Following Scheme 2, the computational-enhanced discovery of novel perovskites begins with the consideration of empirical factors and computational methods, such as Density Functional Theory (DFT) and Molecular Dynamics (MD), to model and understand material properties at an atomic level. These computational approaches feed into high-throughput screening (HTS) processes, which allow for the rapid assessment of numerous material candidates. Finally, Machine Learning (ML) techniques are applied to analyze the data generated from HTS, enabling the identification of promising materials with desired properties more efficiently.

Predicting the structural stability of perovskites remains a significant challenge in the discovery of novel perovskites. For new perovskite materials, the use of empirical factors to assess lattice stability may vary, necessitating adjustments for specific cases. For example, the effective tolerance factor (t _eff) and octahedral index (μ _eff) for quaternary antiperovskites X₆B₂AA′ and X₆BB′A₂ are defined as follows (Han et al., 2021): t e ff   X 6 B 2 AA ′ = r A + r A ′ 2 + r x /   2 r B + r x μ eff X 6 B 2 AA ′ = r B   /   r x t e ff   X 6 BB ′ A 2 = r A + r x   /   2 r B +   r B ′ 2 + r x μ eff   X 6 BB ′ A 2 = r B   + r B ′     /   2 r x where r _i (i = A, A′, B, B′, X) stands for the radii of ions in antiperovskites.

Obtained from DFT calculations, the formation energy is crucial for assessing the stability and synthesizability of perovskites. A negative formation energy indicates that the material is energetically favorable to form and is likely to be stable under standard conditions relative to its constituent elements or compounds. Thermodynamic stability is typically estimated using either the DFT formation energy (E _f, relative to its constituent elements) or the energy above the convex hull (E _hull, relative to competing phases in the phase diagram) (Wang H. et al., 2020). Here, competing phases typically refer to the most stable phases among a range of conditions of temperature, pressure, or chemical composition. The formation energy can be used to identify the most energetically favorable structure, e.g., atomic orderings and types of novel perovskites (Jain et al., 2013; Togo and Tanaka, 2015). This energy is particularly significant when applied in HTS, such as in identifying stable M₃XZ antiperovskites from the Materials Project database (Singh et al., 2018). However, since different compounds would form during the decomposition process under varying conditions (e.g., pressure and temperature), the convex hull will vary. Therefore, compared to E _hull, E _f would be more practical in ML applications (Ong et al., 2008). Moreover, the incompleteness in the phase diagram or artificially stabilized phases from DFT errors can cause significant inaccuracies in E _hull (Chen C. et al., 2020). In contrast, E _f is a more reliable regression target.

In the study of novel perovskites such as antiperovskites and chalcogenide perovskites, structural distortion is of greater significance compared to traditional perovskites. These materials often display unconventional arrangements of A-site and B-site ions, resulting in pronounced structural distortions. For example, chalcogenide perovskites predominantly manifest three phases under ambient conditions compared to ideal cubic perovskite structure, namely, orthorhombic distorted phase, hexagonal phase, and needle-like phase (Tranchitella et al., 1997; Takeda et al., 1976; Lee et al., 2005; Lelieveld and IJdo, 1980). In some cases, the distorted phase exhibits better performances (Sun et al., 2015). Controlling and understanding these distortions is essential for tailoring functionalities. Furthermore, MD simulations conducted under various conditions, such as elevated temperatures, corroborate the robust stability of these hybrid chalcogenide perovskites (Baek et al., 2018; Li N. et al., 2020).

The electronic structure is crucial in the research of novel perovskites such as antiperovskites and chalcogenide perovskites, as their unique electronic properties largely determine their performance. In antiperovskites, understanding the electronic structure helps elucidate their ferroelectric, topological, and transport properties, which are critical for applications in sensors, actuators, and quantum devices. Similarly, optimizing the electronic structure of chalcogenide perovskites can enhance their photovoltaic and thermoelectric performance.

The density of states (DOS) is pivotal in studying novel perovskites. The DOS at the Fermi energy significantly affects their magnetic, transport, thermoelectric, superconducting, and optoelectronic properties. The calculated electronic structure can be illustrated through a computed absorption spectrum, which corresponds to transitions between states with high DOS, providing detailed insights into how novel perovskites absorb light at different wavelengths (Kangsabanik et al., 2018; Ma et al., 2021). Dielectric properties, such as the dielectric constant and loss, impact the perovskites’ ability to store and release electric energy under an applied electric field. For novel perovskites, the dielectric response influences their suitability for various electronic applications, ranging from photovoltaics to electronic devices.

Among the various properties, the bandgap is a crucial parameter that significantly impacts performances. Tuning the bandgap is essential for optimizing the optoelectronic and thermoelectric properties of novel perovskites such as antiperovskites and chalcogenide perovskites. In photovoltaic applications, an optimal bandgap allows for efficient absorption of sunlight and conversion to electricity, maximizing the efficiency of solar cells. The Shockley-Queisser limit dictates that single-junction solar cells with an ideal bandgap of 1.34 eV can achieve a maximum solar conversion efficiency (SCE) of 33% (Rühle, 2016). Consequently, predicting or screening the bandgap is typically the initial step in computationally designing materials for solar cells (Chen C. et al., 2020). For thermoelectric applications, the bandgap influences the Seebeck coefficient and electrical conductivity, which are critical for effective thermal to electrical energy conversion. Additionally, the Seebeck coefficient and electrical conductivity are often calculated within the framework of Boltzmann transport theory using tools such as the BoltzTrap code (Schleder et al., 2019).

The Berry phase plays a significant role in the study of novel perovskites. For instance, it is used to calculate electric polarization in ferroelectric antiperovskites, aiding in determining the magnitude and direction of polarization in various states. Analyzing the change in polarization among different states, such as during a phase transition, can reveal the dynamics of polarization switching (Wang ZX. et al., 2019). Additionally, the Berry phase influences the transport properties of materials, such as the Hall effect and magnetoresistance, providing theoretical support for understanding conductivity and thermoelectric performance. By analyzing the Berry curvature, researchers can also identify and characterize topological phases in antiperovskites, such as topological insulators or Weyl semimetals (Kawakami et al., 2018).

The DFT electronic structure, derived from Kohn–Sham orbitals describing the conduction band minimum and maximum, approximate the real optical excitation problem but neglect excitonic effects; however, the accurate depiction of electronic structure is further complicated by the interplay between strong electron-electron interactions and spin-orbit coupling (SOC), which becomes important for heavy elements significantly reduce the band gap (Das et al., 2022). To address this, researchers often employ ad hoc DFT hybrid functionals tailored to match the band gap of each specific perovskite (IOPscience, 2011). While this approach introduces a degree of empiricism and limits the ability to reliably predict the properties and band gaps of unknown perovskites, it is also common practice to include SOC effects in calculations to improve accuracy (Umari et al., 2014). Through testing, G₀W₀ method performs best compared with experimental result but is computationally remarkably expensive. At the DFT level, HSE method gives overall the better estimation for novel perovskites (Vona et al., 2022; Fuchs et al., 2007). It is because that HSE incorporates a portion of exact exchange from Hartree-Fock theory, which helps improve the accuracy of the electronic structure calculations, particularly for systems with strong correlation effects (Janesko et al., 2009). Thus, HSE have currently widely utilized as a proper practice in the electronic structure calculation (Sun et al., 2015; Liu et al., 2021).

Some workflows were also developed to predict an accurate electronic structure. For example, Gebhardt et al. take the SOC, many-particle theory, and the dynamical behavior of the perovskites into account. The developed workflow could predict the band gaps within 0.2 eV as compared to experimental data. In some cases, the dynamical effects should be considered using the MD simulations, such for the higher symmetry of the α-phase (high-temperature) phase (Vona et al., 2022). Some workflows take the SOC, many-particle theory, and the dynamical behavior of the perovskites into account were also developed to predict an accurate electronic structure. For example, Gebhardt et al. (Gebhardt et al., 2021). developed such a workflow that comprises computations on an equal footing by efficient DFT methods and predict the band gaps within 0.2 eV as compared to experimental data.

It is worth noting that for novel perovskites, complex structural issues such as structural distortion, defects, impurities, and phase transitions under varying conditions can arise. These structural variations not only impact the perovskites’ physical properties but also induce changes in their electronic structure. For example, the electronic structure among different states of rotated BX₆ octahedra reveals that it is significantly impacted by the distortion, due to the intricate hybridization from orbital interactions (Niu et al., 2018a).

In a recent study, two novel classes of pnictogen-based quaternary antiperovskites, with the formulas X₆B₂AA′ and X₆BB′A₂, were devised through ion type inversion and anion ordering on perovskite lattice sites (Han et al., 2021). Their phase stability and tunable band gaps were comprehensively predicted using DFT calculations. Further screening of these materials for photovoltaic applications identified several stable compounds with suitable direct band gaps, small carrier effective masses, low exciton binding energies, and strong optical absorption due to dipoles, making them promising candidates for photovoltaic absorber materials. Notably, the theoretical maximum solar cell efficiencies for these stable antiperovskites exceed 31%, which is comparable to or even surpasses the efficiencies of MAPbI₃ -based (MA = methylamine) solar cells (Han et al., 2021). This simulation study highlights the significant potential of quaternary antiperovskites in the optoelectronic field and provides a novel approach to designing lead-free and air-stable perovskite-based photovoltaic absorber materials.

To predict the quaternary compositions and their corresponding lattice structures, DFT calculations were performed (Perdew et al., 1996; Kresse and Furthmüller, 1996). Unlike the typical perovskite configuration ABX₃, antiperovskites X₃BA feature an electronically inverted structure with one cationic X-site and two anionic A- and B-site, as illustrated in Figure 1. Building on previous reports that all-inorganic antiperovskites X₃NA, where X represents divalent metals and A represents pnictogens, exhibit favorable optoelectronic properties for photovoltaic applications, the structure X₃BAX was transformed into two novel quaternary antiperovskites: X₆B₂AA and X₆BB′A₂ through anion ordering. This process involves splitting the anionic A- or B-site, leading to a total of 48 potential component combinations, as shown in Figure 1.

The prediction of potential antiperovskites began by identifying the most energetically favorable anionic ordering types in two structures (Jain et al., 2013; Togo and Tanaka, 2015). A supercell was constructed by doubling the standard cubic distortion-free unit cell of the antiperovskite X₃BA. Various arrangements of AA′ and BB′ anionic pairs, denoted as A to F, were then considered within this supercell, as illustrated in Figure 2A. The calculated total energies of two A-site ordered quaternary antiperovskites (Mg₆ N₂SbBi and Sr₆ N₂ AsBi) and two B-site ordered quaternary antiperovskites (Mg₆NPSb₂ and Ca₆ NAsBi₂) were presented as examples. Simulation results show that the favored configurations of A- and B-site anion ordering in quaternary antiperovskites align with the cation ordering observed in conventional double perovskite oxides. Specifically, A-site cations tend to exhibit tetragonal layered ordering, while B-site cations prefer cubic rock-salt type ordering (King and Woodward, 2010). It is noteworthy that the simulated energy differences between various configurations of A-site cation-ordered regular double perovskites are typically minor, a finding consistent with previous reports (Gou et al., 2017).

To evaluate the lattice stability of the quaternary antiperovskites of interest, empirical metrics such as the tolerance factor and octahedral index were calculated (Travis et al., 2016; Goldschmidt, 1926; Kieslich et al., 2015; Kieslich et al., 2014). The results, shown in Figure 2B, indicate that most predicted compositions fall within the empirically stable region of traditional perovskites, while several unstable components were excluded.

Equally important as crystalline stability is thermodynamic robustness, which estimates the ease of decomposition for predicted compounds. Generally, a negative decomposition energy or E _hull indicates thermodynamic stability against degradation. Researchers integrated DFT calculations for specific quaternary compounds with data on all relevant elemental substances and binary and ternary phases from the Materials Project database. This approach expedited the assessment of thermodynamic stability, as illustrated in Figure 2C (Jong et al., 2016). By establishing a suitable threshold for E _hull (e.g., 25 meV/atom in this report, corresponding to k _BT at room temperature), potential antiperovskites can be categorized as either thermodynamically stable or unstable, considering the potential for entropic stabilization (Dawson et al., 2018; Lu et al., 2020). Based on this criterion, several specific antiperovskites were identified as thermodynamically stable. Notably, compositions with large E _hull consistently exhibited crystallographic instability, suggesting a correlation between structural stability and thermal stability.

Furthermore, in addition to thermodynamic stability, dynamic stability—reflecting the gradual distortion of the structure over time—was assessed through phonon spectrum computations using the frozen phonon simulation technique (Togo and Tanaka, 2015). As shown in Figure 2D, seven quaternary antiperovskites are dynamically stable because they exhibit no imaginary modes (Han et al., 2021). Interestingly, simulation results reveal that antiperovskites with a higher degree of asymmetry demonstrate greater stability compared to typical cubic perovskites ABX₃ and double perovskites A₂ BB′X₆. This finding is contrary to conventional expectations (Flerov et al., 1998; Glazer, 1972; Howard et al., 2003). As a result, distorted quaternary antiperovskites show promise for photovoltaic applications due to their enhanced dynamic stability and increased structural distortion, which can amplify the photoelectric effect through the boundary-breaking bulk photovoltaic effect.

Ferroelectrics are multifunctional electroactive materials with a wide range of applications (Liu et al., 2018a; Liu et al., 2018b). Their temperature-dependent spontaneous polarization can be modulated by electric fields or mechanical forces, making them highly suitable for temperature sensing, data storage, mechanical actuation, and energy harvesting (Liu et al., 2018c; Hussain et al., 2022; Liu et al., 2017). The phenomenon of ferroelectricity was first discovered in 1921 with Rochelle salt, followed by the identification of ferroelectric properties in other molecular systems. Significant progress in ferroelectric research was achieved with the discovery of ferroelectricity in perovskite materials like barium titanate (BTO) and lead zirconate titanate (PZT) (Lupascu and Rödel, 2005; Heywang, 1971; Luo et al., 2003; Vijatovic et al., 2008).

Unlike all-inorganic ferroelectrics, organic-inorganic hybrid ferroelectrics—often termed molecular ferroelectrics—offer several advantages, including lightweight construction, mechanical flexibility, and environmentally sustainable processing methods (Peng et al., 2020; Siwach et al., 2022; Liu et al., 2020). Recent studies have highlighted significant advancements in molecular ferroelectrics, characterized by high Curie temperatures, superior piezoelectric coefficients compared to all-inorganic ferroelectrics, sensitivity to polarized light due to chirality, photochromic properties, enhanced electrocaloric effects, and lanthanide-mediated fluorescence emission (Xu et al., 2020; Shi et al., 2020b; Xu et al., 2021; Xu et al., 2011; Fu et al., 2011; Tang et al., 2019; Zhang Y. et al., 2020; Shi et al., 2017).

Since ferroelectric properties arise from the polarization asymmetry within the crystal lattice, DFT calculations can provide theoretical insights into the dynamics of polarization switching during the ferroelectric-paraelectric phase transition (Wang ZX. et al., 2019). The following example illustrates meticulously engineered antiperovskite molecular ferroelectric materials. Specifically, substituting one of the methyl groups in [(CH₃)₃NH]-CdCl₃ with an ethyl group disrupted the existing mirror plane, potentially resulting in a polar crystal capable of displaying ferroelectric behavior. To further diminish the crystal symmetry, a fluorination strategy was employed to replace the ethyl group, thereby converting the perovskite structure into antiperovskites, as shown in Figure 3A (Zhang et al., 2020b; Shi et al., 2019). This compound demonstrates a ferroelectric phase below its T _C, while a paraelectric phase emerges above the phase transition point (Wang ZX. et al., 2019).

The observed structural distortion in the ferroelectric phase accounts for both the organic cations and inorganic anions, considering the symmetry transition of the crystal structure. As illustrated in Figure 3B, DFT calculations define the paraelectric configuration as λ = 0 and the ferroelectric phase as λ = 1. Simulation results reveal that the polarization variation along the dynamic path shows that the positive extremum of ferroelectric polarization, initially along the c-axis from the starting state of λ = 1, gradually diminishes to zero at λ = 0 and then reverses to reach the end state of λ = −1 with negative extremum polarization [48]. This progression indicates a ferroelectric-paraelectric-ferroelectric phase transition, in alignment with previous studies on ferroelectric perovskites (Shi et al., 2020a; Wang S. et al., 2020; Pan et al., 2017). Subsequent experimental data have validated the DFT calculations’ accuracy, as depicted in Figure 3C. It is important to note that, according to recent polarization theory, quantum polarization might exaggerate the polarization strength, which should be excluded from calculations.

A fundamental characteristic of ferroelectrics is their electrically switchable spontaneous polarization. Therefore, a local Piezo-response Force Microscopy (PFM)-based hysteresis loop measurement was performed for antiperovskite molecular ferroelectrics, as shown in Figure 3D. The distinct 180° reversal of the PFM phase signal and the characteristic butterfly loop in the amplitude signal are indicative of polarization switching within ferroelectric domains (Fu et al., 2013; Zhang et al., 2013; You et al., 2017; Rabe et al., 2007; Resta, 1994; Spaldin, 2012). Furthermore, to further investigate dynamic ferroelectric switching in antiperovskite molecular ferroelectrics, an equal but opposite bias was applied to the materials. A box-in-box contrast image was then captured during both phase and amplitude transitions, as demonstrated in Figure 3E (Li L. et al., 2020; Zhang et al., 2020c; Wei et al., 2020).

In addition to demonstrating powerful capabilities in predicting compositions and functionalities for quaternary antiperovskites and antiperovskite molecular ferroelectrics, computational methods have also played a significant role in accelerating the development of compositions with advanced X-ray detection capabilities. In a very recent study, a novel antiperovskite (2-Habch)₃Cl(PtI₆) was developed that features indirect transition and low orbital symmetry (Liu et al., 2024). These characteristics enable such material to exhibit a carrier lifetime exceeding 3 ms, resulting in remarkable carrier mobility (μτ = 6.25 × 10⁻³ cm² V⁻¹) and high resistivity (10¹² Ω cm). The electrical performance of this antiperovskite surpasses that of most existing X-ray detector materials. In-depth DFT calculations reveal that the low-dimensional characteristics of this material are the reason for the localized behavior of its band structure in various directions. Additionally, the low symmetry of the Pt 5d orbitals significantly reduces the dipole matrix elements. The indirect band gap nature of the material further decreases the dipole matrix elements.

In another groundbreaking study, researchers developed an atomic-position splitting method to design novel antiperovskites, effectively resolving the issue of suboptimal photovoltaic performance in previously reported antiperovskites (Tang et al., 2024). This research introduced a class of antiperovskite-derived materials with the formula X₃BA₃’, achieved by splitting the A anion, originally positioned at the corner site of the cubic antiperovskite structure, into three edge-centered sites, thereby preserving the three-dimensional octahedral framework. First-principles calculations confirmed that these potential compositions exhibit robust thermodynamic and dynamical stability. Notably, nine promising derivatives demonstrated maximum solar conversion efficiencies exceeding 24.5%, comparable to MAPbI₃. Moreover, interpretable machine learning techniques were developed to identify critical regulatory factors that influence their thermodynamic stability and band gap. Therefore, computational methods play a crucial role in the design and development of novel semiconductor materials, guiding the optimization of their outstanding optoelectronic properties.

Inspired by halide perovskites, chalcogenide perovskites are expected to display distinctive properties due to their ABX₃ configuration, where A represents bivalent metals, B denotes tetravalent cations, and X stands for either sulfur (S) or selenium (Se) (Perera et al., 2016). As illustrated in Figure 4A, unlike the conventional perovskite structure, which is typically free of distortion, chalcogenide perovskites primarily exhibit three phases under ambient conditions, including orthorhombic distorted phase (No. 62, Pnma), hexagonal phase (No. 194, P63/mmc), and needle-like phase (No. 62, Pnma) (Tranchitella et al.; Takeda et al., 1976; Lee et al., 2005; Lelieveld and IJdo, 1980). Throughout these phase transitions, alterations in coordination numbers frequently occur. For instance, in the hexagonal phase, the cation coordination is analogous to that in the cubic perovskite structure, with A/B-site cations adopting a 12/6-coordination arrangement. Conversely, in the needle-like phase, the coordination number of the A cation is reduced to 9, signifying a collapse of the perovskite structure.

The band gaps of predicted chalcogenide perovskites were simulated using various calculation methods with carefully optimized parameters to ensure precision (Perera et al., 2016; Sun et al., 2015; Basera and Bhattacharya, 2022; Guo and Wang, 2019; Sun et al., 2019; Ju et al., 2017). As depicted in Figure 4B, simulation results reveal that, among the same chalcogenide perovskites, the distorted perovskite phase generally exhibits the largest band gap, while the hexagonal phase often shows the smallest band gap. Additionally, sulfide perovskites typically demonstrate larger band gaps compared to their selenide counterparts in both distorted and needle-like phases. This is attributed to the lower energy level of sulfur’s 3p orbitals compared to selenium’s 4p orbitals. Moreover, Hf-based chalcogenide perovskites usually exhibit larger band gaps compared to Zr-based counterparts, owing to the higher energy level of Hf 5d orbitals relative to Zr 4d orbitals. Importantly, the band gap calculations of potential chalcogenide perovskites have identified several promising candidates with suitable optical absorption ranges for solar cell applications. For example, some Zr- and Hf-based chalcogenide perovskites with needle-like or distorted phases and appropriate band gaps are suitable for solar cell fabrication, whereas their hexagonal counterparts, with relatively smaller band gaps, are less effective within the visible spectrum. Furthermore, the simulations confirm that several compositions with direct band gaps exhibit high power conversion efficiencies approaching the theoretical Shockley-Queisser limit, as indicated within the light red range in Figure 4B, highlighting their promising potential for photovoltaic applications (Shockley and Queisser, 1961).

The imaginary component of the dielectric function is a critical parameter for evaluating the optical absorption of semiconductor materials, with a higher dielectric constant generally indicating more intense absorption. Researchers have thus employed calculations to assess the absorption characteristics of chalcogenide perovskites, aiming to further evaluate their effectiveness for solar energy harvesting applications. Figure 4C displays the computational results of the dielectric function, compared to those of well-established solar cell materials (Burst et al., 2016; Adachi, 1985; Rockett and Birkmire, 1991; Ruch and Kino, 1968; Wasim, 1986). Among these compounds, CaZrSe₃ in the distorted perovskite structure shows a dielectric function comparable to that of the commercial CuInSe₂, suggesting its promising potential as a photovoltaic material. In contrast, although Zr- and Hf-based sulfide perovskites in the needle-like phase possess suitable band gaps, their optical absorption edges significantly surpass their fundamental band gaps. Consequently, chalcogenide perovskites in the needle-like phase exhibit indirect band gaps, making them unsuitable for solar cell applications. A deeper understanding of these distinctions can be obtained by analyzing their band structures using computational methods, as illustrated in Figure 4C. The lowest conduction bands display greater dispersion along the direction of the octahedral chains compared to the perpendicular directions, resulting in higher anisotropy of electron mobility in the hexagonal and needle-like phases compared to the distorted perovskite phase.

To identify additional potential chalcogenide perovskites, computational methods combined with stability assessments can be utilized through A- and B-site substitutions. It is noteworthy that substituting A-site constituents generally has a minimal impact on the overall properties of perovskite materials (Baek et al., 2018; Li N. et al., 2020). For example, inorganic A-site metals can be replaced with organic molecular cations, as demonstrated by the case of BaZrS₃ depicted in Figure 4D. Computational results indicate that the band structure and properties of the optimized compounds closely mirror those of the original material. Additionally, AIMD simulations performed at elevated temperatures confirm the exceptional stability of these hybrid chalcogenide perovskites. These findings highlight the crucial role of computational methods not only in predicting material properties but also in expanding the range of possible material types.

Ruddlesden−Popper (R-P) phases, a specific structural type within perovskite materials, are characterized by the general formula A₂' [A_n-1B_nX_3n+1] and form two-dimensional (2D) geometrical configurations (Chen et al., 2018; Yu et al., 2017). These atomically thin layered structures exhibit notable octahedral rotations and distortions, which can lead to non-centrosymmetric configurations essential for polar characteristics and ferroelectric properties (Wang et al., 2016). Like conventional perovskite materials, chalcogenide perovskites can be engineered into two-dimensional R-P layered structures through compositional modifications, as indicated by simulation results. This approach enables the development of a wider variety of chalcogenide perovskite compounds.

The packing structure of R-P A₃B₂X₇ chalcogenide perovskites is illustrated in Figure 5A, where two neighboring corner-sharing BX6 octahedra are separated by an intercalated AX layer (Niu et al., 2018a). To gain a deeper understanding of the bonding characteristics and stability of the 2D layered structure, an electron localization function (ELF) simulation was conducted using Ca₃Sn₂S₇ as an example, as shown in Figure 5B (Du and Shi, 2019). An ELF value approaching zero indicates a metal-chalcogenide ionic bond with minimal electron density between the ions. Conversely, an ELF value approaching one signifies a strong covalent bond. Notably, the simulation reveals a partial covalent bond with an ELF value approximately 0.25 between Sn⁴⁺ and S^2-, which contrasts with the ionic bonds typically found in halide perovskites (Cai et al., 2018). This Sn-S covalent bonding enhances the structural stability and charge transfer efficiency in 2D R-P chalcogenide perovskites. Additionally, compared to halide perovskites, the structural integrity of R-P chalcogenide perovskites is further reinforced by stronger Coulomb interactions among ions with higher valence states.

Simulation methods were employed to investigate the band structure of R-P chalcogenide perovskites. It is important to note that standard DFT calculations tend to underestimate band gaps. Therefore, the modified GGA-1/2 method proved more accurate for determining the true band gap. The three-dimensional band structure, illustrated in Figure 5C, highlights the band edge dispersion features of R-P chalcogenide perovskites. Remarkably, these materials exhibit semiconductor properties like graphene, characterized by linear electronic band edge dispersion and a relatively small direct quasi-particle band gap. Further band structure calculations under various configurations of rotated octahedra show that the electronic structure is notably influenced by the distortion of the BX₆ octahedra, due to the complex hybridization from the interaction between the delocalized p orbitals of S and the s orbitals of Sn atoms (Niu et al., 2018a). According to the optimized band structure, R-P chalcogenide perovskites demonstrate intriguing optical absorption characteristics, as depicted in Figure 5D (Ravindran et al., 1997). They exhibit a broad absorption spectrum extending from the infrared to the ultraviolet regions, with absorption intensity increasing by two orders of magnitude in the infrared range, attributed to their direct band gap. Notably, the absorption edge shifts to higher energies with a decrease in layer number, due to the quantum confinement effect. Furthermore, the optical absorption capacity and spectral width of R-P chalcogenide perovskites surpass those of other advanced photovoltaic materials, such as MAPbI₃ and silicon, highlighting their promising potential for solar cell applications (Wu et al., 2017; Alsalloum et al., 2020).

Mechanical exfoliation techniques are commonly used to obtain 2D monolayer materials from their 3D counterparts, which requires that the layered materials exhibit weak interlayer interactions (Liao et al., 2018; Huang et al., 2020; Yi and Shen, 2015). R-P chalcogenide perovskites, being a type of layered material, are amenable to easy exfoliation. The calculated cleavage energy E _Cl, defined as the minimum energy required to overcome interlayer coupling during the exfoliation process, is depicted in Figure 5E (Medvedeva et al., 1996; Zhao et al., 2014). As the separation distance increases, E _Cl reaches its maximum value but remains significantly lower compared to other layered materials such as Ca₂N (Druffel et al., 2016). Similarly, the cleavage strength σ shows a comparable trend.

Beyond exfoliation characteristics, mechanical strength and elastic strain limits are crucial, determined by analyzing the stress-strain relationships of layered chalcogenide perovskites. The Young’s modulus, obtained from the stress-strain curve using linear regression, is shown in Figure 5F. Notably, the stress-strain curves along the x-direction and y-direction are identical, indicating that 2D layered chalcogenide perovskites are isotropic elastic materials. As tensile strain increases, these perovskites approach their breaking limit, with an elastic strain limit of approximately 20%, comparable to layered MoS₂ and graphene (Andrew et al., 2012; Mortazavi and Cuniberti, 2014).

In addition to optical and mechanical properties, DFT calculations predict the potential for ferroelectricity in R-P layered chalcogenide perovskites. Simulation results demonstrate that ferroelectric chalcogenide perovskites A₃B₂X₇ can transform from their paraelectric ABX₃ counterparts (Wang et al., 2016). Theoretical analysis highlights the tolerance factor as a key determinant of ferroelectric behavior (Zhang et al., 2017). For example, both Ba₃Zr₂S₇ and Ba₃Hf₂S₇, which have large tolerance factors, remain paraelectric due to the suppression of in-phase rotation—an essential feature for hybrid improper ferroelectricity. In contrast, Ca₃Zr₂S₇, Ca₃Hf₂S₇, and Ca₃Zr₂Se₇, with smaller tolerance factors, exhibit in-phase rotation and can stabilize into the ferroelectric phase with significant polarization.

In addition to ABX₃- and A₃B₂X₇-type chalcogenide perovskites, computational methods have predicted the potential of other chalcogenide perovskite variants, including NaBiX₂, A′La₂BX₁₀ (where A′ = Ba, Sr, Ca; B = Hf, Zr), CsLnMX₃ (where Ln = rare earth elements; M = Zn, Cd, Hg), and A₂MM′X₆ (where M = Bi or Sb; M′ = V, Nb, Ta), which are in their early research stage. Each of these materials offers unique advantages. For example, NaBiS₂ exhibits higher absorption coefficients compared to established direct-bandgap thin-film absorbers and has potential as a photocatalyst for degrading organic matter (Huang et al., 2022; Rosales et al., 2018; Kumar et al., 2022). Additionally, A’La₂BX₁₀ shows higher carrier mobility, stronger optical absorption intensity, and an optimal Shockley-Queisser limit, making it a promising candidate for solar cell materials (lang et al., 2020). Lanthanides in CsLnMX₃ can display characteristic emission through intrinsic 4f-4f transitions (Park et al., 2022; Yao et al., 2004; Mitchell et al., 2003; Jin et al., 2007). Furthermore, Sb-doped SrHfSe₃ chalcogenide perovskites are predicted to possess thermoelectric properties due to their p-type semiconducting nature (Moroz et al., 2018).

ML techniques have significantly accelerated the identification of promising materials by efficiently exploring vast chemical spaces. However, a key challenge is developing ML techniques that are not only accurate but also interpretable. Scientific disciplines often prefer simpler, more interpretable models over complex “black box” approaches. To enhance model interpretability, several strategies can be employed:

(1) Graph-Based Models. These models encode bonding relationships between atoms in crystals, creating frameworks that naturally incorporate physical and chemical constraints. This approach helps make the models more interpretable by aligning with known chemical principles.

Another major challenge in applying ML to materials science is the limited availability of high-quality data, particularly for specific and difficult-to-measure properties. While datasets for general properties like formation energies and band gaps are relatively abundant, niche properties such as alkali ionic conductivities or surface binding energies often suffer from data scarcity. To address these challenges, several strategies can be employed.

(1) Transfer Learning. This approach leverages knowledge from well-established models in domains with ample data (e.g., formation energies) to enhance model performance in areas with limited data (e.g., elastic moduli). By transferring insights from one domain to another, transfer learning can help mitigate data scarcity issues and improve predictive accuracy.

By employing strategies, researchers can address the data limitations in the discovery of novel perovskites and improve the effectiveness of ML models.

Although aforementioned challenges related to small data, transfer learning, and data fusion have been well-established in materials science field, they are particularly pertinent in this emerging field where the exploration of novel perovskites often outpaces the availability of high-quality data. Our discussion goes beyond simply acknowledging these challenges by highlighting recent advancements and specific strategies tailored to overcome data limitations in the context of novel perovskites. For instance, we explore how graph-based models and symbolic regression can enhance the interpretability of ML techniques in these materials, making the “black box” nature of models more transparent. Such techniques are particularly usefully in crystals system like perovskites.