Unraveling the water degradation mechanism of CH$_3$NH$_3$PbI$_3$

TL;DR

This study uses ab initio metadynamics to elucidate the water-induced degradation mechanism of CH$_3$NH$_3$PbI$_3$ perovskite, revealing a low energy barrier and spontaneous dissolution process that explain its instability in water.

Contribution

It provides a detailed molecular-level understanding of water degradation in MAPbI$_3$, including a thermodynamic cycle and comparison with inorganic perovskites, advancing the knowledge of perovskite instability.

Findings

Initial dissolution involves I$^-$ ion departure from the surface.

Water dissolution has a low energy barrier.

Dissolution in water is thermodynamically spontaneous.

Abstract

Instability of perovskite photovoltaics is still a topic which is currently under intense debate, especially the role of water environment. Unraveling the mechanism of this instability is urgent to enable practical application of perovskite solar cells. Here, ab initio metadynamics is employed to investigate the initial phase of a dissolution process of CH$_3$NH$_3$PbI$_3$ (MAPbI$_3$) in explicit water. It is found that the initial dissolution of MAPbI$_3$ is a complex multi-step process triggered by the departure of I$^-$ ion from the CH$_3$NH$_3$I-terminated surface. Reconstruction of the free energy landscape indicates a low energy barrier for water dissolution of MAPbI$_3$. In addition, we propose a two-step thermodynamic cycle for MAPbI$_3$ dissolution in water at a finite concentration that renders a spontaneity of the dissolution process. The low energy barrier for the initial dissolution step and the spontaneous nature of MAPbI$_3$ dissolution in water explain why the water immediately destroys pristine MAPbI$_3$. The dissolution thermodynamics of all-inorganic CsPbI$_3$ perovskite is also analyzed for comparison. Hydration enthalpies and entropies of aqueous ions play an important role for the dissolution process. Our findings provide a comprehensive understanding to the current debate on water instability of MAPbI$_3$.

Tables

Table 1. Table 1 : Electronic total energy E tot subscript 𝐸 tot E_{\text{tot}} per formula unit (f.u.), H T − H 0K subscript 𝐻 𝑇 subscript 𝐻 0K H_{T}-H_{\text{0K}} , standard state entropy S T ∘ subscript superscript 𝑆 𝑇 S^{\circ}_{T} , the chemical potential μ ~ T ∘ subscript superscript ~ 𝜇 𝑇 \tilde{\mu}^{\circ}_{T} and standard Gibbs free energy G T ∘ subscript superscript 𝐺 𝑇 G^{\circ}_{T} in the first step of the thermodynamic cycle involving \ch MAPbI3 dissolution in water. Here, we focus on room temperature T = 298.15 𝑇 298.15 T=298.15  K.

Species	$E_{\text{tot}}$	$H_T-H_{\text{0K}}$	$S_T^{\circ }$	${\tilde{\mu }}_T^{\circ }$	$G_T^{\circ }$
	(eV/f.u.)	(kJ/mol)	(J ${\text{mol}}^{-1}{\text{K}}^{-1})$	(eV/f.u.)	(eV/f.u.)
\chMAPbI3 (s)	$-$50.93	44.79a	374.13a	$-$0.69	$-$51.62
\chPbI2 (s)	$-$8.63	19.50b	174.84b	$-$0.34	$-$8.97
\chMA+ (g)	$-$32.84	6.20b	327.7b	$-$0.95	$-$33.79
\chI- (g)	$-$3.40	6.20b	169.26b	$-$0.46	$-$3.86
\chCsPbI3 (s)	$-$14.25	20.28c	219.61c	$-$0.47c	$-$14.72
\chCs+ (g)	3.83	6.20b	169.84b	$-$0.46	3.37
\chMAI(s)	$-$42.36	22.25d	159.7d	$-$0.26	$-$5.69
\chCsI(s)	$-$5.45	13.50e	123.1e	$-$0.24	$-$42.62

Table 2. Table 2 : Hydration enthalpy Δ ​ H hyd ∘ Δ subscript superscript 𝐻 hyd \Delta H^{\circ}_{\text{hyd}} , entropy S T ∘ subscript superscript 𝑆 𝑇 S^{\circ}_{T} (aq) of aqueous ions, and Gibbs free energy G T ∘ subscript superscript 𝐺 𝑇 G^{\circ}_{T} of species involved in the second step of the thermodynamic cycle of \ch MAPbI3 dissolution in water at room temperature 298.15 K.

Species	$\Delta H_{\text{hyd}}^{\circ }$	$S_T^{\circ }$(aq)	${\tilde{\mu }}_T^{\circ }$(aq)	$G_T^{\circ }$
	(kJ/mol)	(J ${\text{mol}}^{-1}{\text{K}}^{-1})$	(eV/f.u.)	(eV/f.u.)
\chMA+ (aq)	$-$284.6a	142.7b	$-$3.33	$-$36.17
\chI- (aq)	$-$305.0c	111.3d	$-$3.44	$-$6.84
\chCs+ (aq)	$-$264.0c	133.1d	$-$3.08	0.75

Equations

$${\text{CH}}_3{\text{NH}}_3{\text{PbI}}_3(\text{s})\stackrel{{\text{H}}_2\text{O}}{\to }(-{\text{CH}}_2-)+{\text{NH}}_3(\text{g})+\text{HI}(\text{g})+{\text{PbI}}_2(\text{s}).$$

$${\text{CH}}_3{\text{NH}}_3{\text{PbI}}_3(\text{s})\stackrel{{\text{H}}_2\text{O}}{\to }{\text{CH}}_3{\text{NH}}_3\text{I}(\text{aq})+{\text{PbI}}_2(\text{s}).$$

$$\tilde{H}(t)=H+\tilde{V}(t,\xi ),$$

$$\tilde{V}(t,\xi )=h\sum _{i=1}^{\lfloor t/t_{\text{G}}\rfloor }\text{exp}\left[-\frac{|{\xi }^{(t)}-{\xi }^{(i\cdot t_G)}{|}^2}{2w^2}\right].$$

$${\xi }_1=\sum _{i=1}^M\frac{1-(q_i/c_i{)}^9}{1-(q_i/c_i{)}^{14}}$$

$$A(\xi )=\underset{t\to \infty }{\lim }\tilde{V}(t,\xi )+\text{const}.$$

$${\text{CH}}_3{\text{NH}}_3{\text{PbI}}_3(\text{s})\stackrel{\Delta G_{\text{diss}}}{\to }{\text{CH}}_3{\text{NH}}_3^{+}(\text{aq})+{\text{I}}^{-}(\text{aq})+{\text{PbI}}_2(\text{s}).$$

$$G_T^{\circ }=E_{\text{tot}}+{\tilde{\mu }}_T^{\circ }.$$

$${\text{CH}}_3{\text{NH}}_3{\text{PbI}}_3(\text{s})\stackrel{\Delta G_1}{\to }{\text{CH}}_3{\text{NH}}_3^{+}(\text{g})+{\text{I}}^{-}(\text{g})+{\text{PbI}}_2(\text{s}).$$

$${\tilde{\mu }}_T^{\circ }=H_T^{\circ }-H_{\text{0 K}}^{\circ }-T{S}_T^{\circ }.$$

$$\Delta G_1=G_{T,{\text{MA}}^{+}(\text{g})}^{\circ }+G_{T,{\text{I}}^{-}(\text{g})}^{\circ }+G_{T,{\text{PbI}}_2}^{\circ }-G_{T,{\text{MAPbI}}_3}^{\circ }.$$

$${\text{MA}}^{+}(\text{g})+{\text{I}}^{-}(\text{g})+{\text{PbI}}_2(\text{s})\stackrel{\Delta G_2}{\to }{\text{MA}}^{+}(\text{aq})+{\text{I}}^{-}(\text{aq})+{\text{PbI}}_2(\text{s}).$$

$${\tilde{\mu }}_T^{\circ }(\text{aq})={\tilde{\mu }}_T^{\circ }+\Delta H_{\text{hyd}}-T(S_T^{\circ }(\text{aq})-S_T^{\circ }).$$

$$\Delta G{}_2=G_{T,{\text{MA}}^{+}(\text{aq})}^{\circ }+G_{T,{\text{I}}^{-}(\text{aq})}^{\circ }-G_{T,{\text{MA}}^{+}(\text{g})}^{\circ }+G_{T,{\text{I}}^{-}(\text{g})}^{\circ }$$

$$\text{Cs}{\text{PbI}}_3(\text{s})\stackrel{\Delta G_1}{\to }{\text{Cs}}^{+}(\text{g})+{\text{I}}^{-}(\text{g})+{\text{PbI}}_2(\text{s}).$$

$${\text{Cs}}^{+}(\text{g})+{\text{I}}^{-}(\text{g})+{\text{PbI}}_2(\text{s})\stackrel{\Delta G_2}{\to }{\text{Cs}}^{+}(\text{aq})+{\text{I}}^{-}(\text{aq})+{\text{PbI}}_2(\text{s}).$$

$$\text{Cs}{\text{PbI}}_3(\text{s})\stackrel{\Delta G_{\text{diss}}}{\to }{\text{Cs}}^{+}(\text{aq})+{\text{I}}^{-}(\text{aq})+{\text{PbI}}_2(\text{s}).$$

$$\mathrm{ch}MAPb{I}_3(\text{s})\to \mathrm{ch}MAI(\text{s})+\mathrm{ch}PbI2(\text{s}).$$

$${\mu }_T\approx {\tilde{\mu }}_T^{\circ }(\text{aq})+k_{B}T\ln (a_{\pm }).$$

$$a_{\pm }=({\gamma }_{\pm }c/c^{\circ }{)}^2$$

Full text

McMaster University] Department of Materials Science and Engineering, McMaster University, Hamilton

McMaster University] Department of Materials Science and Engineering, McMaster University, Hamilton

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1 Introduction

Evolution of hybrid halide perovskite solar cells makes a contribution to the goal of replacement of fossil fuels. High power conversion efficiency and low fabrication cost raise perovskite photovoltaics as a tough competitor against the silicon solar cells. Since the inception of halide perovskite solar cells with 3.8% power conversion efficiency in 20091, within 10 years of development, the world record power conversion efficiency of perovskite photovoltaics has reached 24.2% according to the efficiency chart published by the National Renewable Energy Laboratory. However, the poor stability of perovskite photovoltaic absorbers still remains unsolved and hinders the solar cells entering people’s daily life.

Among the stimuli caused degradation of hybrid perovskite, water is confirmed to degrade \chMAPbI32. Whereas, the role of water incorporation into \chMAPbI3 remains a topic of debate, with conflicting results reported in the literature. It is found the moisture invasion fractures the connection of \chC-N in \chCH3NH3 (MA) and generate ammonia and hydrogen iodide3, 4

[TABLE]

Kakekhani et al. 5 propose a super-hydrous state of water incorporation in \chMAPbI3 to explain deterioration of its photovoltaic properties in a moist environment. Besides, Philippe et al. 6 and Niu et al. 7 proposed a decomposition mechanism relating to the presence of \chCH3NH3I (\chMAI) and \chPbI2,

[TABLE]

In fact, two extreme water content conditions are discussed above: atmospheric moisture and liquid water. Both of the mechanisms are important. For fresh perovskite photovoltaics, moisture degradation is obviously important for the endurance. There are plenty of publications investigating the moisture induced degradation of \chCH3NH3PbI38, 9, 10, 11, 12, 13, 14, 15. As photovoltaics, it has to be considered that different situations the cells will encounter, e.g. after couple of years, cracks of the photovoltaic modules are inevitable16. At this stage, understanding of liquid water degradation mechanism becomes important. Especially, hybrid halide perovskites contain lead element. There are less investigations about the liquid water degradation pathway17, 18, 19. It is still unclear about the mechanism of \chCH3NH3PbI3 degradation in liquid water, such as the energy barrier, decomposition details.

Key challenges in understanding the degradation mechanism of \chMAPbI3 are the difficulties in determining the surface chemistry of the first few atomic layers of the pristine material without any exposure to ambient atmospheric conditions, and, conversely, the difficulties in measuring this same surface chemistry in real time under exposure to realistic environments4. Molecular dynamics (MD) make it possible to explore the degradation mechanism at the atomic level. Mosconi et al. 17, Caddeo et al. 19 simulated the heterogeneous interface between water and \chMAPbI3 to study its water degradation mechanism. Mosconi et al. 17 observed first \chMAI unit dissolved within 8.5 ps using an ab initio molecular dynamics (AIMD). Caddeo et al. 19 observed a fast dissolution of outermost \chMAI-terminated layers within 10 ps using classical molecular dynamics. Whereas, the details of the initial phase of the degradation process, such as energy barriers of corresponding steps, and the preference of ions leaving the surface are still missing. We performed AIMD simulation for water and \chMAPbI3 interface aiming to clarify the degradation mechanism of \chMAPbI3 in water. Contrary to previous reports of a short degradation time, our AIMD simulation of the heterogeneous interface renders no dissolution event happening within 12 ps. This phenomenon questions the immediacy of \chMAPbI3 degradation in water. 2 During 12 ps standard AIMD simulation, we observed both \chI- and \chMA+ ions trying to detach from the \chMAPbI3 surface. As time passed by, the ions retrace back to the \chPb-I framework cavity. Thus, the dissolution event reported in Ref. 17 could be an artefact due to a limited simulation time of about 10 ps.

The ionic nature of \chMAPbI3 8, 20 allows to draw a parallel to the research on simulation of \chNaCl dissolution. Intriguingly, Liu et al. 21 and Chen et al. 22 encountered the same situation when dissolving \chNaCl using MD. A single ionic dissolution is a rare event, which is unlikely to happen on the time scale of an AIMD simulation. Therefore, the dissolution needs to be "driven" artificially22. Metadynamics23, 24, 25 is a powerful algorithm that can be used both for probing the free energy landscape and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. Since the dissolution of \chMAPbI3 in water is viewed as a rare event, it needs a much longer simulation time to capture the dissolution, and this finding raises a question about validity of conclusions drawn from the relatively short 10 ps simulation19.

In the current research, we propose the water degradation mechanism employing the capability of ab initio metadynamics which uses computational sands to fill the initial potential valley and to force the trapped system from the initial basin and explore the energy landscape. And it gives the possibility to describe the heterogeneous interface with a large system from the atomic level, dynamically and considering finite temperature effects. Hence, the method can accelerate and capture the dissolution process of \chMAPbI3 in water. Here, the free energy surface (FES) of water dissolution \chMAPbI3 can be reconstructed based on the historical computational sands added to the basin. The obtained FES suggests a relatively low energy barrier of the first step of the dissolution process. In addition, an analysis based on a thermodynamic cycle for dissolution \chMAPbI3 explains the intrinsic water instability of \chMAPbI3. The low dissolution energy barrier and spontaneous dissolving trend together unravel the fragile nature of \chMAPbI3 when encountering water.

1.1 Computational method

Electronic structure calculations have been performed in the framework of DFT 26 and Perdew-Burke-Ernzerhof generalized gradient approximation27 (GGA-PBE) for the exchange-correlation functional. Van der Waals correction is important for halide hybrid perovskite28, 29. Among different van der Waals corrections, Li and Yang 30 employed both optb86B-vdW31 and PBE+D3 method32 to optimize structures. The results show that both the vdW functionals can give accurate crystal structure predictions. And the PBE+D3 method acts even better than optb86B-vdW when comparing with experimental data. Except for the structural properties, our previous work29 analyzed the polymorphism of \chMAPbI3 employing different functionals including PBE+D3. We concluded that the PBE+D3 can accurately predict the trend of polymorphism of \chMAPbI3. It indicates PBE+D3 can capture the total energy estimation very well. Hence, the PBE+D3 level van der Waals correction is considered for all calculations. Total energies of all compounds were obtained using the Vienna ab initio simulation program (VASP) and projector augmented-wave (PAW) potentials 33, 34, 35.

The phase separation energy difference $\Delta E_{\text{tot}}$ of \chMAPbI3 and \chCsPbI3 are adopted from our previous calculations36. For reciprocal space integration, $3\times 3\times 2$ Monkhorst-Pack grid 37 was used for tetragonal \chMAPbI3, $4\times 4\times 3$ for hexagonal \chPbI2 and $3\times 6\times 2$ for orthorhombic \chCsPbI3. The convergence of $\Delta E_{\text{tot}}$ with respect to the k-mesh density was tested via doubling the density for investigated perovskite structures and corresponding decomposed structures. And the convergence is better than 5 meV. The cutoff energy for a plane wave expansion was set at 400 eV. The lattice constant and atomic positions were optimized such that residual forces acting on atoms did not exceed 2 meV/Å, and the residual hydrostatic pressure was less than 50 MPa.

For AIMD calculations, a semi-empirical scaling method38, 39 is used to achieve a finite-temperature structure of \chMAPbI3 that is self-consistent with PBE functional with the van der Waals correction. According to scanning tunnelling electron microscopy studies of \chMAPbI340, 41, we selected a \chMAI-terminated (001) surface structure of tetragonal \chMAPbI3. The \chMAPbI3 slab was modelled as $2\times 2$ in plane per-optimized tetragonal supercell with the thickness of 7 atomic layers spaced by 18.6 Å filled by water molecules (see Fig. 1). The number of water molecules embedded is 158 which is obtained based on the experimental liquid water density. The dimension of the periodic cell are $a=b=17.72$ Å which corresponds twice of the size of tetragonal \chMAPbI3. In total, we have $c=38.35$ Å for the heterogeneous structure. In order to obtain an initial randomization of the atomic positions, we performed a standard AIMD simulation in two stages: pre-heating followed by a fixed temperature relaxation. Pre-heating from 0 to 300 K was performed in 700 steps (step size of 1 fs) using a linear ramp-up function (VASP tag $\text{SMASS}=-1$). Velocities were scaled every 20 MD steps. Although the orientations of \chMA+ cations on surface are anisotropic after this two-stage relaxation, we noticed the \ch-NH3+ groups of \chMA+ ions are attracted by oxygen atoms from ajdacent water molecules during relaxation. Accuracy of computed Hellmann-Feynman forces was determined by the energy convergence criterion of $10^{-6}$ eV. Only one $k$ point at $\Gamma$ was used to sample the Brillouin zone. Atomic positions and velocities at the end of the preheating stage were taken as the input for the fixed temperature relaxation. The fixed temperature relaxation was conducted at 300 K for $\sim{9.8}$ ps (step size of 1 fs). A Nosé–Hoover thermostat42, 43 was used to stabilize the temperature (VASP tag $\text{SMASS}=0$). Atomic positions during AIMD were stored every 20 steps. Crystallographic information files (CIF) with atomic structures used in calculations can be accessed through the Cambridge crystallographic data centre (CCDC deposition numbers 1919295$-$1919299).

Metadynamics was applied to accelerates the rare events of the heterogeneous interface (VASP tag $\text{MDALGO}=21$). It is realized by augmenting the system Hamiltonian $\tilde{H}(t)$ with a time-dependent bias potential $\tilde{V}(t,\xi)$ which acts on selected collective variables $\xi=\{\xi_{1},\xi_{2},...,\xi_{m}\}$

[TABLE]

where $H$ stands for the original Hamiltonian of unbiased system. $\tilde{V}(t,\xi)$ is defined as a sum of Gaussian hills with height $h$ and width $w$,

[TABLE]

During the metadynamic simulation, $\tilde{V}(t,\xi)$ is updated by adding a new Gaussian with a time increment $t_{\text{G}}$ which is set to 100 fs. A collective variable (CV) is a function of the particle positions. We employed two CVs in the current metadynamics. The first CV ($\xi_{1}$) is defined as the coordination number

[TABLE]

of the departing \chI- (or N atom of monitored \chMA+ during a paralleled \chMA+ dissolution) with the rest \chI- (or N atoms of other \chMA+) in the topmost complete layer of the surface. $M$ is the number of \chI- in the topmost layer except the monitored \chI- (or N atom in \chMA+). $c_{i}$ is defined as the interatomic distance between the monitored \chI- (or N atom in \chMA+) and each rest of \chI- (or N atom in \chMA+) in the initial state. $q_{i}$ is the on-the-fly interatomic distance between the monitored \chI-(or N atom in \chMA+) and each rest of \chI- (or N atom in \chMA+) during the simulation.

The second CV ($\xi_{2}$) records the interatomic distance between the monitored \chI- and \chPb^2+ underneath it. An estimate of the underlying free energy $A(\xi)$ can be obtained via a sufficiently long time simulation,

[TABLE]

The choice of coordination numbers and \chPb-I distance as two CVs is because these CVs vary according to different dissolution stages. CV ($\xi_{2}$) directly indicates the dissolution process of the monitored \chI- ion. However, only CV ($\xi_{2}$) is not sufficient to tell the difference between the states of \chI- ion attached on surface and further dissolution in water. CV ($\xi_{1}$) is able to reflect the bond breaks accompanying the leaving of \chI- ion. Combination with CV ($\xi_{1}$), it is clear to explore an intermediate state. Liu et al. 21 used different combination of CVs and determined that the settings same as we used are the best combination to characterize the dissolution event.

After the standard $\sim{9.8}$ ps MD, the width of Gaussian hill is determined from a continuous 1.8 ps metadynamics which monitors the two CVs without adding hills. The amplitudes of these CVs in the reactant well indicate the width of the well44, and we set $w=0.11$. Considering our large system (more than 800 atoms) and complexity of the dissolution procedure, we set $h=0.026$ eV from IS to IM. After passing the IM state, we increased the Gaussian height to 0.052 eV. To characterize the hydrogen bonds between water molecules and \chI-, we set the bonding searching range to 3.25 Å 45. Plumed package46 and Gnuplot were utilized to reconstruct and plot the FES of dissolution events. VESTA 3 package 47 was used to visualize crystal structures.

2 Results and discussion

2.1 Dissolution energy barrier estimation

In this section, it will be shown that \chMAPbI3 dissolution is a complex multi-step process triggered by the initial departure of \chI- ions from the \chMAI-terminated surface. The choice of the \chMAI-terminated surface as a starting point is based on the scanning tunnelling microscopy topography observations of halide hybrid perovskite surface40, 41. An intermediate state is identified as the departing ion is partially hydrated but still remains within a proximity from the \chMAPbI3 surface. Starting with an equilibrated configuration we performed metadynamics using biasing variables (see Method section) aimed at obtaining the lowest free energy pathway for the detachment of \chI- from the \chMAPbI3 surface.

We begin with the discussion of dissolving \chI- using the metadynamics. An equilibrated heterogeneous interface is taken as the initial structure for metadynamic simulation of the dissolution process. The observation of \chI- or \chMA+ ion backtracking to \chPb-I cavity in the previous discuss is due to the trapping of the system in the initial FES basin using standard AIMD. The configuration trapped at this basin is named as the initial state (IS) shown in Fig. 1.

In the IS, the monitored \chI- (labelled yellow) forms hydrogen bonds with two water molecules above it, and bonds with a lead atom underneath it. Under the action of the metadynamic bias, the system is discouraged to revisit previous explored spots. With accumulating the computational sands, the initial basin is filled and the system is forced to escape from the local minima. We observe the elongation of the \chI-Pb bond shown in Fig.2a and Fig.2b. After around 7 ps of metadynamic simulation, the system arrives at the first transition state ($\text{TS}^{\text{{I}}}$) of the dissolution process shown in Fig. 2c and Fig. 2d, the \chI-Pb bond breaks.

At the transition state, the \chI- ion retains two hydrogen bonds with two water molecules. Besides, the \chI- forms bonds with a hydrogen atom on \ch-NH3+ group of one \chMA+, and with a hydrogen atom on \ch-CH3 group of the another \chMA+. The interatomic distance of the monitored \chI-Pb bond streches from 3.22 Å at IS to 5.27 Å at $\text{TS}^{\text{{I}}}$. We continued the metadynamic simulation after conquering the $\text{TS}^{\text{{I}}}$. The lifted \chI- drifts away from the underneath \chPb^2+. Meanwhile, neighbour \chMA+ cations of the monitored \chI- drift towards the cavity. It is intriguing to find that the departing \chI- ion does not enter solvent immediately and the surrounding \chMA+ cations do not leave the lattice following the \chI- ion. The heterogeneous interface evolves towards a state in which the \chI- is partly hydrated, but remains trapped close to the surface illustrated in Fig. 2e and Fig. 2f. We assign this local energy minimum as an intermediate state (IM). The partially hydrated \chI- is in an adatom-like configuration. Upon transition from $\text{TS}^{\text{{I}}}$ to IM, the coordination number of the \chI- with the solvent water molecules increases from $\sim{2}$ to $\sim{4}$.

During the whole simulation, we find the system spends a long time at IM basin. The partly hydrated \chI- stays on top of one neighbour \chMA+ cation due to an electrostatic attraction. Once the IM basin is filled, the system comes to the second transition state ($\text{TS}^{\text{{II}}}$), the corresponding configuration is shown in Fig. 2g and Fig. 2h. From IM to $\text{TS}^{\text{{II}}}$, the pulls from water molecules acting on the \chI- gradually overwhelm the interactions between the \chI- and underneath \chMA+. The adatom-like \chI- ion detaches from the \chMA+ cation. The number of water molecules in the hydration shell of \chI- increase to 5. The system needs to conquer the barrier of 0.22 eV to reach $\text{TS}^{\text{{II}}}$. This relatively larger energy barrier (compared with the initial 0.16 eV) is explained by breaking of the electrostatic attraction between the leaving \chI- and \chMA+. After passing through the $\text{TS}^{\text{{II}}}$, the system evolves to a final state (FS) shown in Fig. 2i and Fig. 2j. We characterize the FS as a state where \chI- escapes from the \chMAPbI3 surface and fully dissolves in water. In the FS, \chI- ion is coordinated by $\sim{7}$ water molecules, consistent with both experimental and ab initio simulated coordination number of $6-9$48, 45. The overall energy barrier for the initial dissolution event is obtained as the energy difference between the IS and $\text{TS}^{\text{{II}}}$ which is 0.18 eV.

We portray the FES of the dissolution process of \chMAPbI3 in water in Fig. 3.

The ease of the first dissolution event happening is determined by an energy barrier between IS and $\text{TS}^{\text{{I}}}$. Figure 3 suggests that the initial configuration needs to conquer 0.16 eV energy barrier to break the \chI-Pb bond in aqueous environment to reach $\text{TS}^{\text{{I}}}$. For comparison, Caddeo et al. 19 reported an energy barrier of 0.36 eV consisting of a layer-by-layer degradation of \chMAPbI3 in water. Lin et al. 49 reported a larger energy barrier (greater than 0.5 eV) when dissolving an \chI- from \chCsPbI3 surface in water. Releasing the \chI- is a competition between the hydration by water molecules and the electrostatic attraction to atoms on the surface and in the bulk of \chMAPbI3. From a thermodynamic point of view, the dissolution phenomenon is an effect of compensating electrostatic energy stored in the \chMAPbI3 surface by heat released from the hydration of the \chI-. This process is further promoted by the entropy gain during \chI- entering water. Detailed thermodynamic analysis of the overall dissolution process is discussed in the following section. Both the hydrophilicity of \chI- and \chMA+ ion and the intrinsic low electrostatic energy of \chMAPbI38, 36 contribute to these very low energy barriers in Fig. 3.

Simulations of \chNaCl dissolution in water identify a clear preference for the dissolution of \chCl- as the initial step over \chNa+50, 51, 21. To investigate the preference of ions leaving \chMAPbI3 surface at the beginning of the dissolution process, we performed an alternative metadynamic simulation where the dissolution starts with \chMA+. The FES of dissolution of \chMA+ is constructed and it renders a deeper energy basin ($\sim{0.31}$ eV), shown in Fig. S1. However, we only obtained the FES for the inital basin of the dissolution of \chMA+. We find that the initial basin of \chMA+ dissolution is much wider and deeper than the case of \chI- ion. Although we use relative large Gaussian height and weight, it is hard to explore the sequent stages of \chMA+ dissolution in water. A larger Gaussian will accelerate the exploration, however, sacrifice of accuracy is expected. Due to the capability of our facility and limited time, we stopped here for exploring the sequent FES of MA+ dissolution in water. The shape and rotational property of \chMA+ ion may contribute to the large initial basin.

The difference of the initial basins indicates \chI- is relatively easier to dissolve in water. Although \ch-NH3+ group of \chMA+ is hydrophilic, the connected \ch-CH3 group is hydrophobic. When dissolving \chMA+ in water, the hydrophobic \ch-CH3 group needs more space to settle in water molecules52. Seeking for more space in water molecule network and breaking the interactions of \chMA+ with surrounding ions in \chMAPbI3 surface together lead to a higher energy barrier for the first dissolution of \chMA+. As a result, the lower energy barrier suggests a priority of \chI- leaving the surface. Note that in the supporting information of Caddeo et al. 19, their simulation indicates that the first step of the dissolution \chMAI-terminated surface in water is releasing \chMA+ at 5 ps. Differently, during our over 33.5 ps simulation time including equilibrium relaxation and metadynamics, we only observe the dissolution of one \chI- ion in water. Liu et al. 21 indicated a forcefield-based description of \chNaCl dissolution in water failed to capture a preference for \chCl- over \chNa+ dissolution. Limitations related to a proper description of bond breaking or formation in the empirical potential framework may contribute to this discrepancy.

It is worthy to note that we didn’t observe any decomposition of \chMA+ cation during the whole simulation. Compared with the high deprotonation energy ($\sim$4.03 eV) of \chMA+ cation53, the low energy barrier of releasing \chI- suggests the initial degradation \chMAPbI3 in water is the dissolution of \chMAI-terminated layer into water solute. It is meaningful to mention that the energy barrier of transformation of the \chPbI2 2D-planer layer to \chPbI2 trigonal configuration is around 0.26 eV 54. Considering the low energy barriers of dissolving \chI- in water as well the low energy barriers of decomposition of \chPb-I layer, the overall degradation energy barrier of \chMAPbI3 dissolution in water is less than 0.3 eV.

2.2 Thermodynamics of \chMAPbI3 dissolution in water

Followed by the discussion of the initial process of \chMAPbI3 dissolution in water, the thermodynamic analysis of the overall decomposition is proceeded in this section. It is also intriguing to investigate how \chCsPbI3 reacts with water as a comparison. The dissolution of \chMAPbI3 via water can be described as follow:

[TABLE]

Estimation of the change of the Gibbs free energy($\Delta G^{\circ}_{T}$) between the reactants and products is a standard approach for predicting whether a reaction or process will occur spontaneously. Combination of the density functional theory (DFT) calculation with additional thermodynamic data (see Chap. 7 in Ref. 55) is used to predict $\Delta G^{\circ}_{T}$ of phase separation of \chMAPbI356. Kye et al. 57 utilize an ab initio thermodynamic formalism with the effect of solution to investigate the behaviour of defects on phase stability of \chCsPbI3. Here, we apply the combination of theoretical and experimental data to estimate the Gibbs free energy change ($\Delta G_{\text{diss}}$) of \chMAPbI3 dissolution in water at temperature $T$ as stated in Eq. (7). According to Sholl and Steckel 55, $G^{\circ}_{T}$ can be expressed as,

[TABLE]

Here, $E_{\text{tot}}$ is the standard state enthalpy at zero temperature which is evaluated based on DFT total energy calculations. $\tilde{\mu}^{\circ}_{T}$ captures finite temperature effects on the chemical potentials of species involved which is evaluated from NIST-JANAF thermochemical tables as well as other experimental resources.

In order to capture $\Delta G_{\text{diss}}$ at finite temperature, we designed a two-step thermodynamic cycle as shown in Fig. 4a.

The first step of the thermodynamic cycle is the dissociation of \chMAPbI3(s) to oppositely charged ions \chMA+(g) and \chI-(g) and \chPbI2(s),

[TABLE]

During this process, finite temperature effect on enthalpies and entropies of the system from solid inital state to intermediate gaseous state and \chPbI2(s) are evaluated, repectively

[TABLE]

The addition of the resultant $\tilde{\mu}^{\circ}_{T}$ and calculated $E_{\text{tot}}$ generates $G^{\circ}_{T}$ of each species. Related thermodynamic properties of species involved in the first step of the thermodynamic cycle of \chMAPbI3 dissolution in water are listed in Table 1.

According to Table 1, it is feasible to calculate the change in Gibbs free energy $\Delta G_{1}$ for the first step

[TABLE]

The calculated $\Delta G_{1}=5.0$ eV is shown in Fig. 4a. The second step of the designed cycle of \chMAPbI3 dissolution in water involves the hydration of \chMA+(g) and \chI-(g)

[TABLE]

The chemical potentials of aqueous ions $\tilde{\mu}^{\circ}_{T}$(aq) in this step can be obtained via

[TABLE]

$S^{\circ}_{T}$(aq) is the entropy of an aqueous ion. Decreased enthalpies and entropies due to hydration process contribute to the values of $G^{\circ}_{T,\text{MA}^{+}(\text{aq})}$ and $G^{\circ}_{T,\text{I}^{-}(\text{aq})}$. Related thermodyanmic properties of the second step are shown in Table 2.

The change of the Gibbs free energy of the second step

[TABLE]

amounts to $\Delta G_{2}=-5.36$ eV. The strongly negative change of Gibbs free energy in the second step overcomes the Gibbs free energy gain in the first step. Combining the two-step Gibbs free energy change, we can obtain $\Delta G_{\text{diss}}=\Delta G{{}_{1}}+\Delta G{{}_{2}}=-0.36$ eV. The negative $\Delta G_{\text{diss}}$ of the dissolution \chMAPbI3 in water at a finite concentration indicates the reaction in Eq. (7) would proceed spontaneously. The thermodynamic analysis of \chMAPbI3 dissolution process suggests an intrinsic water instability of \chMAPbI3. Although the negative $\Delta G_{\text{diss}}$ reflects a spontaneity of a reaction, it only predicts the trend of the proposed reaction. According to Arrhenius equation, the rate of a reaction is controlled by the energy barrier, i.e activation energy. A low activation energy indicates a high rate constant. The low activation energy obtained from metadynamic calculations for the \chMAPbI3 degradation in water demonstrates the corresponding reaction will proceed quickly. In all, for the reaction of \chMAPbI3 in water, the negative $\Delta G_{\text{diss}}$ renders a thermodynamic instability and the low energy barrier points to a kinetic instability.

Compared with a large amount of discussions on the fragility of \chMAPbI3 in water, stability of \chCsPbI3 in water recently attracts attention and is also under discussion. Lin et al. 49 indicated the water invasion triggered the phase transition of \chCsPbI3 from a high-temperature cubic phase to a low-temperature orthorhombic phase and they found that water is adsorbed on the surface without penetrating the interior of \chCsPbI3. Conversely, Yuan et al. 66 observed the \chCsPbI3 quantum dots degraded in a chamber with a wet gas flow. They confirmed the moisture was responsible for the degradation of these \chCsPbI3 quantum dots. Here, we employ the two-step thermodynamic cycle to the case of \chCsPbI3 dissolution in water to clarify these controversies.

The first step of the proposed thermodynamic cycle of dissolution \chCsPbI3 in water is given as

[TABLE]

Related thermodynamic properties of species involved in the first step of \chCsPbI3 dissolution in water are listed in Table 1. We can obtain the Gibbs free energy change $\Delta G_{1}=5.26$ eV for Eq. (15). The thermodynamic cycle of \chCsPbI3 is shown in Fig. 4b. The second step of \chCsPbI3 dissolution in water involves the hydration of \chCs+(g) and \chI-(g)

[TABLE]

Related thermodyanmic properties are shown in Table 2. Using Gibbs free energies in Table 1 and Table 2, the change of the Gibbs free energy of the second step is estimated as $\Delta G{{}_{2}}=-5.60$ eV. The overall $\Delta G_{\text{diss}}=\Delta G{{}_{1}}+\Delta G{{}_{2}}=-0.34$ eV for the dissolution \chCsPbI3 in water

[TABLE]

The above discussion indicates that the orthorhombic \chCsPbI3 is also prone to decompose in water. The thermodynamic analysis of \chCsPbI3 dissolution in water corroborates the degradation of \chCsPbI3 quantum dots observed by Yuan et al. 66. The energy barrier of the dissolution process determines the rate of the reaction. Compared with the very low energy barrier (about 0.18 eV) for the initial dissolution of \chMAPbI3, the relatively high energy barrier (greater than 0.5 eV49) for releasing \chI- into water from \chCsPbI3 surface suggests a slow process of dissolution of \chCsPbI3 which explains the differences in degradation rates at heterogeneous interfaces: water/\chMAPbI3 vs water/\chCsPbI3 observed by Lin et al. 49.

Zhang et al. 67 first used the energy differences obtained from DFT calculation to characterize the intrinsic instability of \chMAPbI3 and \chCsPbI3, considering a decomposition reaction of \chMAPbI3 into solid state products

[TABLE]

In Fig. 5 we show our calculated $\Delta E_{\text{tot}}$ for \chMAPbI3 and \chCsPbI3 which match well with $\Delta E_{\text{tot}}$ from Zhang et al. 67. According to Zhang et al. 67, a positive value of $\Delta E_{\text{tot}}$ corresponds to a stable perovskite structure.

They proposed the entropy term of \chMAI is higher than that of \chMAPbI3 which will further destabilize \chMAPbI3. However, from the measurements of entropies of \chMAI and \chMAPbI3 listed in Table 1, it clearly indicates a reverse trend. To note that, the entropy contribution of \chPbI2 cannot be neglected. The overall entropy in reaction (18) decreases and stabilizes \chMAPbI3 which has been indicated in Ref. 56. The entropy gains during \chCsPbI3 phase separation which is contrary to \chMAPbI3. The enthalpy change of \chCsPbI3 phase separation is large enough to overcome this entropy gain resulting in a positive $\Delta G$ that is slightly greater than the value of \chMAPbI3.

The positive $\Delta G$ values for phase separation process in Fig. 5 indicate a feasibility of synthesis of \chMAPbI3 and \chCsPbI3 compounds. However, the result should be taken with caution, since the uncertainty in reaction energies obtained with Perdew, Burke, and Ernzerhof (PBE) 27 exchange-correlation functional is of the order of $\pm 0.03$ eV/atom 68. With five atoms per perovskite formula unit (\chMA+ is considered as one cation), the estimated error is about $\pm 0.15$ eV as shown by the errorbars in Fig. 5. When considering a water environment, the Gibbs free energy change of the decomposition reaction mentioned above decreased by 0.39 eV and becomes strongly negative. This decrease is due to hydration of \chMA+/\chCs+ and \chI- ions. The amount of enthalpy change during the designed two-step thermodynamic cycle for \chMAPbI3 dissolution in water corresponding to Eq. (7) is negative (see $\Delta H$ in Fig. 5). This $\Delta H$ indicates the released energy during hydration process of \chMA+ and \chI- in Eq. (12) overcomes the energy consumed in Eq. (9). It renders the dissolution \chMAPbI3 in water is an exothermic reaction. The entropy gain during the dissolution of \chMAPbI3 in water further lowers $\Delta G$ in Fig. 5, suggesting the dissolution process is thermodynamically preferable. Dissimilarly, a postive $\Delta H=0.28$ eV for \chCsPbI3 dissolving in water indicates the released energy during hydration process of \chCs+ and \chI- in Eq. (16) is less than the energy consumed during Eq. (15). This positive $\Delta H$ renders dissolution \chCsPbI3 in water belongs to an endothermic reaction. Interestingly, a large entropy enhancement of dissolution \chCsPbI3 in water brings down $\Delta G$ to a negative value, see in Fig. 5. This large entropy enhancement comes from the difference of a low entropy of orthrhombic \chCsPbI3 and a high entropy of \chCs+(aq). The relative high entropy of \chMAPbI3 and low entropy of \chCsPbI3 in Table. 1 are consistent with the strong anharmonicity of \chMAPbI3 and weak anharmonicity of \chCsPbI3 recently disscussed in Ref. 69, 70. Compared with \chCsPbI3, the large hydration enthalpy of \chMA+ ion and the entropy gain together direct the negative $\Delta G_{\text{diss}}$. In all, we can conclude that the large hydration enthalpies of \chMA+/\chCs+ and \chI- and entropy enhancement as well as the low lattice energies of halide perovskite structures are responsible for the degradation of \chMAPbI3/\chCsPbI3 in water.

So far, we did not discuss an ionic activity $a_{\pm}$ of CH3NH3I solution and its contribution $k_{B}T\ln(a_{\pm})$ to a chemical potential term of an electrolyte when estimating $\tilde{\mu}^{\circ}_{T}$(aq). The actual chemical potential of an electrolyte is expressed as

[TABLE]

The mean ionic activity $a_{\pm}$ of CH3NH3I solution

[TABLE]

is determined by its molar concentration $c$ relative to the concentration in standard state $c^{\circ}=1$ M and the mean ionic activity coefficient $\gamma_{\pm}$, which accounts for non-ideality of the solution. Thermodynamic data listed in Table 1 correspond to $c=1$ M. Bonner 71 and Belvèze et al. 72 reported $\gamma_{\pm}$ of \chMACl is 0.58 when $c=1$ M. This value is taken as an estimation of $\gamma_{\pm}$ for \chMAI. The additional term $k_{\text{B}}T\ln(a_{\pm})$ for \chMAI solution is estimated as $-0.028$ eV at $c=c^{\circ}$, which is relatively small considering $\Delta G_{\text{diss}}=-0.36$ eV. In a dilute solution limit ($c\ll 1$ M), the term $k_{B}T\ln(a_{\pm})$ becomes negative and drives the water decomposition reaction of \chMAPbI356. When decomposition proceeds to reach a finite concentration (e.g., $c=c^{\circ}$), the $\Delta G_{\text{diss}}$ is no longer governed by $k_{B}T\ln(a_{\pm})$ but dominant by enthalpies and entropies of aqueous ions (see $\Delta H$ and $-T\Delta S$ of dissolution process in Fig. 5). Upon further dissolution, chemical potentials of the aqueous solution increase until $\Delta G_{\text{diss}}=0$ eV, the solution is then saturated and the dissolution process ceases.

3 Conclusion

The water instability of \chMAPbI3 is a major problem for commercialization of perovskite photovoltaics. Explanations of the underline mechanism are under debate. Here, we use ab initio metadynamic method to reconstruct the free energy surface of the dissolution process of \chMAPbI3 in explicit water. The predictive power of metadynamics unravels the pathway of water dissolving \chMAPbI3 surface. One intermediate state and two transition states are identified during the initial dissolution process. The first transition state involves breaking of \chI-Pb bond and formation of an intermediate state (\chI-MA interactions) at the surface with a low energy barrier of 0.16 eV. The second transition state corresponds to dissociation \chI-MA interaction and hydration of the \chI- ion with the energy barrier of 0.22 eV. In addition, using DFT calculations augmented with experimental data, the analysis of thermodynamics of \chMAPbI3 decomposition in water at a finite concentration indicates a negative Gibbs free energy change which suggests the spontaneity of water dissolution of \chMAPbI3. It is worthy to mention that a large hydration enthalpy of \chMA+ and a entropy gain under aqueous condition direct the negative $\Delta G_{\text{diss}}$. Combined with the low energy barrier for ease of ions escaping from the \chMAPbI3 surface and spontaneous nature of dissolving in water, it can be explained why the water immediately destroys pristine \chMAPbI3. We also analyze how \chCsPbI3 react with water from the thermodynamic point of view. It is found the Gibbs free energy change of dissolution \chCsPbI3 in water is also a negative value similar as the value of \chMAPbI3, which is consistent with an experimental observation of \chCsPbI3 degradation in a moist environment. Compared with \chMAPbI3, a large entropy enhancement of \chCs+ dominates the negative $\Delta G_{\text{diss}}$ for \chCsPbI3 dissolution in water. Our explanation provides a deeper insight of the water instability of \chMAPbI3 and presents a perspective on improving the instability of perovskite photovoltaics in future.

{suppinfo}

The following files are available free of charge.

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Initial FES of \chMA+: The initial basin of free energy surface for \chMA+ dissolution in water is plotted and compared with the initial basin of \chI- dissolution in water.

{acknowledgement}

Authors are indebted to Prof. Claudine Katan, Dr. Mikaël Kepenekian and Prof. Xavier Rocquefelte from Université de Rennes 1 for advises on setting up the initial perovskite-water interface. The authors also thank Natural Sciences and Engineering Research Council of Canada under the Discovery Grant Programs RGPIN-2015-04518. All the calculations were performed using a Compute Canada infrastructure supported by the Canada Foundation for Innovation under the John R. Evans Leaders Fund program.