Interaction mechanism between water molecules and perovskites

Abstract

In recent years, significant progress has been made in the application of perovskite materials in the field of photovoltaics. However, their stability is still affected by the presence of water molecules. Investigating the interaction mechanism between water and perovskites is of great importance for enhancing their stability and advancing commercialization. This review, based on theoretical calculations, summarizes the mechanisms underlying the interaction between water and perovskites. These mechanisms encompass water molecule diffusion, perovskite decomposition induced by a high concentration of water, phase transitions, as well as the dual impact of water on defects. Furthermore, it discusses the influence of water on the quality and performance of perovskite devices in experimental settings. By comprehensively elucidating the theoretical mechanisms governing the interaction between water molecules and perovskites, this review offers both a theoretical foundation and practical guidance for enhancing the stability and optoelectronic performance of perovskite photovoltaic devices, while also facilitating further exploration of the underlying mechanisms.

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1. Introduction

In recent years, research on perovskite materials has been thriving. The generic molecular formula of perovskites is AMX₃. In this formula, the A-site cation is typically represented by organic cation groups such as CN₃NH₃⁺ (MA⁺), CH(NH₂)⁺ (FA⁺), or larger inorganic cations like Cs⁺. The A-site cation can also be substituted by long-chain organic cations, such as butylamine (BA⁺) and phenethylamine (PEA⁺), resulting in a dimensional reduction from 3D to 2D perovskite structures.¹ The M-site is typically occupied by metal cations such as Pb²⁺ and Sn²⁺, while the X-site is filled with halide anions such as Cl⁻, Br⁻, and I⁻. Perovskite materials exhibit numerous advantages, including high charge carrier mobility and lifetime, high conversion efficiency, tunable optical and electronic properties, cost-effectiveness, and straightforward fabrication processes.^2,3 Consequently, they have found extensive applications in the field of optoelectronic devices. However, the stability of perovskite materials under humid conditions remains a challenge, limiting their practical applications. Numerous studies have shown that perovskite solar cells are prone to degradation in ambient environments, with water being one of the main factors triggering material and device degradation.^4–7 In earlier research, water was widely considered harmful to MAPbI₃ perovskites as it irreversibly degrades the material into PbI₂ and MAI, leading to loss of light absorption and severe electron–hole recombination.^8,9 However, some reports suggest that annealing under humid conditions can actually significantly improve film quality and electronic properties, demonstrating the positive role of water.^10,11 Subsequent studies have indicated both beneficial and detrimental effects of H₂O on perovskites.^12–17 Therefore, understanding the fundamental interaction mechanisms between water and perovskites is of great importance for their commercialization.

Currently, most of the existing reviews on the influence of water on perovskite materials predominantly approach the subject from an experimental perspective. These reviews encompass the effects of water on perovskites, including degradation mechanisms,^18–20 impacts on thin film quality and device performance,^19,21,22 as well as strategies to enhance humidity stability.^23–26 However, comprehensive summaries regarding theoretical computational investigations on the subject are scare. With this goal in mind, we primarily summarize the theoretical and computational studies on the physical and chemical processes between perovskites and water. Scheme 1 summarizes the main interactions between water and perovskites, along with the resulting outcomes of these interactions. Generally, the dominant interaction between perovskites and water is the hydrogen bonding between water molecules and organic cations as well as the inorganic framework, and the consequences of this interaction are closely related to the amount of water or the molar ratio of water to perovskites. In the case of trace amounts of water, water molecules tend to adsorb on the perovskite surface and undergo short-range diffusion, while in the presence of a large amount of water, excess water molecules diffuse to deeper positions and cause structural distortion of perovskites. The presence of surface defects promotes water adsorption and diffusion, but during the fabrication process, water can passivate defects and enhance film quality. Furthermore, a certain amount of water affects the energy barriers for the phase transition of the FA-system and Cs-system, thus influencing the material's phase transition behavior. In this review, we discuss the interaction mechanisms between water and perovskite ions as well as defects, and explore the effects of these mechanisms on perovskite materials.

Scheme 1 Schematic illustration of the interaction between water molecules and perovskites.

2. Interaction between water molecules and perovskites

A water molecule consists of one oxygen atom and two hydrogen atoms. Oxygen has two pairs of lone electrons, giving it a bent molecular geometry. The electronegativity difference between oxygen and hydrogen results in oxygen having a partial negative charge and hydrogen having a partial positive charge. This charge difference leads to polarity. The polarity of water allows it to form hydrogen bonds. Additionally, as a polar solvent, water readily dissolves polar solutes. Therefore, theoretically, for organic–inorganic hybrid perovskites, water molecules can form hydrogen bonds with electronegative atoms, such as nitrogen (N) and halogen atoms that possess lone pairs of electrons. In this section, we verify the formation of hydrogen bonds between water and perovskite ions through a theoretical study that summarizes the interactions between water and perovskite ions, primarily including O–H_N bonds with organic cations and X–H_W bonds with halide ions. Moreover, when there are a sufficient number of water molecules, hydrogen bonds can also form between water molecules. These interactions have different effects on perovskite, including structural distortion, decomposition, phase transition, and electronic properties.

2.1 Model description

In theoretical calculations, the construction of the model plays a crucial role in the accuracy of the computations. When modeling the interaction between water and perovskite, the following factors are generally considered: the quantity and proportion of water molecules relative to the perovskite, the adsorption sites of water molecules on different surfaces of the perovskite, and the relative positions and distances between water molecules and different atoms within the perovskite.

In terms of the model for water on the perovskite surface, it is necessary to consider different surfaces, primarily encompassing two types as illustrated in Fig. 1. One is the AX-terminated surface represented by the blue and orange regions, and the other is the MX₂-terminated surface represented by the green region. When studying the interaction between a single water molecule and the perovskite surface, the specific adsorption site needs to be taken into account. For AX-terminated surfaces, the potential adsorption sites for H₂O can be chosen as near A+ or X−. For MX₂-terminated surfaces, the potential adsorption sites for H₂O can be chosen as near M²⁺, the M–X bond, or above A⁺. Previous studies have employed the calculation of adsorption energy, E_ads = E_surface − H₂O − (E_bare-surface + E_H2O), to determine the most favorable adsorption configurations. For both AX-terminated and MX2-terminated surfaces, the specific E_ads with different atomic species at each site are shown in Table 1. For AX-terminated surfaces, when considering the polarity of the MA⁺ species in the MA⁺-system, the lowest adsorption energy is obtained when a single H₂O molecule is positioned near X⁻ above the surface with the –NH₃ moiety of MA⁺ pointing towards the surface.^27,28 For MX₂-terminated surfaces, the lowest adsorption energy is obtained when a single water molecule is positioned above M²⁺ with the –CH₃ moiety of the surface MA⁺ pointing towards the surface. In both cases, when A, M, and X are different ions, the adsorption energies are negative, indicating that water readily adsorbs onto the perovskite surface.²⁹

Fig. 1 Model of water adsorption on perovskite surfaces. The blue region represents water adsorption on AX-terminated surfaces, from left to right, with MA⁺, FA⁺, and Cs⁺ at the A-site, respectively. The green region indicates water adsorption on MX₂-terminated surfaces, from left to right, with Pb²⁺ and Sn²⁺ at the M-site. The orange region represents water adsorption on MAX-terminated surfaces, from left to right, with I⁻ and Br⁻ at the X-site.

Table 1 The lowest E_ads for two distinct atomic species on different surfaces²⁷

		The lowest Eads (eV)
AX-terminated	MAI	−0.48
	FAI	−0.32
	CsI	−0.19
	MABr	−0.48
MX2-terminated	PbI2	−0.51
	SnI2	−0.44
	PbBr2	−0.50

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2.2 Impact of hydrogen bonding on water adsorption on perovskites

Firstly, concerning the A-site cation, the most common one is MA⁺. Density functional theory (DFT) calculations have revealed that on MAX-terminated surfaces, regardless of the adsorption site, the O of H₂O tends to interact more with one of the H in –NH₃ than with the –CH₃. In other words, in MA⁺, the –NH₃ moiety is hydrophilic, while the –CH₃ moiety is hydrophobic.^27,30,31 The overlap between the Op_y orbital of H₂O and the s orbital of HN, as indicated by the calculated projected density of states (PDOS), suggests the presence of hydrogen bonding interactions between them.³² Further investigations have found that this is due to the weaker N–H bond and the higher polarity in MA⁺ compared to the C–H bond. For FA⁺ and Cs⁺, their AX surfaces exhibit some hydrophobicity, manifested by higher surface adsorption energies compared to MA⁺. This is because in FA⁺, the strength of the N–H bond is similar to that of the C–H bond and both are stronger than in MA⁺, while the polarity of FA⁺ and Cs⁺ is weaker than that of MA⁺.²⁷ Therefore, experimentally, the stability of perovskite can be enhanced by doping with A-site cations. By partially replacing MA⁺ with FA⁺ or Cs⁺, devices with improved humidity stability can be achieved.^33,34

Furthermore, for the M-site cations, common examples include Pb²⁺, Sn²⁺, and other metal cations. Calculations have revealed that the interaction between H₂O and M-site cations differs from the hydrogen bonding interaction with the A-site. H₂O interacts with the M-site ions through a combination of covalent and ionic interactions. Due to the closer electronegativity between Pb and I, the ionic interaction between H₂O–MAPbI₃ is stronger than H₂O–MASnI₃.²⁷ Guo Xie et al. conducted a comparative analysis of the impact of H₂O on MASnI₃ and MAPbI₃, and found that H₂O has a significant influence on the Sn–I bonds on the surface of MASnI₃, suggesting that, in a H₂O atmosphere, MAPbI₃ is more stable than MASnI₃.²⁹ This conclusion contradicts the stability analysis based solely on adsorption energy, emphasizing the necessity in practical research to consider multiple factors rather than relying on a single energy-based indicator to assess structural stability. On MI₂-terminated surfaces, the O of H₂O forms an O–M bond with the M²⁺ acceptor due to its lone pair of electrons. Other factors such as light illumination also influence the interaction between H₂O and M²⁺. Lu Ying-Bo et al. found that above-band-gap light illumination of MAPbI₃ induces a significant photo-induced lattice expansion effect, increasing the electron density around Pb²⁺ and enhancing the bonding interaction between H₂O and Pb²⁺.³⁵

Lastly, regarding the X-site anions, on AX-terminated surfaces, the H of H₂O forms an H–X hydrogen bond with the adjacent X⁻.³¹ On MX₂-terminated surfaces, Shuxia Tao suggests a covalent interaction between H₂O and X⁻,²⁷ while Bin Hu suggests that the interaction between I⁻ on the (011) surface and the H of H₂O is close to an ionic bond.²⁹ The electronic density of the H–I bond is 0.05, indicating a relatively weak covalent interaction, and the H and I⁻ form an antibonding state. However, regardless of the specific bonding analysis, the conclusions regarding Br⁻ and I⁻ are consistent, indicating that the interaction with Br⁻ is weaker than with I⁻.^27,36 Due to the weaker adsorption characteristics of H₂O on Br⁻, experimental studies have improved the humidity stability of solar cells by partially replacing I⁻ with Br⁻.³⁷ Weiguang Zhu et al. investigated the dissolution and degradation mechanisms of isomorphous Cs₂SnCl₆ and Cs₂SnI₆ in direct contact with water. Cs₂SnI₆ undergoes direct dissolution in water, decomposing into CsI and SnI₄, leading to the formation of an intermediate hydrolysis product, Sn(OH)₄. In comparison to Cs₂SnI₆, Cs₂SnCl₆ exhibited greater stability and formed a smaller quantity of amorphous phase due to their different interaction with water molecules. The authors attribute this behavior to the smaller ionic radius of chloride, with chloride having a higher ionic potential than iodide, thereby forming stronger atomic bonds.³⁸

2.3 Water molecule abundance and increased water diffusion depth on perovskites

How do water molecules diffuse into the interior of the perovskite? To elucidate this question, the perovskite region has been divided as depicted in Fig. 2(a) for illustrative purposes. The upper area of the (001) surface is denoted as O, F, and S regions. Region O signifies water adsorption on the perovskite surface, region F represents water molecules residing on the upper side of the first layer, and region S indicates water molecules staying on the lower side of the first layer. Additionally, the number of water molecules is represented by n, and On, Fn, and Sn denote the presence of n water molecules in these respective regions.

Fig. 2 (a) Imaginary typical structure of three-layer (001) surface containing water named O1F1S1. The colored regions in the surface divisions of MAI-terminated (left) and PbI₂-terminated (right) represent the possible locations of water molecules and are named O, F, and S, respectively. Reproduced with permission (left figure).³⁹ Copyright 2015, American Chemical Society. (b) An illustration showing water adsorbed in the (i) O (O5) region, with water residing in the inner regions ((ii) F5 and (iii) F4S1). Reproduced with permission.³⁹ Copyright 2015, American Chemical Society. (c) Snapshots of the key steps for a few water molecules absorbed on MAI-terminated (i) and PbI₂-terminated surfaces (ii). Reproduced with permission.⁴⁰ Copyright 2016, Royal Society of Chemistry.

Firstly, regarding MAPbI₃, whether a single water molecule can diffuse from its surface to the interior was investigated through computational simulations, and the answer to this question is affirmative. Specifically, it was observed that the energy of the system when H₂O is in region F is lower than when it is in region O, indicating that H₂O tends to stay energetically favorable on MAPbI₃. Simultaneously, the diffusion barrier from region O to F is merely 0.04 eV, suggesting a highly facile process with minimal resistance. This behavior can be attributed to the unique structural characteristics of MAPbI₃, featuring a large framework composed of Pb and I atoms with relatively spacious interstices, despite the presence of organic MA⁺ molecules. Furthermore, H₂O diffuses from region F to region S, with a diffusion barrier of 0.31 eV, slightly higher than the barrier from O1 to F1, yet still relatively small, thereby providing the opportunity for water molecules to diffuse from region F to region S. Additionally, compared to water molecules in region F, those in region S exhibit a lower system energy. During this process, H₂O needs to overcome the [PbI₆]⁴⁻ framework. Throughout this entire process, due to the interaction between O in H₂O and HN in MA⁺, the orientation of MA⁺ in regions F and S changes as water molecules diffuse.³⁸ Koocher Nathan et al. discovered through simulations that on the PbI₂-terminated surface, as the –NH₃ groups in MA⁺ in region S are directed towards the surface, water molecules begin to stay within the plane. O interacts with the HN in MA⁺ in region S through hydrogen bonding, while the two H_W atoms interact with the surface I⁻. The penetration of H₂O increases the cavity size, weakening the octahedral rotation due to the interaction between O and H_N, thereby opening adjacent hollow spaces.²⁸ This indicates that water adsorption beneath the surface has a collective influence on neighboring structures. Once H₂O fully enters region S, strong hydrogen bonds form between O and H_N, and the barrier for this process is smaller than that for the reverse process, indicating that once H₂O molecules penetrate the hollow sites, they cannot easily leave.

As the number of water molecules increases, how does the diffusion model differ from that of a single water molecule? For MAPbI₃, simulation studies have found that under high humidity conditions, whether on the MAI-terminated or PbI₂-terminated surfaces, water molecules exhibit strong adsorption at all sites, with hydrogen bonding interactions forming between water molecules.

Firstly, for the MAI-terminated surface, similar to the case of a single water molecule, when water molecules are located in region O, as depicted in Fig. 2(b)(i), the hydrogen bonding interaction between water and MAPbI₃ is weak, and there is no significant structural change after water adsorption. Subsequently, water molecules diffuse to region F, as shown in Fig. 2(b)(ii), where the interaction between water and MAPbI₃ strengthens, leading to disruption of the perovskite structure in region F. Occasionally, certain water molecules can further diffuse to region S, disrupting the structure of region S, as shown in Fig. 2(b)(iii). From an energy perspective, compared to region O, H₂O tends to stay in region F. The changes in MA⁺ positions and the distortion of Pb–I bonds in region F increase with increasing n. The oxygen atom (O) of H₂O forms strong bonding with the remaining exposed Pb, breaking the Pb–I bonds until the structure of region F is completely disrupted. Driven by the high coverage of water molecules, they can further diffuse from region F to S, causing greater distortion of Pb–I bonds.³⁹ Similarly, Lei Zhang et al. using ab initio molecular dynamics (AIMD) simulations, found that the presence of H₂O on the MAI surface within MAPbI₃ not only altered the orientation of MA⁺ but also led to larger fluctuations in Pb–Pb distances and dihedral angles, as illustrated in Fig. 2(c)(i). This indicates that the MAI surface lacks chemical stability due to interactions with water molecules. Furthermore, by extracting snapshots from the AIMD trajectories, it was observed that over time, the ordered structure of the outermost layer of the MAI-terminated surface was disrupted, resulting in a relatively wide diffusion range of water molecules on the surface.⁴⁰

For the PbI₂-terminated surface, some simulation results differ from the MAI-terminated case. Although H₂O exhibits strong interactions with the surface's Pb²⁺, the PbI₂-terminated surface does not undergo decomposition, as illustrated in Fig. 2(c)(ii). This might be attributed to the PbI₂-terminated surface possessing the shortest and consequently strongest Pb–I bonds. A few individual water molecules may enter region S, forming hydrogen bonds with MA⁺ and becoming trapped within the cavity for the remaining simulation time. However, during this process, the inorganic framework of the perovskite undergoes only slight deformation while maintaining its integrity. Yet, when a certain quantity of water molecules accumulates in region S, the perovskite lattice elongates perpendicular to the surface. This suggests that higher water concentrations could weaken the interlayer binding strength in halide perovskites, thereby promoting the decomposition of MAPbI₃.⁴⁰ As the quantity of water molecules further increases, decomposition also occurs on the PbI₂-terminated surface. Claudia Caddeo et al.'s simulation results of water and MAPbI₃ interactions reveal that at a 75% water coverage rate on the MAI surface, an I atom is attracted and lifted from the surface by surrounding H₂O molecules.⁴¹ This forms a hydrogen bond network between water molecules and surface I atoms, causing each molecule's hydrogen bond donor count to approach its ideal value.⁴² Consequently, Pb–I bond rupture occurs, enabling two water molecules to infiltrate the crystal interior, marking the first step of water degradation.

Lu Ying-Bo et al. discovered that under light illumination, the lattice of MAPbI₃ undergoes expansion due to the photo-induced lattice expansion effect, resulting in an increase in the Pb–I–Pb angles. This expansion reduces the hydrogen bonding interactions between the organic and inorganic components. It is well-known that the hydrogen bonding interactions between the [PbI₆]⁴⁻ framework and the MA molecules maintain the unique structure of MAPbI₃.^35,43 Therefore, when water molecules penetrate into the interior of MAPbI₃ under light illumination, they encounter weaker resistance compared to non-illuminated conditions. In experimental studies, Nurul Ain Manshor et al. compared the air stability of MAPbI₃ stored at >70% humidity under dark and light conditions.⁴⁴ It was found that exposure to humidity in the dark also led to slight decomposition of the perovskite into its initial precursors. When exposed to light, the thin film exhibits a degradation rate over 10 times higher in the presence of humidity. This further underscores that the larger voids within the perovskite structure are also one of the contributing factors enabling water molecules to penetrate the interior of the perovskite.

2.4 Disruption of hydrogen bonds on perovskites by water molecules

In the preceding section, we discussed the process of water molecule penetration into the perovskite lattice, which involves lattice distortions and the breaking and reforming of hydrogen bonds. These events lead to a certain level of structural disruption within the perovskite. When water enters the interior of the perovskite, how exactly do hydrogen bond interactions between different atoms contribute to the structural deterioration of the perovskite? Furthermore, it has been observed in the study that during the interaction between H₂O and the perovskite, a hydrated intermediate phase MAPbI₃·H₂O emerges prior to structural disruption. The total energy of this system is lower by 0.526 eV compared to the total energy of MAPbI₃ and H₂O molecules, implying that water can be readily adsorbed onto MAPbI₃.⁴⁵

Dong Xu et al. investigated the neighbor interactions in MAPbI₃ using natural bonding orbital (NBO) analysis and identified two main types of neighboring interactions: (1) (interaction between the lone pair of I atom and the antibonding orbital of H–N bond) and (2) (interaction between the lone pair of I atom and the antibonding orbital of H–C bond).⁴⁵ The stability energy of stereoelectronic interaction (1) is approximately 19 kcal mol⁻¹, which is significantly higher than the stability energy of interaction (2). Upon encountering a water molecule, the weaker donor–acceptor interaction (2) within the MAPbI₃ molecule is disrupted, and the two stereoelectronic interactions (1) are weakened, with the stability energy decreasing from ∼19 kcal mol⁻¹ to ∼13 kcal mol⁻¹. Furthermore, two additional interactions are established between MAPbI₃ and water molecules: (3) and (4) . The stability energy of the donor–acceptor interaction (4) between the lone pair of O atom in water and the antibonding orbital of N–H bond in the organic MA unit is 21.8 kcal mol⁻¹, which is significantly higher than the stability energy between PbI₃ and MA units. As a result, the presence of a water molecule decreases the stability of MAPbI₃. Although one water molecule weakens the interactions between [PbI₆]⁴⁻ and MA units in MAPbI₃, the structure of MAPbI₃ is not completely destroyed. However, when two water molecules encounter a MAPbI₃ molecule, the hydrogen bonds between [PbI₆]⁴⁻ and MA units are almost broken. The interaction (4) between the MA unit and H₂O is much stronger than the interaction between [PbI₆]⁴⁻ and MA units, resulting in the complete decomposition of MAPbI₃. Kakekhani Arvin et al. suggested that the polarization of water's lone pair induces more electron charge density closer to the proton-like H*N, leading to its interaction with the HN group on MA⁺.³² This interaction, in addition to hydrogen bonding, has a small covalent component manifested as a slight charge transfer from water to MA⁺. For a relatively low concentration of H₂O : MA = 0.25, the water is oriented such that most of the highest occupied molecular orbital (HOMO) lone pairs interact with the H*N, lowering the system's energy, while hydrogen bonding exists between H₂O and nearby I⁻ anions. At this point, water causes some distortions in the lattice structure. When the ratio of H₂O : MA ranges from 0 to 1, each H₂O molecule binds to the –HN on MA⁺. Initially, each H₂O perturbs (distorts) the inorganic framework to maximize hydrogen bonding attraction with I⁻ and minimize electrostatic repulsion between O-2p lone pairs and I⁻. At H₂O : MA = 1, as shown in Fig. 3(a), two water molecules form hydrogen bonds with each other, creating a connecting chain of (H₂O–MA–H₂O–H₂O–MA), while the fourth water molecule interacts with two adjacent MA⁺ ions. At high water concentrations (H₂O : MA > 1), due to continuous distortion of water molecules in the presence of MAPbI₃, the system reaches an energetically favorable point for Pb bonding upon embedding. This results in the structure with broken octahedra becoming the actual ground state when sufficient water is present. Adequate water molecules form strong bonds with the ionic components of MAPbI₃ and stabilize this distorted structure through a network of hydrogen bonds with other H₂O molecules, as shown in Fig. 3(b). Experimental observations also indicate that MAPbI₃ films are stable in dry air with humidity at or below 15%. However, in air with humidity as high as 60%, degradation can occur. During the degradation process, water initially decomposes MAPbI₃ into crystalline MAI and PbI₂, followed by the transformation of crystalline MAI into its amorphous form.

Fig. 3 (a) and (b) Ground state water structure for different H₂O : MA concentrations. Color code is O (red), H (white), C (black), N (green), I (brown), and Pb (dark gray). Reproduced with permission.³² Copyright 2019, American Institute of Physics. (c) Water molecule bound to the PbI₂-terminated perovskite slab showing the formation of the Pb–O bond. (d) Water molecule infiltrated within the MAPI crystal showing the formation of the H–O link between the methylammonium and water. Red is O, white is H, pink is I, dark gold is Pb, cyan is C, and blue is N. Reproduced with permission.⁴¹ Copyright 2017, American Chemical Society.

In contrast to liquid water, the case of water vapor is different. In the gas phase, individual water molecules placed in front of the surface are attracted to the crystal, with their oxygen eventually binding to the surface Pb atoms, forming polar Pb–O connections. Once the molecule is anchored in this manner, it does not undergo extensive diffusion on the nanosecond timescale at room temperature, thus water cannot disrupt the [PbI₆]⁴⁻ framework, as depicted in Fig. 3(c). Therefore, it can be concluded that water, as isolated molecules, gradually infiltrates and diffuses without disrupting the crystal until hydrated phases are formed. Conversely, as illustrated in Fig. 3(d), when water accumulates on the surface, irreversible lattice degradation may occur.⁴¹ These simulation results are consistent with the experimental observations by Aurélien M. A. Leguy et al. In their experiments, it was observed that when MAPbI₃ single crystals and films were exposed to water vapor at room temperature, hydrated crystalline phases were formed.⁴⁶ Importantly, this transition can be reversed under dry conditions. In contrast, when exposed to liquid water, MAPbI₃ degrades and forms PbI₂, which is an irreversible process. Under such conditions, degradation is highly efficient, and only minimal amounts of liquid, such as condensed droplets on the film surface or rapid immersion in water, have been observed.^46,47 Similarly, Jong Un-Gi et al., through calculations, found that water interacts with PbX₆ and MA through hydrogen bonding, with the interaction of water intercalation gradually increasing as X changes from I to Br and then Cl, while the hydration interaction remains nearly unchanged. Water-induced hydrogen bonding interactions significantly affect vacancy-mediated ion migration, as water intercalation in halide perovskites reduces the activation barrier. These results indicate that the degradation of perovskite solar cells (PSCs) following exposure to humidity arises from a multi-step process: the formation of water intercalation and hydrated compounds, followed by the decomposition of these compounds.³⁶

3. Interaction of water molecules with defects in perovskite

In general, defect states are commonly present within perovskite materials. Defects in perovskite materials influence non-radiative carrier recombination and ion migration, thereby significantly constraining the energy conversion efficiency and stability of devices. The ionic nature of perovskites renders defect states charged, with deep-level defects arising from these charged defects being principal non-radiative recombination centers.^48,49 Shallow-level defects, on the other hand, may not impact non-radiative recombination but can induce band bending, interface reactions, and phase separation, affecting carrier mobility.^50–52 What then is the interaction between defects in perovskites and water molecules, and what are the resultant outcomes? To address this question, we provide the following summary and analysis.

3.1 Defects in perovskites accelerate their degradation in water

In comparison to the PbI₂-terminated surface, the PbI₂-defective surface structure exhibits a distribution of H–O pairs within the range of 1.5–4 Å, indicating a stronger mutual interaction between H₂O and the PbI₂-defective surface. Consequently, under this interaction, the surface becomes disordered and tumultuous, with the absorbed H₂O on the PbI₂-defective surface able to traverse the PbI₂ layers and reach the cavities formed between the outermost and the second PbI₂ layers, forming hydrated compounds.⁴⁰ Filippo De Angelis et al. also examined the potential role of surface defects in determining the stability of the water/perovskite interface.³⁰ Computational analysis revealed that the PbI₂-defective surface undergoes a rapid degradation process. During this process, two under-coordinated Pb atoms rapidly desorb from the perovskite surface, leading to the formation of solvated species. One of the Pb atoms is initially anchored to the perovskite surface through coordination with four I atoms, while a water molecule is added to the coordination sphere, as shown in Fig. 4(a). The other surface Pb atom is initially bound to three I atoms on the perovskite surface and two interface water molecules, as depicted in Fig. 4(a). Throughout the Car–Parrinello Molecular Dynamics (CPMD) trajectory, both surface Pb atoms depart from the perovskite surface, forming octahedral [PbI₂(H₂O)₄] and [PbI(H₂O)₅]⁺ complexes in solution. In conclusion, defects on the perovskite surface may potentially trigger further degradation of MAPbI₃. Hence, the growth of defect-free crystals and films seems crucial for stabilizing perovskite materials and maintaining their integrity in the presence of humidity.

Fig. 4 Representative geometrical structures of the formation of (a) [PbI₂(H₂O)₄] and (b) [PbI(H₂O)₅]⁺ complexes. Reproduced with permission.³⁰ Copyright 2015, American Chemical Society.

Accelerated degradation of the perovskite structure invariably leads to deterioration in device performance. Pezhman Darvishzadeh et al. modeled the variation of open circuit voltage (V_OC) over time, demonstrating that ion migration and PbI₂ defects are the primary causes for the degradation of V_OC exposed to humidity.⁵³ Sohrabpoor Hamed et al. also concluded that the defect profile plays a pivotal role in the instability of the device.⁵⁴

3.2 Influence of water molecules on defect formation

In their study, Run Long et al. investigated how the interaction between lead vacancies and water influences non-radiative electron–hole recombination in MAPbI₃.⁵⁵ Computational results indicate that the presence of water reduces the formation energy of both neutral and charged lead vacancies to values below −2 eV, facilitating their spontaneous creation. Notably, MAPbI₃ with lead vacancies introduces localized shallow energy levels for holes, which merge with the valence band edge, attenuating the electron–phonon coupling between ground and excited states. Consequently, this leads to a reduction in non-radiative electron–hole recombination rates. When water molecules coexist with vacancies, unsaturated iodine atoms near lead vacancies form iodine dimers, introducing deep energy levels for electron capture. This accelerates electron–hole recombination, shortening the recombination time to approximately one-fourth of the original MAPbI₃ system. Furthermore, they found through calculations of electron–hole recombination times that relative humidity plays a significant role in determining the excited state lifetime.⁵⁴ Simulations suggest that moderate humidity prolongs the excited state lifetime, while high humidity reduces it. A small amount of water localizes electrons on the surface, simultaneously avoiding deep trap states and decoupling electrons from holes. Additionally, the quantum coherence time decreases. Both effects reduce the nonradiative charge recombination. Under high humidity conditions, water aggregates on the surface of perovskite, forming a continuous hydrogen bonding network. The interaction between perovskite and water is weaker than water–water interactions, thus the disturbance caused by continuous water layers on the perovskite surface is less pronounced compared to isolated water molecules. With increasing water content, the delocalization of electrons into the bulk and the overlap of electron–hole pairs recover, resulting in a nonadiabatic coupling that exceeds the value of the bare surface, accelerating recombination. These theoretical studies provide valuable insights into seemingly contradictory experimental phenomena, with some measurements indicating that increased humidity enhances the excited state lifetime of MAPbI₃, thereby improving the performance of solar cells.¹²

Yun-Hyok Kye et al. investigated the defect processes in MAPbI₃, water-intercalated MAPbI₃_H₂O, and monohydrated phase MAPbI₃·H₂O.⁵⁶ They considered the formation energies of isolated and clustered vacancy defects with different charge states under iodine-rich and iodine-poor conditions. The study found that the formation of V_PbI2 from its isolated vacancy defect is spontaneous. However, due to the significantly lowered kinetic barrier for I⁻ migration upon hydration, the concentration of V_I should be reduced to prevent this formation, which can be achieved by imposing iodine-rich conditions. In hydrated compounds, the formation of individual point defects V_I and V_MA is easier than that of V_MAI. Therefore, during decomposition, I₂ or CH₃NH₂ or HI can be formed instead of MAI. Unlike in pristine MAPbI₃, all vacancy defects lead to the creation of deep transition energy levels in hydrated compounds. This is attributed to electrostatic interactions with water molecules, suggesting the degradation of halide lead perovskites when exposed to humidity.

Yun-Hyok Kye et al. also calculated the thermodynamic transition levels ε(q1/q2) between defect states of different charge states q1 and q2. Fig. 5(a) depicts the potential transition levels along with the relative positions of MAPbI₃_H₂O and MAPbI₃·H₂O with respect to MAPbI₃. Water molecules inserted through the membrane surface extract electrons, causing the valence band maximum (VBM) to shift to lower energies and the conduction band maximum (CBM) to higher energies, consequently altering the bandgap from the original phase to the water-intercalated and monohydrated phases. Evidently, in the case of MAPbI₃, all vacancy defects possess shallow transition levels, while in the context of hydrated compounds, vacancies exhibit deep trap behavior. This can promote charge carrier recombination, leading to the degradation of solar cell performance. Specifically, in MAPbI₃, V_I and V_MA act as shallow donors and acceptors, as evidenced by their respective transition levels ε(1+/0) and ε(0/1−) near the CBM and VBM. In the case of hydrated compounds, transition levels are situated deep within the bandgap, with the transition level for V_MA not far from the valence band. Notably, V_Pb in MAPbI₃ lacks a transition level within the band (ε(0/2−)), but in hydrated compounds, it could possess two deep transition levels, ε(0/1−) and ε(1−/2−). Both V_MAI (with two transition levels) and V_PbI2 (with two/four transition levels in pristine/hydrated MAPbI₃) exhibit such characteristics.

Fig. 5 (a) Band alignment and thermodynamic transition levels in MAPbI₃, water-intercalated MAPbI₃_H₂O, and monohydrate MAPbI₃·H₂O, where deep-lying Pb 5d levels are used as a reference for the VBM and CBM of each phase. Reproduced with permission.⁵⁶ Copyright 2018, American Chemical Society. (b) Minimum energy level of π*2p of O₂ absorbed at the interstitial space on a PbI₂-terminated surface as a function of water content. Reproduced with permission.⁵⁹ Copyright 2019, John Wiley and Sons.

Water not only influences defect formation but also passivates defects. Water molecules passivate deep-level defects by forming hydrogen bonds with I atoms in the perovskite structure.⁵⁷ Wenke Zhou et al. verified the defect passivation effect of water molecules on MAPbI₃ thin films using thermal admittance spectroscopy. Initially, the authors measured control MAPbI₃ perovskite films without water treatment and identified deep-level defects at 0.295 eV, typically associated with Pb–I anti-site defects. After appropriate water treatment, the deep-level position shifted closer to the conduction band, indicating effective passivation of Pb–I anti-site defects by water molecules. Upon further drying the water, the defect level position deepened. This outcome suggests that an appropriate amount of water can effectively passivate deep-level defects, and the process is reversible.

Apart from 3D perovskites, H₂O can also passivate defects in 2D perovskites. Xinlu Guo et al., through DFT calculations, discovered that a suitable number of water molecules can preferentially occupy V_I defects in Dion–Jacobson (DJ) phase perovskites, reducing trap centers, forming hydrogen bonds with surrounding atoms, enhancing the structural stability, and making them more robust. Concurrently, experimental observations showed that devices prepared under humid conditions exhibit improved photovoltaic performance and stability.⁵⁸ However, compared to 3D perovskites, there has been limited research on the interaction of water and defects in 2D perovskites, and theoretical investigations in this context are particularly lacking. Conducting research on issues related to 2D perovskites could significantly promote the advancement of this field.

Light- and oxygen-induced degradation of MAPbI₃ is a primary factor limiting the lifespan of PSCs. Yixin Ouyang et al. revealed through calculations that due to the weak affinity between oxygen and MA, as well as the capture of iodine vacancies, O₂ cannot spontaneously diffuse from the surface into the internal lattice of MAPbI₃.⁵⁹ The slow diffusion properties lead to photodegradation concentrating on the perovskite surface. Induced by the MAPbI₃ surface, the degenerate π*2p energy level of O₂ slightly splits into two bands. When H₂O approaches O₂, the π*2p energy level of O₂ decreases, moving it closer to the valence band of MAPbI₃. The pronounced polarization effect of water enhances oxygen's electron affinity, causing a reduction in the O₂ energy level. Changes in H₂O content also impact this process. With more H₂O molecules progressively surrounding adsorbed O₂, the oxygen state shifts further downward. For O₂ adsorbed at hollow sites on the PbI₂-terminated surface, the transition of oxygen states is significantly influenced by water content. As illustrated in Fig. 5(b), as water content increases, more charge is transferred from surface I atoms to O₂ due to water molecules. This results in a deceleration of the reduction in the O₂ energy level. H₂O acts as a bridge on V_MA points, facilitating the transmission of changes between I atoms and absorbed O₂. In conclusion, stable perovskite thin films necessitate crystal surfaces terminated with defect-free MAI.

4. The influence of water molecules on the morphology and performance of perovskite devices

The inevitable interactions between water molecules and perovskites also inevitably influence their fabrication processes, the resulting film quality, and device performance. Currently, experimental evidence has indicated that specific humidity conditions favor the preparation of perovskite thin films.^60,61 In light of these findings, it is imperative to elucidate the role of water in this context. We present the following summary and analysis.

4.1 The effect of moderate water on phase transitions in FAPbI₃ and CsPbX₃

Unlike MAPbI₃, for FAPbI₃, it is prone to undergo a phase transition from the α phase to the δ phase under humid atmospheric conditions. How do water molecules impact this phase transition process? The hydrogen bond interactions between water molecules and the perovskite structure of FAPbI₃ are considered the primary factors influencing its phase transition.^62,63 Dongxu Lin et al. through DFT calculations, demonstrated that water molecules can form both O⋯H–N and I⋯H–O hydrogen bonds with FAPbI₃. Within a certain concentration range, this leads to anomalous contraction of the α phase and lowers the energy barrier between the two phases' transition states. At an appropriate water concentration, when the energy barrier is minimized, the α phase can easily and completely transform into the δ phase, and vice versa. The entire phase transition process is depicted in Fig. 6(a). Concurrently, experimental findings also reveal that under high humidity conditions, pure δ-FAPbI₃ can be obtained, and further annealing produces high-quality α-FAPbI₃ films.⁶⁴ Chunqing MA et al., based on XPS and EXAFS data, concluded that water molecules adsorb on the surface of FAPbI₃ perovskite through the formation of –OH groups, resulting in structural distortions with weakened Pb–I bonds. These distortion and weakening processes promote the δ phase transition at room temperature. Further theoretical calculations of water molecule interaction energy with the (100) and (111) crystal facets were performed. The adhesion energies for the two surfaces with H₂O were found to be 93.08 and 85.12 mN m⁻¹, respectively. Thus, the (100) surface is more favorable for H₂O adhesion in terms of energy, indicating its susceptibility to degradation caused by humidity. Therefore, when α-FAPbI₃ is exposed to H₂O, the (111) surface is thermodynamically more stable.⁶⁵

Fig. 6 (a) Lattice evolution of α- and δ-FAPbI₃ with increasing H₂O concentration and an indication of phase transition path. Reproduced with permission.⁶⁴ Copyright 2022, John Wiley and Sons. (b) Schematic diagrams of high-T CsPbI₃ (left, orthorhombic structure with three-dimensionally connected corner-sharing octahedra) to low-T CsPbI₃ (right, orthorhombic structure with one-dimensional chains of edge-sharing octahedra) phase transformation triggered by moisture. (c) Illustrative energy diagram of CsPbI₃ (thick red line) comparison with common moisture induced modification (faint red line) of the energy scheme. Reproduced with permission.⁶⁹ Copyright 2021, Elsevier.

Similar to FAPbI₃, CsPbI₃ is also prone to undergo a phase transition from the high-temperature (high-T) γ phase to the low-temperature (low-T) δ phase under atmospheric conditions,^66–68 as shown in Fig. 6(b). Zhenni Lin et al. employed molecular dynamics simulations and found that when a thin layer of water contacts the metastable perovskite surface, the large solvation enthalpy of I⁻ and its associated low formation energy of vacancies enhance the halide vacancies at the water–perovskite interface. These halide vacancies can be considered as defect sites that lower the activation energy barrier (PT barrier) between the metastable γ- and stable δ- of CsPbI₃, as illustrated in Fig. 6(c), effectively catalyzing the phase transition.

Further increasing the relative humidity (RH) results in an exponential increase in vacancy equilibrium concentration. Based on this, it can be predicted that elevated RH levels lead to an exponential increase in the nucleation rate of δ phase CsPbI₃.⁶⁹ Moreover, Kyoung E. Kweon et al. utilized DFT calculations to study the water-induced effects of H₂O molecules and their dissociation species (H⁺/OH⁻) during the γ- to δ-transition of CsPbI₃. They discovered that the reaction energy barrier is significantly lowered when H₂O or OH- is present within CsPbI₃, while the influence of H+ on kinetics can be neglected.⁷⁰ Corresponding phenomena have also been experimentally observed and quantitatively validated the computational conclusions. Daniel B. Straus et al. experimentally observed the vapor-induced transformation of γ-CsPbI₃ to δ-CsPbI₃ through synthetic variations and in situ PXRD measurements.⁷¹ Similarly, for CsPbBr₃, Jiayu Di et al. found through calculations that the presence of water during crystal growth reduces the formation energy of γ-CsPbBr₃ and promotes the reaction in that direction.⁷² This can explain recent observations that atmospheric humidity accelerates the phase transition kinetics without significantly altering the transition enthalpy.

4.2 Optimization of crystallization

Beyond its impact on phase transitions, water molecules can influence the crystallization process of perovskites through specific interactions. Weili Fan et al., through DFT simulations, proposed that in the synthesis of FAPbI₃, the introduction of a certain amount of H₂O facilitates the ionization of FAI due to the high solubility of the organic salt FAI in water.⁷³ This leads to enhanced mobility of FA⁺ and I⁻ ions. The activation energy for FAPbI₃ synthesis, both with and without water, was computed. The presence of water resulted in a negative activation energy, indicating a spontaneous reaction. Water also affects PbI₂, as revealed by calculations of water molecule adsorption on the PbI₂(001) and (102) surfaces. Water molecules tend to adsorb on the (102) surface, retarding its growth and thereby promoting oriented growth of the PbI₂(001) plane. Similarly, Kaikai Liu et al. proposed that in hybrid organic–inorganic perovskites, water molecules enhance the mass mobility of hydrated salts through hydrogen bonding with organic salts.⁷⁴ This facilitates greater penetration of organic salts into the PbI₂ thin film, generating more crystallization sites for perovskite formation and ultimately favoring the development of high-quality perovskite films.⁷⁵ A schematic representation of its crystal structure is shown in Fig. 7(a). Experimental observations also corroborate that under controlled humidity conditions, modulation of the crystallization process through water manipulation leads to the fabrication of higher quality perovskite films with reduced defects.^12,76–78 Furthermore, Yangyang Du et al. found that after participating in the completion of crystallization regulation, water molecules migrate to the grain boundaries of perovskite thin films. This facilitates effective passivation of crystallization defects, ultimately leading to the formation of high-quality perovskite thin films.⁷⁹

Fig. 7 (a) Schematic illustration of H₂O in regulating the crystallization process. Reproduced with permission.⁷⁵ Copyright 2022, Springer Nature. (b) The PDOSs for three surfaces. Reproduced with permission.⁴⁰ Copyright 2016, Royal Society of Chemistry. (c) Illustration of the perovskite–moisture interaction, leading to electron transfer, hydration, and degradation. Reproduced with permission.⁸¹ Copyright 2019, American Chemical Society.

4.3 Impact of water on perovskite band structure and photoelectric performance

The interaction between H₂O and perovskite materials generally has an impact on the electronic structure of perovskites and the optoelectronic performance of devices. Lei Zhang et al. simulated the effects of H₂O on the band structure of MAPbI₃.⁴⁰ When water is adsorbed on the surface of the perovskite, for both the water-absorbing MAI-terminated and PbI₂-terminated surfaces, the calculated band gaps fluctuate around 1.879 eV and 1.578 eV, corresponding to standard deviations of 0.210 eV and 0.094 eV, respectively. Relative to the bare surface, induced by water molecules, the strongly surface-reconstructed water-absorbed MAI-terminated surface exhibits a broader distribution of energy gaps, while its average gap remains nearly identical to that of the dry surface. Furthermore, as shown in Fig. 7(b), the composition of the VBM and CBM is not predominantly derived from the outermost layers’ states. For the PbI₂-terminated surface, the main contribution to the VBM comes from the outermost layer of the surface. Charge transfer induced by water molecules adsorbed on the surface causes the surface's VBM to shift downward, resulting in a wider band gap. The water-absorbing PbI₂-terminated surface's PDOS remains similar to that of the bare surface, due to the preservation of surface structure. On the water-absorbing MAI-terminated surface, surface reconstruction generates shallow surface states, which might capture photo-generated holes. These surface states are confined to the vicinity of the VBM without intruding into the bandgap of MAPbI₃, implying intrinsic defect tolerance in MAPbI₃.

Andrew M. Rappe et al. discovered that when the H₂O : MA ratio typically ranges from 0 to 1, and the addition of water generally leads to an increase in the bandgap.^32,80 This gap variation is caused by structural deformation and lattice expansion. Generally, the introduction of water reduces the connectivity of the primary structure of MAPbI₃, weakening bonds, narrowing bands, and increasing the bandgap. When the ratio of H₂O : MA falls within the range of 1 to 2, water molecules exhibit a “chemical” effect in determining the bandgap. At higher water concentrations such as H₂O : MA = 2, the orbitals of water more significantly contribute to the VBM and CBM due to increased covalency with the inorganic framework's I⁻ and Pb²⁺. This is a consequence of the fractured octahedra, leading to direct binding of water with the inorganic framework (i.e., Pb²⁺).

The interaction of water molecules alters the geometry and electronic structure of MAPbI₃, and undoubtedly influences the material's optical properties. Lei Zhang et al. computed snapshots of the absorption spectra for molecular dynamics (MD) trajectories, and at the beginning of the simulation, the initial structure exhibited optical responses similar to the bulk phase.⁴⁰ As the simulation progressed and water molecules penetrated the interior layers of the MAI-terminated surface, significant changes in the perovskite structure occurred, resulting in a pronounced decrease in absorption in the visible range, particularly around 550 nm. However, the situation is slightly different on the water-adsorbed PbI₂-terminated surface. Initially, the absorption decreases significantly and then remains stable over time, indicating the relative stability of the PbI₂-terminated surface. The evolution of the absorption with time suggests that interacting water molecules gradually disrupt the perovskite structure, subsequently diminishing the performance of PSC devices. Ali Kachmar et al. calculated the absorption spectra of MASnI₃ before and after water infiltration into the crystal structure, showing that water molecules enhance the absorption of photon energies within the range of approximately 1–2 eV. However, as the photon energy further increases, the absorption coefficient of the monohydrated perovskite system decreases. Moreover, the introduction of water molecules into the system eliminates two distinct peaks in the absorption curve at 2.5 and 3.5 eV. Only at photon energies starting from 4.5 eV (i.e., after the maximum absorption peak) do the absorption coefficients become nearly equal.³¹

Md Azimul Haque et al. fabricated MAPbI₃ microstrips on a flexible substrate and observed a four-order-of-magnitude decrease in the microstrip resistance as the relative humidity levels varied from 10% to 95%. Additionally, the photocurrent response decreased with increasing humidity, and at a relative humidity level of 85%, the perovskite device no longer exhibited a photoresponse. The authors demonstrated a potential scenario for the interaction between perovskite and humidity. As shown on the left side in Fig. 7(c), moderate humidity or short-term exposure to high humidity conditions led to electron transfer from water molecules to the perovskite lattice. However, as depicted on the right side in Fig. 7(c), prolonged exposure to high humidity conditions resulted in degradation through different pathways in the perovskite.⁸¹

Thermalization of hot carriers is one of the main sources of efficiency loss in solar cells. Ali Kachmar et al. investigated the thermal electron cooling in both MASnI₃ and MASnI₃·H₂O within the tetragonal phase. In the case of the monohydrated perovskite, the cooling time is less than 1 ps. The overall trend is that the cooling process of hot electrons is faster in the MASnI₃·H₂O system compared to the MASnI₃ system. For energies higher than 2 eV, the cooling time of hot electrons appears to be less influenced by water molecules. This is because, in the case of the monohydrated system, the electron–phonon coupling (coupling between states in the conduction band) is stronger compared to the pristine system.³¹

5. Conclusions and outlook

In conclusion, the primary interaction between water molecules and perovskites is through hydrogen bonding between H₂O and the perovskite. This interaction has been summarized as various effects on the perovskite lattices and defects, which ultimately affect the crystal quality and the optoelectronic performance of devices. With an understanding of the diverse and significant effect of water molecules, component doping,^82,83 surface modification,^84,85 optimizing photovoltaic device encapsulation,⁸⁶ and process optimization^87,88 have been employed to enhance the stability of perovskite materials and devices. For example, Hongjun Chen et al. achieved robust and durable monolithic perovskite-based devices with the aid of rare-earth co-catalysts and effective charge transfer engineering at the co-catalyst interface. This resulted in a single-piece photoelectrode displaying a remarkable total solar-to-hydrogen efficiency of 8.54% without external assistance.⁸⁹

We observe that water's influence on perovskites presents both beneficial and detrimental aspects. The advantageous effects predominantly manifest at lower water concentrations, while escalated water concentrations or typical environmental conditions tend to elicit adverse repercussions on perovskite stability. This culminates in material degradation, significantly compromising device performance and ultimately impeding the commercialization trajectory of perovskite devices. Consequently, a more profound exploration of the interactions and mechanisms between water and perovskites is imperative. This endeavor aims to guide experimental endeavors in effectively enhancing perovskite humidity stability, thereby expediting their commercialization endeavors.

By employing these methods, the humidity stability of perovskite optoelectronic devices has been improved to a certain extent. However, further optimization of these approaches is still required to enhance stability under various environmental conditions.

From the perspective of theoretical calculations, there are several challenges in studying the influence of water molecules on perovskites:

(1) Complex interactions: the interactions between perovskites and water involve numerous chemical bonds and forces, making theoretical calculations highly complex. Consideration of factors such as charges, ion radii, bond lengths, and bond angles is necessary, posing significant challenges for computer simulations and theoretical analyses.

(2) Dynamics: the interaction between perovskites and water molecules exhibits high dynamics. Water molecules can form various complexes on the surface and within the perovskite, leading to continuous structural changes. This implies that theoretical calculations need to account for a large number of structural configurations and interactions, increasing computational difficulties.

(3) Time scale: the influence of water on perovskites is a long-time scale process under realistic conditions. Theoretical calculations require simulation over sufficiently long time-scales to capture various possible interactions and structural changes. This may result in computationally intensive tasks that require substantial computing resources.

(4) Temperature: in practical applications, perovskites may be exposed to different temperature conditions. These conditions can affect the interactions between water molecules and perovskites, thereby influencing their stability. When performing theoretical calculations, these factors need to be considered to accurately simulate real-world scenarios.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work was financially supported by the National Natural Science Foundation of China (Grants No. 62174072, 61674070, 12104345 and 11804117), the Natural Science Foundation of Guangdong Province (Grant No. 2022A1515010276) and the Uniqueness and Innovation Projects for the Universities in Guangdong Province (2022KTSCX010).

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Footnote

† These authors contributed equally to this work.

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