strongly with H₂O if H₂O is inserted. Considering its abundancy, the transformation from V_Pb²⁻ to V_Pb⁰ and the strong binding with H₂O are expected to cause H₂O to catalyze the α-to-δ phase transformation of CsPbI₃.

To further illustrate the interaction between the defects and H₂O, we calculated the formation energies of V_Cs, V_Pb, and V_I in α-CsPbI₃ with and without H₂O insertion, as shown in Figure 7. The formation energy is calculated with the following equation [39,41,42,43,44,45]:

$$∆H_f\left(q\right)=E\left(q\right)-E\left(\mathrm{p}\mathrm{r}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{i}\mathrm{n}\mathrm{e}\right)+{\sum }_i{n}_i\left[{\mu }_i+E\left(i\right)\right]+q\left[E_{\mathrm{F}}+{\epsilon }_{\mathrm{V}\mathrm{B}\mathrm{M}}\right]$$

(2)

where E(q) represents the energy of the defect system in charged state q, E(pristine) represents the energy of the pristine system, ε_VBM represents the energy of the valence band maximum (VBM), and E_F represents the Fermi energy in reference to ε_VBM. n_i represents the number of atoms i added (n_i < 0) or removed (n_i > 0) from the system, E(i) represents the energy of the element solid i, and μ_i represents the chemical potential in reference to E(i). The choice of E(i) for Cs, Pb, and I were the same as those in [33,40], and the E(i) for H₂O represents the energy of one H₂O molecule.

As shown, the formation energies of the defects without H₂O insertion are generally consistent with those in [33]. We compared the formation energies with and without H₂O insertion. As shown, H₂O insertion reduces the formation energy of the defects due to binding between H₂O and the different defects. Specifically, the formation energy of V_Pb⁰ could become lower than that for V_Pb²⁻ when the Fermi energy is near the VBM, and this is in accordance with the estimation we derived from binding energy analysis, in which V_Pb²⁻ is able to transform into V_Pb⁰. Regarding the large deformation promoted in V_Pb⁰, the formation of V_Pb⁰ is expected to be capable of promoting phase transition. Moreover, the formation of V_Pb⁰ tends to occur close to the VBM; the p-type samples synthesized under low-Pb-level conditions are expected to be affected more. We estimated the effect of charge–charge correction [42,44,45]. The charge–charge interaction between the periodic images could be estimated in the form ~q²/4πεL [46], where q represents the charge on the defect, L represents the lateral size of the supercell, and ε represents the relative static dielectric constant, which is around six in α-CsPbI₃ [47]. We took V_Pb²⁻ with the higher valence of −2 for the estimation, and the interaction energy is around 0.2 eV within the 3 × 3 × 3 supercell. This correction may move the 0/−2 transition level of V_Pb by around 0.1 eV; however, the main conclusions state that V_Pb²⁻ can transform into V_Pb⁰ when the Fermi energy located near the VBM does not change. On the other hand, we mainly compared the formation energy of the defects before and after H₂O insertion in this work; the electrostatic energies from the spuriously repeated charges were expected to be canceled out. Moreover, regarding the defect levels of V_Pb that reside within the band gap between the unoccupied conduction bands, the main conclusion in this work is expected to be unaffected by the band filling effect [48].

It must be noted that polymorphous symmetry breaking may occur in α-CsPbI₃, where α-CsPbI₃ possesses a polymorphous network arranged with local structural motifs of the low-temperature phase with low-level symmetry [24,49]. However, the dominant defects in the low-temperature β- or γ-CsPbI₃ are also V_Pb, V_I, and V_Cs, as calculated in the previous literature [32]; thus, the defects that we chose to study in this work are reasonable. We conducted further calculations to explore the effect on the defect formation energy. In this work, we found that the dominant role that the defects may play in phase transition when H₂O is present is that H₂O can promote both the rearrangement of I atoms into PbI₆ octahedrons and the Pb–I bond breakage nearest to V_Pb⁰, which can eventually promote phase transition. We then conducted a calculation for H₂O insertion into V_Pb⁰ in γ-CsPbI₃. However, as can be seen in Figure 8, no significant bond breakage or I atom rearrangements were found. This indicates that whether V_Pb⁰ takes effect indeed depends on the surrounding structures, and that limited deformation can occur in the low-level symmetry system, which is consistent with its higher stability. However, the cubic structure can possess more local deformations [24], revealing its higher flexibility. As a result, this depends on whether V_Pb⁰ in the cubic phase with local deformation can be deformed by H₂O insertion. Moreover, there may be fluctuation in the local environment of V_Pb⁰ in the cubic phase, which may deserve further study.

4. Conclusions

In this paper, first-principles calculations based on the density functional theory are used to theoretically study the interaction between H₂O and CsPbI₃, including the pristine lattice and intrinsic vacancies therein, and the α-to-δ phase transition of CsPbI₃ catalyzed by H₂O is analyzed. First, we compared the binding of H₂O on the surface and in the bulk of α-CsPbI₃, and the binding energy is higher in the bulk than it is on the surface, at −1.26 and −0.60 eV, respectively. Thus, H₂O tends to diffuse into the bulk once it adsorbs on the surface. We further studied the interaction between three intrinsic vacancies, V_Pb, V_I, and V_Cs, in the α-CsPbI3 bulk and H₂O insertion. It was found that the insertion energy of H₂O decreased or was almost unchanged upon the insertion of the charged vacancies, V_Cs⁻¹, V_I⁺¹, and V_Pb⁻², and neutral vacancies, V_I⁰ and V_Cs⁰, while the introduction of V_Pb⁰ significantly increased the binding energy of H₂O and, thus, promoted the insertion of H₂O into the lattice. The strong binding between H₂O and V_Pb⁰ induced Pb–I bond breakage and new I–I bond formation, which are expected to play roles in the phase transition from α-CsPbI₃ to δ-CsPbI₃. Moreover, H₂O adsorption onto V_I⁺¹ contributes to a larger distortion in the vicinity of V_I⁺¹, which is expected to enhance the phase transition effect of V_I⁺¹. The result is expected to provide guidance for the improvement of the stability of α-CsPbI₃, especially in humid environments.