Data-driven optimization and machine learning analysis of compatible molecules for halide perovskite material

Aqueous photocurrents of molecules/CH₃NH₃PbI₃

The systematic aqueous photoelectrochemical measurement highlights the interplay among solvents, additives, and post-treatment molecules for the resulting optoelectronic properties, which is in distinctive contrast with the bare halide perovskite film that produces negligible photocurrent in the aqueous solution. For example, the solvent and additives molecules mainly modified the halide perovskite surface near the electron transporting layer (TiO₂) and perovskite/perovskite grain boundary regions, while the post-treatment molecules predominantly control the perovskite surface in the solid/liquid (aqueous solution) boundary. The experimental data of 96 diverse perovskite materials with variable precursor solvent ratio, additive and post-processing dye molecules (Fig. 3a–t), in an effort to obtain an optimal molecular combination to stabilize aqueous optoelectronic properties of perovskites. Four measurements at different water immersion time (70 s, 110 s, 150 s, and 190 s) are carried out to account for the time-dependent water degradation, since the water molecules can swiftly infiltrate into MAPbI₃ film within seconds even at a low relative humidity of 10%¹². The photocurrents of the molecule-modified halide perovskite film in aqueous solution are obtained with a light on/off interval of 20 s and a total of 200 s measurement period. The water immersion time is associated the water stability of the halide perovskite film with the molecular modification. Interestingly, the calcein dye offers improved optoelectronic properties of CH₃NH₃PbI₃ when it is employed as the post-treatment species, which is attributed to the optimal light absorption properties and minimized hydrophilic groups in the calcein dye molecule (vide infra). Additionally, the solvent ratio of 1:1 for the precursor solution is optimal for the target output; this is ascribed to the modest intermolecular interactions and surface compact layer formation when both DMF and DMSO are present. Furthermore, the contribution of additive in the precursor solution is non-negligible, with NH₄Cl leading to an inferior aqueous photocurrent (< 20 μA) attributed to the lack of metallic species that results in poorer Lewis acid-base interactions in the molecule/perovskite surface. The comprehensive aqueous photoelectrochemical study witnesses a champion system based on the combination of “DMSO+PbBr₂+calcein”, with an aqueous photocurrent reaching 34 μA and a retention rate of 92.50% within 200 s (Fig. 3o), signifying balanced optoelectronic property and aqueous stability. The superior aqueous performance of this hybrid system is owing to the intricate contributions such as appropriate intermolecular bonding, hydrophilicity, charge state, and molecular topology revealed in the machine learning models and DFT calculations (vide infra). Apart from “DMSO+PbBr₂+calcein”, alternative high-ranking hybrid systems are available, preferring the incorporation of the calcein dye as the post-treatment species, namely “DMSO + CsBr + calcein”, “DMF + DMSO + calcein” and “DMSO + LiCl + calcein”. To sum up, the systematic aqueous photoelectrochemical measurement highlights the efficacy of multiple surface molecules to activate the aqueous photocurrents of the perovskite material, and calls for a global optimization strategy that comprehensively address diverse surfaces and interfaces in the perovskite photoelectrodes.

Machine learning

An accurate machine learning model describing the photoelectrochemistry of the multi-molecule-modified perovskites is constructed using the extra-trees algorithm based on the molecular and experimental features surviving the RFE process (Fig. 4a). The extra-trees model achieves a large area-under-curve (AUC) value of 0.86 for the test dataset in the receiver operating characteristic (ROC) plot; the corresponding confusion matrix further demonstrates the accurate stability classification model, with 100 samples correctly classified (82 true positive and 18 true negative samples). Furthermore, the AUC value of the train set displays a high accuracy of 0.94, with the confusion matrix indicating that 253 true samples are correctly identified (Fig. 4b, c). In conclusion, the extra-trees model presents a high accuracy in assessing the aqueous performance of the molecule-modified lead halide perovskites and establishes a solid foundation for the subsequent SHAP-based feature analysis.

Genetic model

In order to provide alternative machine interpretability and complement the black-box machine learning model, a genetic model clearly revealing the structure of the machine learning model via mathematical equations relating the descriptors and the photoelectrochemical stability is constructed. This gives rise to the following molecule-photocurrent stability relationship:

where the detailed explanations of the variables are provided in the Supplementary Table 2. The genetic model demonstrates decent accuracies (i.e., 83% for the test set and 86% for the train set) to describe the photoelectrochemical outputs. The following chemical and materials insights can be provided by the genetic model:

• The mathematical equation describing the aqueous photocurrents of the hybrid systems consists of multiple terms (joint contribution from both molecular and experimental details) connected by at least seven mathematic operators (+, −, ×, ÷, √, tan, cos, and log).

• f₁ corresponds to the surface area in a molecule with a specific electrotopological state of halide additive in the precursor solution (i.e., A_EV), and the feature A_EV has a negative impact on residue index (the larger value of A_EV, the poorer photocurrent stability). We attribute this to the undesirable perovskite crystal formation process in the presence of additives with larger surface area (represented by higher A_EV value) in the precursor solution, with a tendency to form less compact layers that is detrimental to the aqueous stability. In addition, the presence of A_LA in the denominator with two subtraction operations suggest the negative correlation with the target stability, which is attributed to the larger surface area that leads to more significant interaction with the neighboring solvent molecules (A_LA describes the molecular solubility via measuring the surface area on the compound molecule exposed to a solvent). To sum up, the first term (f₁) describing the perovskite photoelectrochemical stability is a sophisticated interplay among the three types of surface molecules (solvent, precursor and post-treatment dye), especially the intricacies of electrotopological and surface area exposed to solvents for the target property.

• f₂ is another critical factor revealed in the genetic model (the second term) focusing on the S_v feature, with negative influence on the perovskite stability. The S_v parameter in f₂ is associated with the hydrophilicity of the post-treatment molecule, and higher value implies a higher solubility of dye molecules in water, which may ultimately lead to weaker surface layer protection and thus poorer stability. This can be confirmed by the optimal combination “DMSO+PbBr₂+calcein” which has a lower value of A_EV and S_v. In addition, f₂ is negatively correlated with the stability output because of the negative first derivative (slope) of the function cos S_V–S_V (0 + 2kπ < S_v < π + 2kπ where k = 5). As a result, the aqueous stability of the molecularly modified perovskite material can be decoupled into f₂ which highlights the negative correlation of the hydrophilicity of the post-treatment molecule to the material stability, which agrees with chemical intuition.

• f₃ is associated with the experimental parameter T and is negatively correlated with the stability output as demonstrated in the last term (\(-\sqrt{\tan T}-\tan T\)); this agrees with experimental instinct where T corresponds to the water immersion time and the prolonged water immersion leads to more dramatic degradation of the photoelectrode materials. As a result, the third mathematical term in the genetic model represents the experimental observation that longer water immersion severely degrades the halide perovskite materials.

Feature analysis

The SHAP method is utilized to understand the molecular contribution and structural importance based on the extra-trees machine learning model (Supplementary Fig. 3). The top three most important features using the SHAP method are A_PV, D_R, and A_SV (Fig. 5a), and the complete feature ranking for aqueous photocurrent is: A_PV > D_R > A_SV > A_M > A_K3 > A_EVS > T_PSA > A_HA > A_LA > V_E8 > S_V > A_K1 > F_DM1 > F_DM2 > M_APC > M_EI > T > M_PC. It is interesting to observe that most molecular descriptors exhibit much higher ranking than the important experimental factor T (T is negatively correlated with the target output), indicating the strong influence of these structural, topological and property descriptors of the multi-molecules in diverse surfaces and interfaces on aqueous photocurrent. The temperature T survives after the RFE feature selection step. Importantly, it is only minor compared with other survived feature, but is much more important than most features before the RFE feature selection step. As a result, the temperature should not be eliminated in the post-hoc machine learning analysis. In the summary plot of SHAP, the lower values (blue points) of the features A_PV, A_SV, A_EVS, T_PSA, A_HA, A_LA, V_E8, S_V, and A_K1 distribute on the positive side of the SHAP values (the color of dots represents the magnitude of SHAP values, with a darker red color representing higher values), specifying that judicious selection of surface molecules with lower values of these features benefits the water stability of the lead halide perovskite film. The highest-ranking feature A_PV is related to the atomic charge distribution and functional group of additives, signifying the strength of the connection of the molecules to an actual charged atom; as a result, the additive molecules with higher A_PV values are associated with more charged regions that benefit the connections to the charged species in the precursor solution and thus lead to improved quality of the perovskite film. A_SV is another high-ranking molecular feature, which is associated with the hydrophilicity of molecular additives; as a result, lower values of A_SV are desirable to mitigate the interaction with the air-water interface and subsequent material degradation. In order to design aqueous stable halide perovskite materials, it is recommended to choose halide additives with lower A_SV and A_PV values suggested in the SHAP analysis. On the other hand, the larger values (red dots) of the features D_R and A_M distribute on the positive side of the SHAP values, indicating that larger values of these features are preferred to designing water-stable perovskites. D_R corresponds to the ratio between DMF and DMSO, suggesting the solvent concentration of both solvents should be considered in the materials design process. A_M is referred to the degree of lipophilicity of the compound and the larger value is favored to alleviate water solubility. This agrees with the experimental intuition to improve optoelectronic stability via minimizing water contact and infiltration. The SHAP feature analysis highlights the hydrophilicity and lipophilicity of the organic molecules for the perovskite aqueous optoelectronic stability. Hydrophilicity refers to the tendency of a substance to interact favorably with water, while lipophilicity refers to the tendency to interact favorably with lipids or non-polar solvents. The van der Waals surface area has been demonstrated to be strongly related to lipophilicity and the negative SlogP_VSA2 is related to high hydrophobicity to alter the perovskite dimensionality^34,35,36. Apart from that, the higher-ranking features in the importance histogram according to SHAP (Fig. 5b) are not solely contributed any particular molecules in a single surface/interface; rather, the aqueous photocurrent generation of the perovskite film is contributed by solvents, precursor additives, and post-treatment molecules in a synergistic manner, with the hydrophilicity and lipophilicity of the organic surface modifiers playing critical role.

Post-hoc DFT calculation

DFT is employed to uncover the detailed intermolecular interactions of the champion system (DMSO+cacein+PbBr₂) on MAPbI₃ surface (Fig. 6a, b) presuming an adsorption model with molecular adsorbates. In addition, a H₂O molecule is introduced to the molecule-modified perovskite supercell surface system (Fig. 6c, d) to better understand the aqueous influence on the halide perovskite surface structure and optoelectronic properties. The calculation identifies the co-existence of anion···π, halide bond and hydrogen bond molecular interactions to stabilize the overall molecule-perovskite interfacial structure (Fig. 6e). The calcein molecule displays a hydrogen bond of 4.65 Å with the perovskite surface lead species, and an anion···π interaction between the DMSO molecule and the perovskite surface iodine species at a distance of 4.27 Å; additionally, a hydrogen bond of 3.90 Å forms between the calcein adsorbate (hydroxyl hydrogen) and perovskite surface (iodine). Moreover, DMSO forms a hydrogen bond of 3.27 Å with the perovskite surface; PbBr₂ demonstrates a halogen bond of 3.64 Å with the perovskite surfaces iodine, and a hydrogen bond of 4.42 Å with the calcein molecule. It is noteworthy that the H₂O molecule does not disrupt the structure integrity of the interfacial perovskite surface system; this is attributed to the presence of complex intermolecular bonding among the organic molecules in addition to the adsorbate···adsorbent interactions, which form a compact self-assembled multilayer³⁷ to prevent direct damage to the perovskite system by water molecules.

The projected density of states (PDOS) spectra are determined to reveal the joint contributions of post-treatment calcein molecule, additive PbBr₂, and precursor solvent DMSO in the electronic properties of the perovskite system (Fig. 6f). The adsorbed molecules contribute strongly to both conduction band and valence band of the perovskite system via their p orbitals. In particular, the PbBr₂ adsorbate contributes more significantly to the conduction band edges while the calcein molecule contributes extensively to both conduction and valence band edges in the PDOS spectra, signifying possible chemical bond formation and intimate physical contacts via effective hybridization between the p orbitals of the post-treatment chromophore and neighboring materials.

The simulated UV-vis absorption spectra (Fig. 6g) demonstrate the improved light-harvesting performance of the molecule-modified perovskite system (Supplementary Fig. 4) compared with the bare system in terms of visible light (400 nm ~ 800 nm) conversion into electrons, which aligns with the experimental findings^38,39. This suggests the possibility of simultaneous improvement in the light absorption properties and insulation against water damage when these adsorbent molecules are present on the halide perovskite substrate. Furthermore, the molecule-modified hybrid system has a smaller work function (5.44 eV) than the bare system (5.98 eV), indicating that the champion system can emit photoelectrons at a smaller excitation energy in addition to decent conductivity (Fig. 6h, i). Moreover, the incorporation of these adsorbed molecules results in a reduction of band gap in the perovskite system: the band gap of the molecule-modified system is reduced to 1.439 eV (c.f., the bare system has a band gap of 1.795 eV) (Table 1), favouring a promoted energy transition from occupied energy levels to occupied ones for valence electrons. Noteworthily, the incorporation of the molecules does not introduce unnecessary in-gap states corresponding to detrimental deep-level defects, which is in vast difference with those undesirable molecular adsorbate systems in the literature^40,41. The potential plot and density of states spectra of the perovskite systems without water adsorption are also obtained via the DFT calculation, suggesting larger work function of both bare and molecule-modified perovskite systems in the presence of water. In addition, the water adsorption leads to larger band gap, which is detrimental to the optical properties (Supplementary Fig. 5). To sum up, the presence of calcein, DMSO and PbBr₂ on CH₃NH₃PbI₃ surface leads to a stable interfacial structure via multiple intermolecular bonds with improved optoelectronic properties and absence of deep-level defects.

Shockley Queisser (S-Q) and spectroscopic limited maximum efficiency (SLME) values are calculated to evaluate the application for photovoltaic device of molecule-modified perovskite system. The theoretical S-Q efficiency of the bare perovskite system is only 27.2% (Fig. 7); when the incident light enters the perovskite system, 53.6% of energy is not absorbed, 10.9% is lost due to thermalization, 8.2% is lost due to extraction and only 27.9% energy of incident light is available for absorption. Additionally, the bare system only has an SLME efficiency of 26.84%, which is slightly larger than the S-Q counterpart because the latter method neglects the absorption process and only considers the band gap contribution. In contrast, the theoretical S-Q efficiency of the molecule-modified system is 32.9%, which is 1.2 times higher than that of the bare system; the corresponding deconvolution demonstrates 35.1% of the coming light energy is not absorbed, 19.9% is lost due to thermalization, 12.1% is lost due to extraction and 32.9% available for subsequent energy conversion. Meanwhile, the SLME efficiency of the molecule-modified system is 32.27%, which improves by 20% compared with that offered by the bare system. Besides, the presence of water molecule leads to inferior SLME and S-Q efficiency, which agrees with chemical intuition (Supplementary Table 2 and Supplementary Fig. 6). To sum up, both S-Q and SLME efficiency estimation methods confirm the superiority of the molecule-modified perovskite systems to offer enhanced solar energy conversion performance.

A comprehensive photoelectrochemical investigation on 96 different molecule-modified CH₃NH₃PbI₃ halide perovskite materials is performed, which helps evaluate the molecular influence (solvent molecule ratios, halide additives and post-treatment molecules) on the halide perovskite aqueous optoelectronic stability. A champion system based on ‘calcein+PbBr₂ + DMSO’ is identified; it delivers a large aqueous photocurrent (3 × 10⁻⁵A/cm²) and an improved aqueous stability (retention index) of 92.5% after 200 s water immersion. An accurate extra-tree machine learning model is constructed, with SHAP feature analysis highlighting the hydrophilicity and lipophilicity of the organic molecules for the perovskite aqueous optoelectronic stability. An accurate genetic model is provided to offer alternative machine interpretability and address the ‘black-box’ issue. A more approachable machine learning model with the mathematical expression of Stability = f₁+f₂−f₃ is designed to describe the perovskite stability. The resulting expression decouples the molecular contributions into hydrophilicity, electrotopology and surface areas of the tri-molecules. The post-hoc DFT calculation suggests the possibility of multiple surface intermolecular bonds, such as hydrogen bonds and anion··π surface interactions in the self-assembled layer to stabilize the interfacial structures in the champion system. The calculation suggests the absence of deep-level defects, improved light harvesting properties and higher S-Q and SLME efficiencies in the ‘calcein+PbBr₂ + DMSO’ system. The present study confirms the efficacy of the proposed ‘global optimization’ strategy to address the aqueous instability issue of halide perovskite materials, and calls for more multi-mode modeling studies to comprehensively evaluate the molecule-modified materials.