Compositional effect on water adsorption on metal halide perovskites

The moisture-induced instability of metal halide perovskites is one of the major challenges for perovskite de- vices. Although compositional engineering has been widely employed to improve the overall stability of perovskites, its effect on the moisture-induced instability received little attention. Here, we systematically study the interaction of water with the surfaces of primary perovskites, AMX 3 (A + = MA + , FA + , Cs + ; M 2+ = Pb 2+ , Sn 2+ ; X − = I − , Br − ), by using Density Functional Theory (DFT) calculations and comprehensive chemical bonding analysis. We reveal that the hydrophilic group NH 3+ of MA + cation may be the cause for instability issues. We find that the adsorption of water on FAPbI 3 and CsPbI 3 are much weaker than on MAPbI 3 due to the less polarity of FA + and Cs + . When exchanging M 2+ cations, water adsorption on MASnI 3 is also less en- ergetically favorable than on MAPbI 3 because of the weaker ionic interaction of H 2 O-MASnI 3 . When exchanging X − anion, water adsorption on MAPbBr 3 is slightly weaker than on MAPbI 3 due to the slightly weaker covalent interaction of H 2 O-MAPbBr 3 . Our results present a comprehensive understanding of the compositional effect on the interactions of water with perovskites and provide rational design strategies to improve their stability against moisture via compositional engineering. respectively. We finally discuss the effect of perovskite composition on the water adsorption and their underlying mechanisms and implications of our findings.

Moisture-induced degradation of the metal halide perovskites and perovskite solar cells are one of the most important stability issues [20][21][22][23][24]. Considerable efforts have been devoted to the understanding of the underlying mechanisms. It is generally believed that water adsorbs on the surface of perovskites and forms intermediate species, weakening the intrinsic structure of perovskites and facilitating the decomposition of perovskites to the binary compounds (namely PbI 2 and MAI) [25][26][27][28][29][30][31][32]. It is also proposed that water adsorption on the surfaces of the perovskites, as the first step, plays a key role in the degradation of the perovskites [33][34][35][36].
Some researches focused on the water adsorption on the mostly common studied MAPbI 3 . Koocher et al. [33] calculated the interaction of water and MAPbI 3 on both MAI-and PbI 2 -terminated surfaces at both low and high water concentration. They found the water is more likely to adsorb on MAPbI 3 when NH 3 group of MA + closed to the surface instead of CH 3 group. Mosconi and his colleagues [35] observed solvation of MAI on MAI-terminated surface and PbI 2 acts as a protective layer on PbI 2 -terminated surface due to the short Pb-I bond but the PbI 2 defects initiate the degradation of MAPbI 3 .
To improve the stability towards the moisture, several strategies, such as encapsulation, interface engineering and compositional engineering were widely explored [37][38][39][40][41][42]. For example, Jiang et al. [43] compared formation energy of the air molecules (H 2 O, O 2 , N 2 and CO 2 ) in the APbI 3 (A + = MA + , FA + and Cs + ) perovskites and found more hygroscopic of MAPbI 3 than FAPbI 3 and CsPbI 3 supported by the more negative formation energy of water in MAPbI 3 but left the mechanisms unexplained. He et al. [44] studied how water influences the adsorption energy and decomposition energy of APbI 3 . They concluded that CsPbI 3 shows better stability towards moisture than MAPbI 3 and FAPbI 3 due to the less decomposition energy of CsPbI 3 than that of MAPbI 3 and FAPbI 3 . Zhang et al. [30] found stronger water adsorption on MAPbI 3 than on MAPbBr 3 and they detailed the effect of halide anion on the deprotonation process of MA + cation. Jong et al. [45] investigated the water intercalation in MAPbX 3 and they presented a decreasing interaction strength when X − change from I − to Br − and Cl − , which means the increasing water resistant ability. Nevertheless, the effect of A + cation and M 2+ cation was not considered in their work. Thus, researchers studied either the effect of A + cation or M 2+ or X − anion on the interactions of water on metal halide perovskites. However, a comprehensive theoretical study on a complete comparison of all perovskites -including various and combined substitutions and different surface terminations is rarely seen. Moreover, a quantitative analysis of the composition-structure-property relation between water with a complete set of perovskite compositions is also missing.
In this work, we focus on the effect of the composition of perovskites on the water adsorption. By using DFT calculations and chemical bonding analysis, we show that the substitution of FA + or Cs + for MA + , Sn 2+ for Pb 2+ and Br − for I − changes the interaction strength between water and perovskites, therefore, changing their water-resistant property. In the rest of this article, we first present the computational details and then show all structural models and name the possible adsorption sites of water on perovskites. Thereafter, we report the atomistic structures, the adsorption energies and the chemical bonding characteristics of water adsorption on MAPbI 3 . We then compare the results of MAPbI 3 with other perovskites, where the A + or M 2+ or X − are exchanged in AMX 3 (A + = FA + , Cs + ; M 2+ = Pb 2+ , Sn 2+ ; X − = I − , Br − ) respectively. We finally discuss the effect of perovskite composition on the water adsorption and their underlying mechanisms and implications of our findings.

DFT Calculations
The DFT calculations were performed with PAW pseudopotential method as implemented in the Vienna Ab Initio Simulation Package (VASP) [46,47]. The Perdew, Burke, and Ernzerhof (PBE) functional within the generalized gradient approximation (GGA) exchange correlation was utilized [48]. The cut-off energy of the plane-wave basis was set to be 500 eV. Tetragonal structures were used for MA + and FA + perovskites and orthorhombic structures were used for Cs + perovskites for the structural optimization of the bulk. Then, the optimized bulk structures were used to cleave 1 × 1 (0 0 1) surface slabs with four repeating unit cells (including 4 AX-layers, 4 MX 2 -layers and one AX-/ MX 2 -terminated surface) in the z direction, including a vacuum of 15 Å. Top four layers and water molecule were allowed to relax until the residual force on each atom is smaller than 0.02 eV/Å. A 4 × 4 × 3 and 4 × 4 × 1 k-point mesh is used for bulk and surface calculations, respectively. The adsorption energies of water on the surface of perovskites were calculated as following: water surface surface water @ The positive value of E ads means water adsorption on the surface of metal halide perovskites is energetically unfavorable, indicating the hydrophobicity of perovskites. While the negative value of E ads represents water adsorption on the surface of perovskites is energetically favorable, indicating the hydrophilicity of perovskites.

Chemical bonding analysis
In addition to the energy calculations, we have also carried out an in-depth analysis of the chemical bonding for a thorough understanding of the energy variations at each adsorption site of each perovskite surface. The atomic population analysis method, Density Derived Electrostatic and Chemical (DDEC6) [49][50][51] was used. The bonds of main interests are those between water and the perovskite surfaces, as well as the bonds with the subsurface layer of the AMX 3 perovskites. The strength of the chemical bonding was analyzed by analyzing both the ionic and covalent contributions to a bond. The ionic component of the bond was evaluated from the investigation of the DDEC6 net atomic charges, which quantifies the electron transfer between atoms. The negative net charge indicates the atom is gaining electrons; positive net charge indicates the opposite. The covalent component can be identified from the investigation of the DDEC6 bond order. Quantifying the number of electrons dressed-exchanged between two atoms, the DDEC6 bond order is a functional of the electron and spin magnetization density distributions. Its formalism allows it to overcome limitations which are present in other bond order formulations. Thus, DDEC6 bond order approach exhibits good results when used in combination with various quantum chemistry methods (DFT-or wavefunction-based) and over a diverse set of materials and interactions [51]. Its values correlate well with the bond energies, within families of sufficiently similar materials [52,53]. The higher the bond order, the stronger the covalent bond. Similar approach has been used previously to investigate the interactions and reactivity of various systems, e.g. metal halide perovskite [54,55], 2D materials [56,57], porous media -zeolites, MOFs [58][59][60], hydrogen diffusion [61], etc.

. Perovskite surfaces and water adsorption sites
We first created ( Fig. 1a-d) two types of metal halide perovskite surfaces, i.e., AX-terminated and MX 2 -terminated surfaces. We, however, note that perovskites with MA + cation have two distinct surfaces on each termination (four surfaces in total) due to the different orientation of MA + cations. (+) denotes surfaces with NH 3 pointing to surface ( Fig. 1a, b) and (−) denotes surfaces with CH 3 pointing to the surface (Fig. 1c, d). Both FAPbI 3 and CsPbI 3 have only two possible surfaces ( Fig. 1e-h) because of the high symmetry of FA + and Cs + cations. We have then identified several possible adsorption sites for water on each of the possible surfaces shown in Fig. 1. We have detailed all specific adsorption sites and their atomic structures in Table 1 and Fig. 2, respectively.

Water adsorption on MAPbI 3
We start with the study of water adsorption on MAPbI 3 since it is the most commonly studied perovskite composition [31,36,62]. We note here that negative adsorption energies (E ads ) indicate the adsorption of water on the surface of MAPbI 3 is energetically favorable. Summarized in Table 2, we found the E ads to fall in the range from −0.11 eV to −0.51 eV, indicating water readily adsorbs onto all sites at surfaces of MAPbI 3 . The E ads obtained in this study are in good agreement with previous reports, with the maximum differences of less than 0.1 eV (see Table 2 for comparison). The differences can possibly be attributed to the use of different DFT codes, the calculation parameters and the convergence criterion.
A closer examination of the adsorption energies of water on MAPbI 3 allows us to identify a few trends: (1) on the MAI-terminated surface, the E ads at the (+) sites (NH 3 group pointing to surface) are generally more negative than those on (−) sites (CH 3 group pointing to surface); (2) the opposite is true for PbI 2 -terminated surfaces although the energy differences here are much smaller. This implies that water is readily adsorbed at (+) sites (NH 3 group pointing to surface) on MAI-terminated surface and the all sites PbI 2 -terminated surface.
The trends observed in the energies can be explained by the local atomistic structures. Indeed, the H 2 O-MAPbI 3 distance at (+) sites is overall shorter than that at (−) sites on MAI-terminated surface (Table  S1). The oxygen atom of the water (O) tends to interact with one of the hydrogen atoms of NH 3 (H N ), compared to the hydrogen of CH 3 Fig. 3d), which is also longer, and therefore weaker (adsorption energy of −0.16 eV) than the one at the (+) site. For the other sites on MAI-termination (i.e. β and γ sites), bond lengths of O-H N are evidently shorter (about 0.7 Å) than O-H C at β − and γ-sites, supporting overall weaker water adsorption at (−) sites than at (+) sites on MAI-terminated surface.
A detailed chemical bonding analysis of H 2 O-MAPbI 3 allows us to get a deeper understanding of the underlying reasons for the observed trends in energies and structures. We see the consistent agreement between the stronger bond order of H 2 O-MAPbI 3 , and the more negative adsorption energy of water on MAPbI 3 (Fig. 3a, b). The only exception is the δ sites and the underlining reason is discussed in supporting information and shown in Fig. S1. In agreement with the energies and structures, on MAI-terminated surface, a stronger bond (larger bond order) between O and H N at (+) sites is found than that between O and H C at (−) sites. The different bond strength of the two OeH bonds is a consequence of a competition within the bonding of OeHeN (C), where the O is part of H 2 O and H is part of NH 3 or CH 3 groups. The CeH C is stronger (bond order is 0.87) than NeH N (bond order is 0.74) (see also Table S2). The weaker NeH N bond leads to stronger OeH N (bond order: 0.21 at α + site) than OeH C (0.00 at α − site). In addition, NeH bond is more polar than the CeH, and therefore more prone to be involved in hydrogen bonding [63]. As a result, NH 3 group is hydrophilic; while CH 3 is hydrophobic. Similar preference is found for the interaction of water with other absorption sites, where water maximizes its interaction with H N (bond order of O-H N : around 0.12 at β + and γ + ) and minimizes it with H C (bond order of O-H C around 0.05 at β − and γ − ), explaining the fact the adsorption energies on the (+) sites are overall more negative (above 0.20 eV) than those on the (−) sites.
In contrast with the drastic changes in both energies and structures on the MAI-termination, the changes on the PbI 2 -termination are relatively small. This is because the effect of MA + cation (now located in the sub-surface) is less dominating now. Indeed, the main difference is coming from the interaction strength of MA + with the inorganic framework on the surface: a slightly stronger hydrogen bond of I-NH 3 (total bond order of 0.14) than I-CH 3 (total bond order of 0.04) leads to slightly weaker adsorption of H 2 O on (+) sites than on (−) sites (Table  S3). Therefore, water slightly favors (−) sites than (+) sites. However, we note that here all adsorption energies found on the PbI 2 -termination are quite large due to the very strong O-Pb bonds (bond order: ~0.30, Fig. S2) and moderately strong H 2 O-I interaction (bond order: around 0.17 at (+) sites and 0.26 at (−) sites, Fig. S2).
All the above analysis indicates that the adsorption of water on all MAPbI 3 surfaces are overall strong, with the only exception when it is in direct contact with the hydrophobic CH 3 group of MA + cation. This agrees with the previous reports on the strong interaction of water on the MAPbI 3, in particular with the NH 3 group [26]. This strong interaction is the first step before its degradation reaction, namely, the deprotonation of the NH 3 group of MA + to form the volatile CH 3 NH 2 [25,26,30].

The effect of A + cation
To evaluate the effect of A + cation, we investigated the adsorption of H 2 O on FAPbI 3 and CsPbI 3 surfaces and further compared them with those on MAPbI 3 surfaces. We find that the adsorption energies on FAPbI 3 and CsPbI 3 surfaces are generally less negative than those on MAPbI 3 (Fig. 4a), which indicates that water is less favorable to adsorb on FAPbI 3 and CsPbI 3 . We rationalize the findings below by comparing the structures and analyzing the chemical bonding, while the exception of water bonding at β − and δ sites is discussed in the supporting information.
On AI-termination, as shown above with the case of MA + , the difference in the optimized position of water between α + site and α − site depend very much on the hygroscopicity (polarity) of A + cation: water prefers to adsorb at the sites where the hydrophilic NH 3 group points to the surface rather than the hydrophobic CH 3 group. Interestingly, the optimized position of water as well as their adsorption energies at α + site of FAPbI 3 and CsPbI 3 are similar to α − site of MAPbI 3 , when the hydrophobic CH 3 group points to the surface. As presented in Fig. 4c- As shown earlier, the evaluation of bond order between H 2 O and MAPbI 3 is a useful tool to understand and quantify the effect of various adsorption sites on the absorption energies of H 2 O. However, it's not straightforward to compare the chemical bond strength from bond orders when bonds with various covalent/ionic ratios are present. This is possibly the reason we observe certain discrepancies when we vary the A + cation and we look at the bond orders of the bonds between H 2 O and the surfaces of APbI 3 (Fig. 4a, b). Very different characters of A + cation (organic, inorganic) lead to bonds which are significantly different and not easily comparable [52,53]. In Fig. 4f we observe that the FA + bonds including NeH (bond order of 0.95 to 0.99) and CeH (bond order of 0.99) are with similar strength, and much stronger than the NeH (0.74) and slightly stronger than CeH (0.87) bonds from MA + . As a consequence FA + will be less reactive than MA + Furthermore, MA + is more polar than FA + and Cs + [64], evidenced by the less symmetric bond orders in Fig. 4f and charge distribution from net atomic charges of all atoms in Fig. S2a·H 2 O as a polar molecule tends to interact with polar cations. Less polarity in FA + and Cs + lead to energetically unfavorable absorption of water on FAPbI 3 /CsPbI 3 than MAPbI 3 . Therefore, our analysis suggests that substituting or mixing polar molecule MA + cation with less polar cations, such as FA + , Cs + and GA + (C(NH 2 ) 3 + ) can be a feasible strategy for improving the water resistance of metal halide perovskites [38]. On PbI 2 -termination, the adsorption energies of water on FAPbI 3 and CsPbI 3 do not change as significantly (energy differences within 0.04 eV) when comparing with MAPbI 3 , as it was the case for the AXterminated surfaces, with majority of interactions being slightly weaker (bond length of OePb with differences within 0.05 Å). 1 And the adsorption energies of FAPbI 3 and CsPbI 3 are closed to the more hydrophobic (+) surfaces of MAPbI 3 , except for the δ sites. This is because of the stronger interaction of the subsurface cations with the surface I atoms leads to overall slightly weaker H 2 O-I interactions. In particular, FA + -I bonds with a total bond order of 0.39 (in Table S5) and Cs + -I bonds with a total bond order of 0.18 are both larger than that of the (+) surface of MA + -I (0.17).

The effect of M 2+ metal
M 2+ divalent cation also affects water adsorption on perovskites. The calculated adsorption energies of water on MASnI 3 are generally  less negative than those on MAPbI 3 . We observe the same trend in adsorption energies influenced by the orientation of MA + cations, i.e., on MAI-termination, E ads at (−) sites being less negative than that at (+) sites; on MI 2 -termination, E ads at (+) sites are less negative than that at (−) sites. The adsorption energies on MAI-terminated surface do not show an obvious change for each adsorption site when Pb 2+ is exchanged with Sn 2+ (Fig. 5a), with differences in energy within less than 0.05 eV. On the MI 2 -termination, the adsorption energies of water on the SnI 2 -terminated surfaces are in general (about 0.1 to about 0.3 eV) less negative than those on PbI 2 -terminated surface. We note here that the structural details including bond lengths and bond orders of H 2 O-MAPbI 3 and H 2 O-MASnI 3 do not provide direct evidences for the energy differences (Table S6). For example, at ε − site from Fig. 5c, d, we find slightly shorter MeO bond (0.09 Å shorter) as well as slightly longer H W -I (0.06 Å and 0.09 Å longer) bonds on MASnI 3 than those on MAPbI 3 . This can be further understood by considering both the covalent and ionic interactions of water molecules with the surfaces of MAMI 3 as following.
On MI 2 -terminated surface, the O with the lone pair electron interacts with the metal divalent acceptor, while H W acceptors interact with Iodine which act as the donors. On the one hand, we found very similar covalent interaction of H 2 O-MASnI 3 and H 2 O-MAPbI 3 from bond orders in Fig. S3a; on the other hand, we observe significant differences in net atomic charges in Fig. 5b, which depends significantly on the electronegativity of M 2+ cation. With an electronegativity of Pb (2.3) being closer to that of I (I: 2.5, Sn: 1.8) [65][66][67], the net atomic charge of Pb (~0.84) is more positive than Sn (~0.70) as depicted in Fig. 5b. As a result, the attraction of Pb with O is stronger than that of Sn, i.e. stronger ionic interaction of OePb (1.92 × 10 9 N) than OeSn (1.64× 10 9 N) according to Coulomb's law (Eq. (1)). Furthermore, the net atomic charge of I (−0.50) in MAPbI 3 is more negative than I (−0.44) in MASnI 3 . Consequently, it leads to a stronger interaction between H W -I on MAPbI 3 than on MASnI 3 . Taking into account the where K e is Coulomb's constant (K e ≈ 9 × 10 9 N⋅m 2 ⋅C −2 ), q and q' are the charges of the two atoms, and the r is the distance between these two atoms.

The effect of X − halide
Water adsorption on perovskites is slightly influenced by the Xhalide. Overall, from Fig. 6a, the change in E ads between MAPbI 3 and MAPbBr 3 is small, with the values on MAPbBr 3 being slightly less negative than those on MAPbI 3 . For instance, at the γ − sites, water adsorption energy on MAPbBr 3 is slightly less negative by ~0.04 eV than those on MAPbI 3 (see Fig. 6a). Moreover, the same trend as in Section 3.2 in adsorption energies is found on MAX-termination, E ads at (−) sites are less negative than that at (+) sites; on PbX 2 -termination, the trend in E ads is reversed. This shows that the orientation of MA + dominates the changes in the adsorption energies on both MAX-terminated and PbX 2 -terminated surfaces regardless of the types of metal cation or halide anion.
The bond length of H 2 O-MAPbX 3 (Table S7) also demonstrates that water has slightly less affinity with surfaces of MAPbBr 3 than those of MAPbI 3 . This is attributed to the slightly weaker covalent interaction of H 2 O-Br than H 2 O-I (shown in Fig. 6b and Fig. S4a). This is demonstrated also by the example shown in Fig. 6c, d, where water interacts with two I atoms (with bond orders of 0.11 and 0.06) on MAPbI 3 surface, but only with one Br atom on MAPbBr 3 (bond order of 0.14), as the second bond H W2 -Br 2 (3.96 Å) is too long and does not lead to an interaction (bond order: 0) Adding all contributions altogether, the interaction strength of H 2 O-MAPbBr 3 is slightly weaker than that of H 2 O-MAPbI 3 . The exception case of α − site is discussed in the supporting information.
On PbX 2 -termination, similar trends are observed, slightly less negative E ads (within 0.05 eV) of water on MAPbBr 3 than on MAPbI 3 . This is proven by the slightly weaker interaction of H 2 O-MAPbBr 3 than H 2 O-MAPbI 3 (difference of bond order within 0.03, the differences of bond length of O-Pb less than 0.04 Å and H W -X less than 0.3 Å). This indicates that water generally interacts less strongly with MAPbBr 3 not only for the MAX-termination but also for the PbX 2 -termination. The above finding demonstrates that the substitution of I by Br is beneficial to repel water and to avoid the degradation induced by moisture.

Discussion
Our new results are further discussed and analyzed here in the context of the existing experimental results. In this work, we focus on the impact of the compositional change in the adsorption strength of water on diverse halide perovskite surfaces. We note that directly comparing our results with experiments is not straightforward because understanding the overall stability of perovskites is a complex scientific problem. In addition to the stability towards moisture, tuning the composition of the perovskite also impact the structural/phase stability [22], the morphology [54], the types and the concentration of intrinsic defects [68] and more. Moreover, the moisture induced degradation of perovskites is a collective/multistep process, involving adsorption on the surfaces/grain boundary, infiltration and diffusion into the bulk, and dissociation reactions [35,36,69].
Nevertheless, our analysis of the water adsorption strength on different perovskites is consistent with the existing experimental findings that partially substituting MA + with FA + and Cs + [38,39] or partially substituting I − with Br − [1] enhanced the stability of MAPbI 3 towards moisture. This indicates that the initial chemical bonding interaction of water with the surface has important implications on overall degradation processes.
To obtain a more comprehensive understanding of the degradation processes, molecular dynamics [36,70,71] is a very useful method to investigate kinetics and to study temperature effect. For example, rotation of methylammonium was discovered in both experiments [72] and theoretical simulations [73,74]. The rotation of MA + was found to be possible at room temperature and become more pronounced with increasing temperature [75]. Consequently, a dynamical interaction of water with MA + cations can be expected at high temperature. Particularly, the metal halide perovskites with a polar A + cation (such as MA + and FA + et al.) would be notably affected by the change of temperature. Another important aspect that is not covered in this work is the effect of water vapor (instead of one isolated water molecule). Water vapor was previously proposed to play an important role in solvating MA + and I − ions and inducing degradation reactions [35].
However, all above-mentioned dynamical properties are beyond the scope of this study due to the high cost of ab-initio methods. To fully understand the collective mechanism of the water induced degradation of perovskites, our future plan is to expand the current DFT study to classical molecular dynamics simulations using reactive force fields [76][77][78].

Conclusions
In summary, using DFT calculations and chemical bonding analysis, we have investigated water adsorption on several primary metal halide perovskites. We studied the adsorption energies, adsorption structures and chemical bonding between water and MAPbI 3 and elucidated the compositional effect of the perovskites by substituting FA + and Cs + for MA + , Sn 2+ for Pb 2+ and Br − for I − on their interactions with water. We find that the adsorption of water on MAPbI 3 is overall strong with the exception of surface sites near the hydrophobic CH 3 group of MA + cation. This points to the general knowledge of the instability of MAPbI 3 towards moisture. When substituting FA + or Cs + for MA + , adsorption of water on the surface of FAPbI 3 and CsPbI 3 is less favorable than on MAPbI 3 . This is mainly due to the smaller or zero polarity (which means the more hydrophobic nature) of FA + or Cs + (which leads to more hydrophobic surfaces). Our results indicate that substituting or partially substituting the polar MA + with less polar FA + or nonpolar Cs + can potentially increase the stability of the resulted perovskites. When exchanging M 2+ cations (Sn 2+ for Pb 2+ ), due to the weaker ionic interaction of H 2 O-MASnI 3 than H 2 O-MAPbI 3 , MASnI 3 shows slightly better water resistance than MAPbI 3 . For different X − anion, the adsorption energy of water on MAPbI 3 and MAPbBr 3 are comparable. Surprising result is that the interaction of water with bromides is weaker than iodines though the ionicity of MAPbBr 3 is higher than MAPbI 3 . The substitution of Br − for I − slightly weakens the covalent interaction of H 2 O-MAPbX 3 , decreasing the possibility of adhesion of water on MAPbBr 3 . The stronger interaction of I with water has to do with a stronger covalent bonding and a better geometrical compatibility of the water molecule with the I atoms at the surfaces (e.g. two H-I bonds compared to the single H-Br bond). Our study provides a comprehensive understanding of the effect of the perovskite composition on water adsorption on metal halide perovskites and further provides the rational strategies to improve the stability against moisture through compositional engineering.

Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.