Identifying MOFs for electrochemical energy storage via density functional theory and machine learning

Abstract

Electrochemical energy storage (EES) systems demand electrode materials with high power density, energy density, and long cycle life. Metal-organic frameworks (MOFs) are promising electrode materials, while new MOFs with high conductivity, high stability, and abundant redox-reactive sites are demanded to meet the growing needs of EES. Density Functional Theory (DFT) could calculate these properties of MOFs and provide atomic-level insights into the mechanisms, based on which machine learning (ML) can screen MOFs for EES efficiently. In this review, we first review the exploration of mechanisms based on DFT calculations. We focus on the conductivity, stability, and reactivity of MOFs in EES systems. Then, we review the steps to apply ML in screening MOFs. Establishing datasets of MOFs, extracting features from MOF structure, and applying ML in screening MOFs are discussed. Finally, the review proposes the future avenue of DFT and ML to make up the gaps in the knowledge of MOFs.

Introduction

Advancements in electrochemical energy storage (EES) systems, such as supercapacitors and batteries, are necessary to meet the demands of rapidly growing electric vehicles and large-scale energy storage^1,2,3,4,5. Supercapacitors are distinguished by their high power density, which enables rapid charging and discharging within seconds, as well as their exceptionally long cycle life, exceeding 10⁶ charge-discharge cycles^6,7. In contrast, lithium-ion batteries (LIBs) and other metal-ion batteries (sodium, potassium, and zinc, battery systems) are characterized by their high energy densities and relatively limited cycle life (a few thousand cycles)^7,8,9,10. Both batteries and supercapacitors encounter challenges in achieving higher energy density, power density, and long cycle life simultaneously^7,11. The performance of EES is limited by the electrode materials: (1) low electrical conductivity and the high solubility of organic electrode materials lead to low power density and cycle life^12,13, and (2) inorganic electrode materials exhibit low energy density^13,14. Consequently, the development of electrode materials with excellent electrical and ionic conductivity for high power density, robust stability for extended cycle life, high accessible specific surface area, and numerous active sites for achieving high energy density has become a critical focus in advancing high-performance EES systems¹⁵.

Metal-organic frameworks (MOFs) are a class of crystalline porous materials constructed from metal ions or clusters coordinated with organic ligands, which are distinguished by their high specific surface areas, significant porosity, and tunable structure enabling different functionalities^16,17,18. These properties make MOFs highly suitable as electrode materials for EES systems, and several MOFs have already been applied in such systems^19,20. For instance, Ni₃(2,3,6,7,10,11-hexaiminotriphenylene)₂ (Ni₃(HITP)₂) which exhibits a high surface area of 630 m² g⁻¹ and a conductivity of 40 S cm⁻¹ has been utilized as an electrode material for supercapacitors without the need for binders or conductive additives²⁰. However, the conductivity of MOFs remains relatively low compared to materials like graphene and graphite, which significantly affects the rate performance^21,22,23. Furthermore, the structural integrity of MOFs can be compromised during the charge and discharge cycles, leading to poor cycle stability²². To meet the needs of the growing energy sector, more MOFs with high electrical conductivity, stability, and abundant active sites are demanded^11,24,25. One of the most intriguing aspects of MOFs is their tunable structure and composition, which can be tailored by assembling various building blocks to achieve distinct properties suitable for diverse applications^26,27,28. Moreover, the disordered nature of porous carbon complicates modeling efforts, making it challenging to investigate structure–performance relationships²¹. In contrast, the highly organized and well-defined structures of MOFs facilitate modeling, offering clearer insights into the correlation between structures and performance²¹. Therefore, to design MOFs optimized for EES systems, it is necessitating to investigate the mechanisms of electrical conductivity, stability, and redox reactions.

Using density functional theory (DFT), the Schrodinger equation can be approximately solved and various physical and chemical properties of MOFs, such as band structure, reaction potential, and cohesive energy, can be determined²⁹. These calculations provide insights into the conductivity, stability, and redox activity of MOFs, offering a deeper understanding of the underlying mechanisms^30,31. This atomic-level understanding gained through DFT calculations is instrumental in the rational design and screening of MOFs for EES systems. For instance, linker aromaticity of 2D conductive MOFs, as determined by a combination of DFT calculations and NICS-xy scans, was found to reduce charge mobility, suggesting that modifying non-coordinating functional groups can adjust conductivity by influencing linker aromaticity^32,33. With the advancement of computational capabilities, high-throughput calculations of MOFs become feasible and tons of data are generated which is beyond the limitation that a human expert can process^34,35,36. By identifying patterns within data generated by DFT, machine learning (ML) becomes a powerful tool to rapidly establish complex relationships between MOF structures and their properties, allowing ML to quickly predict MOF properties without solving the complicated Schrodinger equation³⁷. ML enables us to efficiently explore the vast chemical space of MOFs which would be inaccessible using traditional methods because the number of possible structures of MOFs is too large^38,39,40,41. With the development of ML, models have become more accurate but increasingly difficult to interpret, limiting our understanding of the relationships between structures and properties³⁷. Enhancing the interpretability of ML models is essential for investigating mechanisms and designing MOFs³⁴.

In this review, we focus on the use of DFT and ML for screening and designing MOFs as electrode materials in EES systems. First, we discuss strategies for enhancing conductivity, chemical and mechanical stability, and redox-active sites based on DFT calculations. We then provide an overview of ML approaches for predicting MOF properties, covering database construction, feature engineering, and various ML applications. Finally, we discuss the remaining challenges and outline future directions to guide the design of MOFs.

DFT insights into the mechanisms of MOF properties

Conductivity of MOFs

Power density is largely influenced by electrode conductivity, as conductivity determines how quickly electrons can be transported within electrode materials¹¹. Most MOFs are composed of carboxylate linkers, which form robust ionic bonds with metal ions, contributing to structural stability but resulting in poor conductivity^42,43. However, due to their tunable structures and functionalities, conductive MOFs have been successfully developed^44,45. Gaining deeper insights into the relationship between structure and conductivity is crucial for designing more conductive MOFs. Charge transport in electrodes can be described through one of two primary mechanisms: hopping transport and band transport^24,30. In the case where sites are spatially separated and the interactions between them are weak, charge carriers transport between sites via hopping, typically found in the disordered materials²⁴. Conversely, when sites are sufficiently close to allow strong interactions, as commonly found in crystalline inorganic materials, continuous energy bands form that enable charge transport, and if the energy levels of these sites are also well-aligned, the electronic structure can be further tuned to enhance charge delocalization^24,46.

In the following section, we will first analyze the electronic structure of MOFs calculated using DFT within the framework of band theory to explore their conductivity. For the hopping mechanism, several models have been developed to describe the electronic structure and electrical properties^47,48,49. For detailed introductions, please refer to these reviews^30,50. We will then discuss the mechanisms behind electrically conductive MOFs and strategies to improve their conductivity.

Electronic structure

Band structure plays a key role in enabling physicists, chemists, and materials scientists to analyze and understand the properties of materials^29,51. In band theory, the electronic band structure describes the range of energy levels that an electron in a material can occupy, providing insights into the material’s electrical properties²⁹. In particular, the band structure is plotted along the wave vector (k) in the first Brillouin zone, then the band gap can be obtained from the energy difference between the valance band and the conduction band⁵¹. Intrinsic conductivity is largely determined by the band gap, which defines the intrinsic differences between a conductor, semiconductor, and insulator⁵¹: A conductor has a band crossing the Fermi level (E_F); A semiconductor usually has a band gap (E_g) smaller than 2 eV, allowing charge carriers to cross the band gap to the conduction band through thermal or optical excitation; in contrast, an insulator has a larger band gap^52,53,54,55. The band gap is a direct descriptor for identifying conductive MOFs. The accuracy of DFT calculations is influenced by the exchange-correlation (XC) functional. Band gap is usually underestimated by the Perdew–Burke–Ernzerhof (PBE) functional due to self-interaction error⁵⁶. Although hybrid functionals tend to offer more accurate band gap predictions, their significantly higher computational complexity of $O({N}_{e}^{3}\log {N}_{e})$ than PBE of $O({N}_{e}^{2}\log {N}_{e})$ limits their widespread application^29,57. Another approach to addressing the PBE underestimation without incurring substantial additional computational costs is incorporating a Hubbard U correction. However, the accuracy of DFT + U calculations depends on the selection of the effective Hubbard parameter, U_eff, which can vary with different systems or conditions⁵⁸. The GW method, adopting Green’s function and screened Coulomb interaction to represent the self-energy, greatly reduces self-interaction error and yields reliable band gap values^59,60. For instance, Nisar et al. ⁶¹ evaluated the band gap of pristine kaolinite using PBE, HSE (Heyd-Scuseria-Ernzerhof), and G₀W₀ (an approximation of the GW method), reporting values of 4.9, 6.2, and 8.2 eV, respectively, and inferring that the true band gap likely lies between 6.2 and 8.2 eV. In a separate comparison, Yang et al. ⁶² conducted a comparative study of hybrid functionals (HSE and PBE0) and the quasiparticle self-consistent GW method with vertex corrections for several extended systems, finding that the GW approach provided the most accurate band gap predictions when compared with experimental data. Besides the intrinsic conductivity, the conductive direction of MOFs can also be obtained through the band structure. As illustrated in Fig. 1a, the band structure reveals that Ni₃(HIB)₂ (HIB = hexaiminobenzene) exhibits conductivity in the in-plane direction, as evidenced by bands crossing the Fermi level⁴⁵. In contrast, LaHHTP (H₆HHTP = 2,3,6,7,10,11-hexahydroxytriphenylene) is conductive in the direction perpendicular to the 2D sheet (Fig. 1b), with bands crossing the Fermi level along the out-of-plane direction⁶³. These anisotropic conductivities exhibited in MOFs contribute to the distinct conductivity mechanisms, which will be discussed in section, “Mechanisms and improvements of conductivity”.

Fig. 1: Different conductive directions observed through electronic band structure.

a Calculated band structure of bulk Ni₃(HIB)₂ and Cu₃(HIB)₂ and the corresponding first Brillouin zone and high-symmetry K-points, indicating conductive in the in-plane direction. Reproduced with permission from ref. ⁴⁵ Copyright 2017 American Chemical Society (ACS). b Calculated band structure and density of states (DOS) of LaHHTP and the corresponding first Brillouin zone and high-symmetry K-points, indicating conductive in the direction perpendicular to the 2D sheet. Reproduced with permission from ref. ⁶³ Copyright 2019 Springer Nature.

As for conductive MOFs, their conductivity can be further evaluated. Electrical conductivity (σ) quantifies how efficiently a material can transport electrical charge when subjected to an electric field and is related to charge carrier concentrations (n) and mobility (μ)⁵¹:

$$\sigma =q\left({n}_{e}{\mu }_{e}+{n}_{h}{\mu }_{h}\right),$$

(1)

where q is the elementary charge and the subscripts e and h refer to electrons and holes³⁰. The concentration of charge carriers (n) is primarily governed by the ratio ${E}_{g}/{K}_{B}T$, representing the relationship between the band gap and temperature. When this ratio is large, the intrinsic carrier concentration becomes relatively low⁵¹. The charge mobility (μ) is inversely proportional to the effective mass (m^*) of the electrons or holes and is influenced by the scattering time (τ) within the material⁵¹:

$$\mu =\frac{q\tau }{{m}^{*}}.$$

(2)

The effective mass m^* can be calculated from the band structure, which is denoted as⁵¹:

$$\frac{1}{{m}^{* }}=\frac{1}{{{{\hslash}}}^{2}}\frac{{\partial }^{2}E}{\partial {k}^{2}},$$

(3)

where ℏ is the reduced Plank constant and $\frac{{\partial }^{2}E}{\partial {k}^{2}}$ is the band curvature at k point. If the band curvature is negative, the charge carrier is considered to be a hole, whereas a positive m^* corresponds to an electron. A band with greater curvature means a smaller m^*, leading to higher μ and σ. Except for m^*, τ is also needed to calculate μ. While m^* can be easily obtained from the band structure, accurately calculating n and τ based on DFT is challenging, making it difficult to directly determine conductivity. Most of the studies compare the charge mobility or conductivity by evaluating m^* under specific conditions. Clough et al. ⁶⁴ calculated the effective mass in different directions of a 2D MOF. The smallest effective mass in the in-plane direction is 1.27 m_e which is much bigger than the minimum effective mass of 0.29 m_e along the c-axis. This means easier transport in the c-axis and indicates that the main conductive pathway is through the c-axis. Band curvature represents a specific characteristic of energy band dispersion, quantifying the degree of curvature of the energy band. Therefore, we can use the band dispersion instead of calculating band curvature to compare m^*. Wang et al. ⁶⁵ reported that the conductivity is dominated by the interlayer direction by comparing the band dispersion.

DFT calculations are typically based on ideal crystal structures, whereas experimentally synthesized materials inherently contain defects, leading to discrepancies between experimental results and DFT predictions⁶⁶. Ni₃(HITP)₂ was first synthesized in 2014, and its conductivity was found to increase with temperature from 77 to 450 K, indicating semiconducting behavior⁴⁴. However, Ni₃(HITP)₂ was predicted to be metallic, as DFT calculations revealed a zero band gap^67,68,69. To address this discrepancy, Foster et al. ⁷⁰ constructed MOF structures containing two kinds of defects, grain boundaries, and stacking faults (Perpendicular grain boundary, Strike-slip fault between grains, and layer–layer displacement defect) and calculated the band structure of these structures. The calculation results revealed that all defects would lead to dispersionless or open a band gap. They concluded that the conductivity of Ni₃(HITP)₂ was dominated by the charge hopping between the microstructure⁷⁰, and the same inference was made for Ni₃(HIB)₂ and Cu₃(HIB)₂⁴⁵. To determine the actual structure of Ni₃(HITP)₂ at 293 K, Zhang et al. ⁷¹ performed ab initio molecular dynamics (AIMD), which revealed that the layers slip in-plane and expand or contract out-of-plane, thereby introducing stacking faults into the structure. These defects lead to an energy difference of 50–200 meV in the in-plane direction and produce a relatively flat band out-of-plane. Debela et al. ⁶⁶ investigated the impact of hydrogenic defects on the conductivity of Ni₃(HITP)₂. Hydrogenic vacancies and interstitials were found to significantly affect the electronic structure, often converting the predicted metallic behavior into semiconducting properties.

Ogle et al. ⁷² synthesized Cu-BHT (BHT = benzenehexathiol) using two different methods: solid–vapor (S-V) and vapor–vapor (V-V) chemical vapor deposition (CVD) approaches. They found that the S-V method produced structures with lower Cu vacancies and larger single-crystalline domain sizes compared to the V-V method⁷². Additionally, the S-V synthesized Cu-BHT tended to form AB stacking, whereas the V-V synthesized structures exhibited AA stacking⁷². These structural differences were attributed to the observed electrical properties, with the S-V approach resulting in metallic behavior and the V-V approach yielding semiconducting behavior⁷². The effect of copper vacancies on conductivity was further investigated by Luo et al.⁷³ and they found that copper vacancies did not alter the metallic behavior. This finding was supported by a zero band gap calculated using density functional theory (DFT) and the reciprocal relationship between temperature and conductivity⁷³. However, Cu-BHT with a higher density of copper vacancies exhibited lower conductivity, as the vacancies disrupted charge transport⁷³. Skorupski et al. ⁶³ investigated linker vacancies in MOFs composed of lanthanide ions and H₆HHTP. They discovered that the absence of a linker disrupts π-π stacking between the linkers, leading to the localization of the linker electronic wavefunctions and reduced band dispersion in the out-of-plane direction⁶³. Additionally, the authors attributed the semiconducting behavior to metal vacancies identified via X-ray diffraction, as well as to the presence of grain boundaries and anisotropic conductivity⁶³.

On the other side, experimental efforts have focused on synthesizing single-crystal MOFs to eliminate the influence of defects on conductivity. Day et al. ⁷⁴ successfully synthesized a single crystal of Ni₃(HITP)₂ which exhibited an intrinsic metallic nature and the conductivity was up to 150 S cm⁻¹. The result is consistent with the DFT calculations and provides insights into the charge transport from an experimental point of view. Skorupskii et al. ⁷⁵ synthesized new porous MOFs, Ln_1.5HOTP (Ln = La, Nd; HOTP = 2,3,6,7,10,11-hexaoxytriphenylene), of which single crystals are metallic and the conductivity reached 1000 S cm⁻¹. These reports showed that the conductivities of polycrystalline MOFs are influenced by the crystallinity^74,75.

Mechanisms and improvements of conductivity

The ionic nature of the bonds between metal nodes and organic linkers tends to localize electrons, making efficient electrical conduction challenging⁷⁶. Additionally, the high porosity of MOFs, while beneficial for applications of EES systems, often reduces the overlap between electronic states²⁴. This reduced overlap impedes the free movement of charge carriers, leading to lower conductivity. Therefore, porosity seems to inherently conflict with conductivity²⁵. Through-bond and through-space are two effective methods for enhancing conductivity²⁴. In the through-bond approach, coordination bonds between organic ligands and metal nodes form networks for charge transport²⁴. Pathak et al. ⁷⁷ reported a MOF, {[Cu₂(6-Hmna)(6-mn)]·NH₄}_n (1, 6-Hmna = 6-mercaptonicotinic acid, 6 mn = 6-mercaptonicotinate). Calculations revealed greater band dispersion along the direction of the (-Cu-S-) plane, with Cu-d and S-p states contributing to the valence band maximum (VBM)⁷⁷. These results indicate that the continuous transport routes along the (-Cu-S-) plane make the MOF electrically conductive⁷⁷. In graphene-like 2D MOFs, extended π-d conjugation enables efficient electron delocalization between coordination bonds⁴⁵. Electrons delocalize not only over the organic ligands but also across the metal centers, leading to a continuous electronic network within the MOF. M₃(HIB)₂ (M = Ni, Cu) features trigonal organic ligands and square-planar mononuclear metal nodes, which assemble into 2D sheets⁴⁵. These structural features promote effective charge delocalization via extended π-d conjugation between the metal nodes and ligands⁴⁵. In the through-space approach, organic ligands interact with each other to form through-space charge transport pathways^63,64,78. This interaction, known as π-π stacking, is commonly observed in 2D MOFs^63,64,78,79. Lanthanide ions (Ln³⁺) possess valence electrons in deeply buried 4 f orbitals, leading to predominantly ionic bonding⁶³. However, LnHHTP demonstrated electrical conductivity, attributed to π-π stacking interactions between the ligands, which facilitate effective charge delocalization⁶³. These different approaches can be recognized through DFT calculations. For extended π-d conjugation and through-space mechanisms, MOFs typically exhibit conductivity in specific directions: in-plane direction for extended π-d conjugation approach⁴⁵ and out-of-plane direction for through-space approach^63,64,78. Furthermore, the density of states (DOS) near the Fermi level is jointly contributed by both ligands and metals for the extended π-d conjugation approach⁴⁵, whereas it is primarily contributed by the ligand in the through-space approach^63,64,78. Conductive MOFs based on the through-bond mechanism can conduct electrons either in a specific direction or in all directions. Partial charge density plots of the VBM and conduction band minimum (CBM) can aid in identifying conductive pathways and, thereby, determining the conductive mechanism⁷⁷.

Based on the understanding of charge transport mechanisms, several methods have been proposed to improve conductivity. Softer coordination atoms, such as nitrogen or sulfur, can enhance the covalency of coordination bonds, thereby improving conductivity^42,77. Incorporating bimetallic nodes is also an effective strategy for enhancing conductivity, as the introduction of an additional metal node increases the concentration of charge carriers^80,81,82. Demuth et al. ³² suggested that the aromaticity of the linker influences charge mobility, as aromatic linkers tend to stabilize π-electrons. In the through-space approach, a smaller stacking distance results in stronger π-π stacking interactions, leading to higher conductivity^63,83. The highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of ligand core and metal-organic linkage should be well aligned to form dispersed bands crossing the Fermi level, thereby enhancing charge mobility^78,79,84.

Additionally, charge transport in MOFs can occur via hopping mechanisms²⁴. Conductivity can be improved by incorporating redox-active metals or ligands into MOFs as sites for charge hopping, which facilitates the formation of continuous charge transport pathways²⁴. NDI (naphthalene diimide) is a redox-active linker that forms a series of conductive MOFs with various metals^85,86,87,88. Introducing mixed valency into MOFs has also been shown to be an effective strategy for enhancing conductivity^46,89,90. Upon exposure to the atmosphere, Fe₂(BDT)₃ (H₂BDT = 5,5’-(1,4-phenylene)bis(1H-tetrazole)) underwent partial oxidation, resulting in the emergence of mixed valency states of iron, which led to an increase in conductivity by more than 5 orders of magnitude⁹⁰. Furthermore, incorporating electroactive guest molecules into the pores of MOFs can modulate the conductivity, although this often severely compromises porosity, thereby affecting their applicability in EES^24,91. Talin et al. ⁹¹ introduced the molecule 7,7,8,8-tetracyanoquinododimethane (TCNQ) into the MOF Cu₃(BTC)₂ (BTC = benzene-1,3,5-tricarboxylic acid) resulting in six orders of magnitude increase in conductivity compared.

Based on the understanding of the conductive mechanisms, a lot of porous conductive MOFs have been designed and synthesized^23,90,92. Nd_1.5HOTP exhibits a remarkable conductivity of 1080 S cm⁻¹ at room temperature, demonstrating the highest conductivity reached in porous MOFs or other intrinsically porous materials⁷⁵.

Stability of MOFs

The stability of electrode materials determines the cycle life of EES systems, but the instability of MOFs significantly limits their application in these systems. Therefore, understanding the factors that influence stability and developing strategies to enhance it are of critical importance to MOF-based EES. The cycle life is influenced by both chemical and mechanical stability, as the framework structures of MOFs are prone to collapse under harsh chemical conditions or mechanical stress, significantly affecting their performance during extended cycling⁹³. Here, we focus on the efforts to understand the mechanisms of chemical stability and mechanical stability and design new stable MOFs based on this understanding.

Chemical Stability

Chemical stability refers to the ability of MOFs to retain their structural integrity under aqueous acidic or alkaline conditions⁹⁴. The coordination bonds between metal ions and organic linkers play a crucial role in determining the overall chemical stability of the framework^3,82,94. To prevent coordination bonds from breaking and subsequent structural, two methods have been developed to protect coordination bonds: constructing robust coordination bonds^{80,95,96,97,98}, and preventing coordination bonds from being attacked^80,99,100.

According to Pearson’s hard and soft acid-base (HSAB) theory, strong and stable bonds are preferentially formed when Lewis soft acids coordinate with Lewis soft bases, or when Lewis hard acids coordinate with Lewis hard bases¹⁰¹. Based on the HSAB theory, a series of stable MOFs are designed and synthesized^80,95,96,97. Among these MOFs, iron(III)-tetraamino-benzoquinone (Fe-TABQ) demonstrated high chemical stability, retaining 95% of its capacity after 200 cycles as a LIB electrode, which DFT calculations attribute to a strong d-π orbital interaction between Fe and TABQ⁹⁷. The Paddlewheel framework (Fig. 2a) has been proven to be a stable structure because of multiple bridging-chelating coordination and robust metal-metal bond^80,98. Based on the HSAB theory, Chen et al. ¹⁰² designed and synthesized a series of {[Ln₄(μ₄-O)(μ₃-OH)₃(INA)₃(GA)₃](CF₃SO₃)(H₂O)₆}_n (denoted as Ln₄-MOFs, Ln = Gd, Tm, and Lu, INA = isonicotinic acid, GA = glycolic acid). These MOFs demonstrated remarkable stability across challenging conditions, including high moisture, acidic and basic pH environments, and extreme temperatures, while maintaining excellent conductivity, a characteristic rarely observed in highly stable MOFs¹⁰². Protecting coordination bonds away from the attack of guest molecules can also effectively maintain structural integrity. To enhance water stability, hydrophobic groups, such as methyl groups, are introduced into the ligands to prevent the degradation of coordination bonds by water molecules^80,100. Huang et al. ⁹⁹ designed two identical MOFs, one with cationic and another one with neutral frameworks, namely PFC-8 and PFC-9 (Fig. 2b). They found that PFC-8 exhibited higher chemical stability than PFC-9 under acidic, oxidative, reductive, and high ionic strength conditions which proved that a cationic framework can improve chemical stability. To investigate the protective mechanisms of the cationic framework on coordination bonds, they performed DFT calculations. As evidenced by the DFT calculation, the Ni center in PFC-9 adopts a square planar geometry, while in PFC-8, due to the coordination of Cl^- ions, the Ni center forms an octahedral geometry of which the large steric hindrance protects the Ni-N bond from the reactive species. Besides, the Bader charge analysis revealed that the Ni ions in PFC-8 have a higher positive charge density. This increased positive charge enhances the repulsive interaction between the cationic framework and positively charged guest species, effectively protecting the fragile Ni–N bonds. The calculations of the binding energies showed that protons preferentially bind to the nitrogen atoms in PFC-9, leading to the cleavage of Ni–N bonds. In contrast, the presence of Cl^- ions in PFC-8 reduces the corrosive effect on the Ni–N bonds, significantly improving its stability.

Fig. 2: Different ways to prevent coordination bonds from breaking.

a Structure of Co-bpy and paddlewheel SBU. Reproduced with permission from Ref. ⁸⁰ Copyright 2021 Wiley. b Schematic representation of the structures of cationic PFC-8 and neutral PFC-9. Reproduced with permission from Ref. ⁹⁹ Copyright 2020 Wiley. c The upper line shows the mechanism of water absorption on dehydrated STAM-17-OEt. When water adsorbs onto the open metal site, energy is released and utilized to break the weak interactions between Cu and O. The bottom line illustrates the mechanism of coordination bonds breakdown in HKUST-1. During the Hydration, energy is released and used to break metal–carboxylate oxygen bonds in the paddlewheel. Reproduced with permission from ref. ¹⁰³ Copyright 2018 Springer Nature.

A novel mechanism is reported to protect the coordination bonds¹⁰³. STAM-17-OEt exhibits superior hydrolytic stability compared to HKUST-1, which has a similar chemical composition and structure. In STAM-17-OEt, sacrificial Cu-O bonds form during dehydration and break upon rehydration, allowing the structure to revert to its hydrated form as shown in Fig. 2c. In contrast, without these sacrificial bonds, the coordination bonds in HKUST-1 are broken, leading to structural degradation (Fig. 2c). Two idealized models are generated based on the experimental structures, one with weak Cu–O interactions and one without. The DFT results showed that the experimentally observed dehydrated model (with weak Cu–O interactions) is 0.228 eV lower in energy than the hypothetical dehydrated model, which lacks these weak interactions. The calculations demonstrated that the formation of weak Cu–O bonds not only contributes to the thermodynamic stability of the framework but also prevents the release of sufficient energy to break the more critical framework bonds.

Mechanical stability

Mechanical stability refers to the ability to maintain the structure integrity under various mechanical loads. During the activation process of MOFs, where solvents are removed from the pores, capillary forces often induce structural degradation⁹⁴. In batteries and pseudo-capacitors, redox reactions lead to electrode expansion and contraction due to the insertion and extraction of ions⁹³. These mechanical stresses can result in instability, leading to phase transitions, partial pore collapse, or even amorphization of the material. Therefore, it is crucial to enhance the mechanical stability of MOFs. Similar to chemical stability, mechanical stability benefits from robust coordination bonds and high connectivity. Cavka et al. ⁴³ designed a zirconium-based MOF, UiO-66, which exhibits exceptional stability and they attributed the stability to the robust Zr–O coordination bonds. Redfern et al. ¹⁰⁴ validate the conclusion that robust coordination bonds contribute to mechanical stability by exploring the influence of different metal nodes. They reported that the bulk modulus of Ce-UiO-66 is lower than that of Zr-UiO-66 and Hf-UiO-66. The DFT calculations revealed that the coordination bond (M-O bond) shortens more rapidly under pressure in Ce-UiO-66 than in Zr-UiO-66. This suggests that the Ce-O bond is weaker and more flexible, leading to lower bulk modules. Wu et al. ¹⁰⁵ further identified high metal-organic coordination as another key factor behind UiO-66’s extremely high bulk modulus. Hobday et al. ¹⁰⁶ explored the mechanical stability of two zirconium-based metal-organic frameworks (MOFs) with UiO topology, specifically UiO-67 and UiO-abdc (abdc: 4,4’-azobenzene dicarboxylate). The study combines both computational and experimental approaches to understand how disorder in the linkers affects their behavior under high pressure. The research reveals that dynamic disorder in the ligands has a significant impact on the mechanical properties of the framework. UiO-abdc, which features a more flexible and disordered azobenzene linker, shows a decrease in the elastic modulus and increase in resistance to pressure compared to UiO-67, which has a more rigid biphenyl dicarboxylate linker.

Redox activity of MOFs

MOF-based supercapacitors

Currently, MOFs are frequently used as electrode materials for supercapacitors and batteries. Supercapacitors are generally categorized into two types: electrical double-layer capacitors (EDLCs) and pseudo-capacitors (PCs)⁶. EDLCs store energy through the reversible adsorption of electrolyte ions onto the nanopores of the electrodes and form electrical double layers (EDLs)⁶. Conductive MOFs, due to their high surface area and conductivity, are well-suited as electrode materials for EDLCs. For example, Ni₃(HITP)₂ has demonstrated a high conductivity of 40 S cm⁻¹, resulting in an excellent specific gravimetric capacitance of 111 F g⁻¹ (at the discharge rate of 0.05 A g⁻¹)²⁰. The energy storage process of EDLCs is purely physical, involving no chemical reactions, and can be described using classical molecular dynamics simulations. Recent works on EDLCs have been reviewed in recent studies^88,107.

Compared to EDLCs, PCs generally exhibit higher capacitance and energy density since they store energy through faradaic reactions occurring on the surface of electrode materials^108,109. For instance, the typical redox-active MOF, Ni-HAB (HAB = hexaaminobenzene), exhibits a high capacitance of 420 F g⁻¹, attributed to its pseudocapacitive charge-storage mechanism^19,110. Therefore, significant efforts by DFT calculations have been devoted to understanding this pseudocapacitive mechanism in MOFs to further enhance capacitance and energy density¹¹¹. Ni₂[CuPcS₈], Ni₂[CuPc(NH)₈], and Ni₂[CuPcO₈] exhibited different storage mechanisms in various electrolytes^112,113. In a 1 M TEABF₄/acetonitrile electrolyte, Ni₂[CuPcS₈] demonstrated an outstanding pseudo-capacitance of 312 F g⁻¹. DFT calculations based on cluster models suggest that this enhanced capacitance is due to the localized LUMO of the NiS₄ linker (Fig. 3a), which facilitates efficient delocalization of the injected electrons¹¹³. In the aqueous electrolyte of 1 M Na₂SO₄, Ni₂[CuPc(NH)₈] demonstrated a higher capacitance of 400 F g⁻¹. The calculated molecular electrostatic potential (MESP) for truncated MOF molecules indicates the presence of nucleophilic and electrophilic regions, which enable the adsorption of SO₄^2- and Na⁺ ions (Fig. 3b). As shown in Fig. 3c, continuous Faradaic reactions occur through the adsorption/desorption of Na⁺ on the NiN₄ linkers and the desorption/adsorption of SO₄^2- on the CuPc building blocks¹¹². Co-CAT and Ni-CAT (CAT = catecholate) also feature dual redox sites in a Na₂SO₃ electrolyte¹¹⁴. DFT calculations based on cluster models indicate that the binding energy for SO₃²⁻ adsorption on Co-CAT is lower than that on Ni-CAT, leading to a more effective attraction and reaction of SO₃^2-. Therefore, it is crucial to find a suitable match of MOFs and electrolytes to achieve higher capacitance. MOFs can be modeled either as periodic solids or approximated to clusters. The cluster approximation requires careful validation to ensure the truncated molecular model is sufficiently large to minimize errors¹¹⁵. It is important to note that the cluster approach may yield inaccurate results for properties that rely on the extended symmetry of the material¹¹⁶. On the other hand, for local properties, such as chemical bond analysis, the cluster approximation allows the application of high-level theoretical methods that are often infeasible for solid-state materials¹¹⁵. The comparison of these two methods in terms of accuracy, computational efficiency, and suitability for different scenarios has been discussed in detail in this review¹¹⁵.

Fig. 3: Charge storage mechanisms of three MOFs in various electrolytes.

a Spatial distribution of LUMOs in the Ni₂[CuPcS₈], Ni₂[CuPcN₈], and Ni₂[CuPcO₈]. Reproduced with permission from ref. ¹¹³ Copyright 2023 ACS. b MESP distribution of Ni₂[CuPc(NH)₈] Reproduced with permission from ref. ¹¹² Copyright 2021 ACS. c Electronic states of the repeating unit of Ni₂[CuPc(NH)₈] during the charge/discharge process. Reproduced with permission from ref. ¹¹² Copyright 2021 ACS.

MOF-based batteries

Conductive MOFs can also serve as electrodes in batteries, and a bunch of highly conductive have been synthesized and applied in metal-ion batteries^{117,118,119,120,121,122,123}. However, the limited number of redox sites in MOFs results in low energy density. Therefore, designing MOFs with abundant redox-active sites has the potential to significantly enhance energy density, but remains a challenging task.

Redox reactions commonly occur on ligand cores and metal-organic linkages. In conductive 2D MOFs, the metal-organic linkages, CuO₄ units, have been proven to effectively enhance the energy density of MOF-based batteries^{119,124,125,126,127,128,129,130}. Dioxolene ligands and the metal Cu form the CuO₄ units where the dioxolene moiety undergoes a series of oxidation steps between catechol, semiquinone, and quinone, transferring two electrons¹²⁷. Additionally, the reduction of Cu²⁺ to Cu⁺ contributes a one-electron transfer, further enhancing the density of redox-active (Fig. 4a)¹²⁴. In addition to metal-organic linkages, efforts have been made to incorporate more redox-active sites into ligands^127,131. Incorporating quinone compounds into ligands is a potential approach to enhance the capacity of MOFs, as they contain numerous redox-active sites. Based on this approach, Yan et al. ¹²⁷ incorporated tricycloquinazoline (TQ) as the ligands into the MOF, Cu-HHTQ, which achieved a high capacity of 657.6 mAh g⁻¹ at 600 mA g⁻¹ and outstanding cycle stability. Through the electrostatic potentials and binding energies of the lithiation of TQ, they confirmed their hypothesis that TQ will undergo a nine-electron reaction for Li⁺ storage. Similarly, quinone groups in Cu-TBPQ were demonstrated to be attractive to Zn²⁺ by the calculation of MESP distribution and experimental spectroscopic analysis¹³¹.

Fig. 4: Charge storage mechanisms of MOF-based batteries.

a Schematic diagram of the insertion and removal processes of Na⁺ in the (CuO₄) units. Reproduced with permission from ref. ¹³⁰ Copyright 2024 Wiley. b The binding sites of Li⁺ on Cu-HATN and the distribution electrostatic potential surfaces of Cu-HATN, Cu-HATN+12Li, Cu-HATN+36Li, and Cu-HATN+48Li. Reproduced with permission from ref. ¹²⁹ Copyright 2023 Wiley. c DFT calculations on two possible distributions of sql-Cu-TBA-MOF with 4 K⁺ during redox reaction and the corresponding binding energies. Reproduced with permission from ref. ¹³² Copyright 2024 Wiley. d DFT calculations on three possible distributions of kgm-Cu-TBA-MOF with 6 K⁺ during redox reaction and the corresponding binding energies. Reproduced with permission from ref. ¹³² Copyright 2024 Wiley.

It is crucial not only to incorporate redox-active sites but also to maximize their exposure to ions to facilitate effective reactions. Two MOFs, Cu-HATN (HATN = hexaazatriphenylene) and Cu-TAC (TAC = triazacoronene) achieved high capacities of 763 mAh g⁻¹ and 772.4 mAh g⁻¹ at 300 mA g⁻¹, which features redox-active sites exposed within the pores, making them more accessible to Li⁺ ions (Fig. 4b)^128,129. Furthermore, MOFs with the same composition but different topologies can result in different numbers of accessible redox-active sites. For instance, the rhombus structure (sql-Cu-TBA-MOF) of Cu-TBA (TBA = octahydroxyltetrabenzoanthracene) exhibited higher capacity in potassium-ion batteries (PIBs) than the kagome structure (kgm-Cu-TBA-MOF) due to its higher surface area, uniform pore size (Fig. 4c), and larger layer space¹³². The calculated binding energies also revealed that sql-Cu-TBA-MOF is more attractive to K⁺ as shown in Fig. 4c, d¹³².

Except for the intercalation of the cations in the metal-ion batteries discussed above, studies have shown a novel storage mechanism in which both anions and cations are stored. Chen et al. ¹³³ compared different storage mechanisms of Zn-HHTP and Cu-HHTP in SIBs. As the experiment observed, Cu will undergo a redox reaction of Cu²⁺/Cu⁺ during the charging process while Zn remains redox inactive¹³³. Although Zn²⁺ is not involved in the redox reaction, the ligand of Zn-HHTP can successively store anions (PF₆⁻) and cations (Na⁺) while the ligand of Cu-HHTP can only store cations¹³³. The calculated intercalation/de-intercalation potential of PF₆^- in Zn-HHTP consists well with the experimental redox potential, which further proved the storage of PF₆^- in Zn-HHTP¹³³. Both Zn-HHTP and Cu-HHTP went through a three-electron redox reaction and exhibited similar capacity, but Zn-HHTP exhibited better cyclability because of redox reactions of only ligands¹³³. Similarly, Ni₃(HATQ)₂ (HATQ = 2,3,7,8,12,13-hexaaminotricycloquinazoline) achieved a co-storage mechanism of anions (PF₆^-) and cations (Na⁺)¹³⁴. The electrostatic potentials and charge density distribution demonstrate that Na⁺ is attracted to the N atom of the NiN₄ unit, while PF₆^- is drawn to the N atom of the TQ cores, with binding energy results further confirming this tendency¹³⁴. Cheng et al. ¹³² reported a MOF with rhombus structure, sql-Cu-TBA which exhibited 146.6 mAh g⁻¹ at 0.1 mA g⁻¹ in PIBs. To gain insight into the charge storage mechanism, they performed cyclic voltammetry (CV) analysis, XPS spectra, and FT-IR spectra and found that both K⁺ and PF₆⁻ could be stored¹³². They further performed DFT calculations and the calculated reaction voltages accord with the experiment results which demonstrated that 3 K⁺ and 1 PF₆⁻ are combined with each CuO₄ unit¹³². They also calculated the binding energies of different stages during the interaction of K⁺ and PF₆^- with sql-Cu-TBA¹³². The negative values at each stage indicate that the structure is stable throughout the process and the process is feasible¹³².

ML Workflow for Predicting MOF properties

ML can be divided into three categories: supervised learning, unsupervised learning, and reinforcement learning^38,41,135. In supervised learning, both features and labels of materials are available, allowing the establishment of relationships between features and labels⁴¹. In unsupervised learning, only features are accessible, enabling the discovery of patterns within the data⁴¹. Reinforcement learning focuses on finding optimal behaviors that maximize rewards through an agent’s interaction with its environment¹³⁶. Supervised learning is the most widely used form of ML today, and it will be the focus of our discussion. Algorithms in machine learning can be broadly divided into two categories: shallowing learning algorithms and deep learning algorithms¹³⁷. Shallowing learning algorithms, such as support vector machines (SVM)^138,139, k-nearest neighbors (KNN)¹⁴⁰, decision trees (DT)¹⁴¹, and artificial neural network (ANN)¹⁴², rely heavily on expert knowledge to design and generate meaningful descriptors to represent materials features. These algorithms work well with small datasets¹³⁷. Additionally, they are highly interpretable, making it easier to understand and explain how predictions are made¹³⁷. With the emergence of big datasets composed of hundreds of thousands of samples, deep learning algorithms, such as convolutional neural networks (CNNs), transformers¹⁴³, and recurrent neural networks (RNNs), become achievable. They can automatically extract features directly from raw data, eliminating the need for manual feature engineering and facilitating reliable mapping relations between features and targets¹³⁷. Nevertheless, it is challenging to interpret deep learning models, due to the elusive physical meaning of descriptors and convoluted mapping relations³⁴. Therefore, some methods have been developed to interpret the model³⁴, such as SHAP (SHapley Additive exPlanations)¹⁴⁴.

To apply ML in predicting MOF properties, we first need to collect or generate data on these properties. Next, we extract the relevant features of MOFs based on the specific problem and algorithm. Finally, these features and properties are used as inputs to the algorithm to establish the relationships between them. The model generally needs to be validated before being used for making predictions. Typically, the dataset is divided into a training set and a test set, where the training set is used for model training, and the test set is used to evaluate its performance³⁸. High-quality and abundant data, feature engineering, and ML algorithms are essential for ML models to accurately learn the relationships and predict the properties. Furthermore, experts in material science not only need MOFs with high performance but also the influence factors of MOF properties to design new MOFs.

Constructing databases of MOFs

The challenge of rapidly collecting material data has driven the development of several platforms that compile and provide access to extensive material datasets. These platforms, such as Materials Project (MP)¹⁴⁵, AFLOW¹⁴⁶, OQMD¹⁴⁷, Materials Cloud¹⁴⁸, and NOMAD¹⁴⁹, aim to make material data readily accessible and reusable for users. The quantity and quality of data are crucial for prediction accuracy, which presents a significant challenge in the field of MOFs. Data on MOF structures and properties collected from high-throughput calculations or experiments can often be inconsistent, incomplete, and sourced from different origins^38,41. To address this, databases of MOF properties have been developed to facilitate the application of ML in MOF research. The Cambridge Crystallographic Data Centre (CCDC) has characterized various MOFs and generated the Cambridge Structural Database (CSD) subset, which is continuously updated with newly experimental synthesized and reported MOFs^150,151,152. The experimental structures of MOFs normally contain solvent molecules and partially occupied or disordered atoms, making it difficult to calculate. In 2014, the Computation-Ready Experimental (CoRE) MOF database was established, comprising approximately 4,700 MOFs from the CSD¹⁵³. By removing solvent molecules and correcting partially occupied or disordered atoms, MOFs in the CoRE database are well-suited for high-throughput computational screening. Recently, the CoRE MOF database was updated to include over 14,000 MOF structures¹⁵⁴. With the structures of MOFs, high-throughput DFT calculations can be performed and various properties of MOFs can be obtained. Rosen et al. ¹⁵⁵ introduced the QMOF database based on PBE functional, which includes quantum-chemical properties for over 14,000 MOFs gathered from the CSD and CoRE database, such as optimized geometries, band gaps, density of states, charge densities, partial atomic charges, and net magnetic moments.

Several methods have been developed for generating hypothetical MOFs^156,157. Notable examples include the ToBaCCo¹⁵⁸, ToBasCCo¹⁵⁹, and PORMAKE methods¹⁶⁰, which have been employed to generate hundreds of thousands of potential MOFs. Moosavi et al. ¹⁶¹ generated 200 hypothetical MOFs based on the ToBasCCo method and calculated mechanical properties using molecular dynamics simulations. Majumdar et al. ¹⁶² produced approximately 20,000 hypothetical MOFs using the ToBaCCo method and evaluated their adsorption performance for CO₂ and H₂, as well as their effectiveness in separating CO₂ from flue gas using Grand-canonical Monte Carlo (GCMC) simulations. Nandy et al. ¹⁶³ employed ML models to identify stable MOFs, which they deconstructed into organic nodes, organic edges, and inorganic nodes. Using PORMAKE, they recombined these building blocks to generate 50,000 hypothetical MOFs¹⁶³. Elastic modulus calculations for nearly 10,000 MOFs demonstrated their excellent mechanical stability¹⁶³. Zhang et al. ¹⁶⁴ recombined the organic linkers and metal nodes to generate 1057 bulk and monolayer structures of 2D conductive MOFs, termed EC-MOF database. This database provides various properties of electrically conductive MOFs calculated based on DFT, such as band gap, d-band center, formation energy, largest cavity diameter, gravimetric and volumetric surface area, and void fraction. Burner et al. ¹⁶⁵ compiled the ARC-MOF database with approximately 280,000 MOFs, including experimental and computationally generated structures. It features DFT-derived partial atomic charges using the REPEAT method and provides ML-ready descriptors¹⁶⁵.

There are also some databases that gather experimentally characterized properties of MOFs from the literature. Nandy et al. ^166,167 used natural language processing (NLP) to identify manuscripts reporting solvent removal stability or thermogravimetric analysis data, assembling a dataset of 2179 MOFs with solvent removal stability and 3,132 with thermal decomposition temperatures. Iacomi and Llewellyn¹⁶⁸ processed adsorption isotherms from the NIST Isotherm Database (ISODB)¹⁶⁹, a repository of experimental and simulated adsorption isotherms collected from the scientific literature. To prepare the data for meaningful analysis and potential machine learning applications, they implemented stringent filtering criteria to ensure relevance and comparability among the isotherms¹⁶⁸. Luo et al. ¹⁷⁰ used NLP to extract MOF synthesis conditions from the literature, establishing the SynMOF database which contains 983 MOF structures and their synthesis details, including the metal source, linkers, temperature, synthesis time, solvents, and additives).

Feature engineering

In materials science, effective representation of materials is important, as it contains essential information that allows ML models to establish robust relationships between input features and target properties^171,172. The process of feature extraction varies depending on the problem and the algorithm used^41,171,172. Classical machine learning models rely heavily on domain experts to engineer features that are highly relevant to the problem at hand, allowing for solid performance with fewer data than deep learning typically requires⁴¹. In contrast, deep learning integrates feature extraction directly into the model’s learning process, automatically discovering useful representations^41,135. As a result, deep learning models reduce the dependence on expert-driven feature engineering but demand significantly more data¹⁷². Deep learning can potentially uncover patterns or regularities that are not immediately apparent to human experts¹³⁷. For MOFs, which are highly ordered crystalline solids, an ML model can recognize the similarities and capture the differences among the structures in the training set and leverage that insight to predict the properties of new structures without calculation or experimental measurements¹⁷³. However, representing this complex structural information in a form suitable for ML models presents significant challenges due to the need to capture both local atomic environments and long-range periodicity inherent to crystalline materials.

MOFs are composed of secondary building units (SBUs) and organic linkers, which can be either characterized separately or treated as extended periodic crystals¹¹⁵. Janet et al. ¹⁷⁴ introduced revised autocorrelation functions (RACs) to capture molecular characteristics based on molecular graphs. Moosavi et al. ¹⁷⁵ subsequently revised the RACs to enable their application to MOFs by partitioning the frameworks into SBUs, organic linkers, and functional groups. By calculating RACs for each of these components separately, they generated a unique feature for each MOF. Besides, MOFs are characterized as highly ordered, periodic extended MOFs. Because MOFs are highly ordered and inherently periodic, preserving their translational, rotational, and permutation symmetries when describing their structures remains a critical challenge⁴¹. Efforts have been made to describe the structures of crystals. In 2014, Schütt et al. ¹⁷⁶ reported a representation that can describe crystal structures better than Coulomb matrices. They proposed partial radial distribution functions (PRDF), which capture the distribution of pairwise atomic distances within a crystal (Fig. 5a) and are invariant to translation, rotation, and the choice of the unit cell¹⁷⁶. Faber et al. ¹⁷⁷ reported three ways to represent periodic systems: the Ewald sum matrix, extended coulomb-like matrix, and sine matrix. The Ewald sum matrix is an extension of the coulomb matrix used in molecular systems. Each element of the matrix is the Ewald sum, which separates the electrostatic interaction into a short-range component and a long-range component. In this way, the Ewald sum matrix not only represents the infinite repetition of atoms within a crystal system but also ensures convergence in the calculation of these long-range electrostatic interactions. An extended coulomb-like matrix modifies the traditional coulomb matrix by including interactions with atoms in neighboring unit cells to account for periodic systems. The key difference from the Ewald sum matrix is that this method does not aim to compute the interaction over the entire infinite lattice but rather considers only a finite number of neighboring unit cells. Therefore, this method is more computationally efficient than the Ewald sum matrix but less accurate in long-range interactions. The sine matrix is based on using a sine function to model the periodic nature of crystal structures. It is designed to be simpler and computationally cheaper while still capturing the essential periodicity of the atomic arrangement. Schütt and Faber developed methods to modify the Coulomb matrix for representing periodic systems, but these approaches did not account for bond angles. Seko et al. ¹⁷⁸ combined elemental and structural representations to describe the chemical composition and atomic arrangement of materials. Elemental properties include atomic number, atomic mass, first ionization energy, electron affinity, covalent radius, and other atomic characteristics. Structure properties include PRDF, generalized radial distribution functions (GRDF), bond-orientational parameters (BOP), and the angular Fourier series (AFS). BOP provides information about local symmetry and the relative orientations of neighboring atoms, while AFS integrates both radial and angular information to describe the full spatial distribution of atoms. Isayev et al. ¹⁷⁹ proposed new descriptors called Property-Labelled Materials Fragments (PLMF), which converted the crystal structure into a graph. They used Voronoi Tessellation to partition crystal structures into atom-centered polyhedrals. If atoms share the Voronoi face and are within a certain distance (based on the sum of covalent radii), atoms are considered to be bonded (Fig. 5b). Based on this method, the crystal structure is transformed into a graph containing connectivity within the material. The full graph is divided into two kinds of fragments, path fragments and circular fragments (Fig. 5b). Each fragment is assigned elemental properties based on the atoms it contains. In addition, global structural properties of the entire crystal are also included, such as lattice parameters, angles, space group, and point group.

Fig. 5: Methods to represent the crystal structure.

a Alternative crystal representations. Top: a crystal unit cell indicating the Bravais vectors (blue) and base (pink). Bottom: illustration of one shell of the discrete partial radial distribution function with α and β representing different atom types. Reproduced with permission from ref. ¹⁷⁶ Copyright 2014 American Physical Society. b Schematic representing the construction of the Property-Labelled Materials Fragments (PLMF). Reproduced with permission from ref. ¹⁷⁹ Copyright 2017 Authors, licensed under a CC BY license. c Schematic construction of the crystal graph with node vectors representing atoms and edge vectors representing bonds. Reproduced with permission from ref. ¹⁸⁰ Copyright 2018 American Physical Society.

The descriptors mentioned above, based on classical ML models such as kernel ridge regression, have performed well in predicting various properties of materials. In contrast to classical ML models, Deep learning can automatically learn representations from raw data, reducing the reliance on expert-designed features⁴¹. Xie and Grossman¹⁸⁰ proposed crystal graph convolutional neural networks (CGCNN) to represent and predict the properties of periodic systems. They employed Isayev’s method to transform the crystal structure into a crystal graph, where the nodes represent atoms and the edges represent the connections between them (Fig. 5c)¹⁸⁰. Both the nodes and edges are characterized by feature vectors that encode the information of atoms and bonds, respectively¹⁸⁰. Different from the traditional ML model, CGCNN is capable of automatically identifying and learning the most critical characteristics of a material for predicting target properties. Initially, each node starts with basic information about a specific atom¹⁸⁰. When the model performs its first “convolution”, the node gathers more details, incorporating not only information about the atom itself but also about the bonds and neighboring atoms within a defined radius¹⁸⁰. As this process is repeated through several convolutions, each node ends up with rich information about its surrounding chemical environment¹⁸⁰. The number of convolutions determines how far this information reaches, whether it’s just local details or a broader structure¹⁸⁰. After this process, the model combines all this information to create a new feature that describes the material¹⁸⁰. Through training, this feature is refined to represent the material in a way that best predicts the target properties¹⁸⁰. Similarly, Chen et al. ¹⁸¹ proposed MatErials Graph Network (MEGNet) models that utilize graph networks to represent both molecules and crystals. Different from CGCNN, MEGNet incorporates global state variables as additional descriptors to enhance the prediction of properties that depend on external conditions and establish relationships between structure, state, and properties¹⁸¹. MEGNet incorporates temperature, pressure, and entropy as global states and developed a unified molecule free energy model that can predict internal energy at 0k and room temperature, enthalpy, and Gibbs free energy¹⁸¹.

ML models and applications in screening MOFs

ML model plays a crucial role in accurately predicting the properties of MOFs. For a detailed introduction to algorithms, please refer to the following articles^38,41,135. We will focus on introducing ML models developed for MOFs, as well as the application of ML techniques for identifying MOFs suitable for EES systems. The transformer architecture is useful in processing long sequences efficiently¹⁴³. Based on transformer architecture, MOFormer and MOFTransformer are proposed to predict the properties of MOFs^182,183. During the self-supervised pretraining phase, MOFormer and CGCNN are jointly employed to capture comprehensive information about the MOFs¹⁸². After pretraining, the learned weights are transferred to MOFormer for fine-tuning on downstream tasks¹⁸². MOFormer using text string representation (MOIFid) outperforms the structure-agnostic descriptors in predicting band gaps after self-supervised pretraining¹⁸². As for MOFTransformer, it incorporates atom-based graph embeddings to capture local features and energy-grid embeddings to capture global features during pretraining¹⁸³. Atom-based graph embeddings are generated using CGCNN without pooling layers and energy-grid embeddings are calculated using energy grids derived from the interaction between MOFs and methane molecules¹⁸³. Subsequently, MOFTransformer was integrated into ChatMOF as a predictor¹⁸⁴.

Recently, many efforts have been devoted to exploring the properties of MOFs using ML techniques^166,185,186. He et al. ¹⁸⁵ first applied ML to the exploration of conductive MOFs in 2018. They trained four ML models, logistic regression (LR), support vector classification (SVC), NN, and random forest (RF), using a dataset of 52300 inorganic materials. These models were subsequently applied to screen 2937 MOFs, predicting their band gaps through a multivoting approach that combined the outputs of the four models. Nine MOFs were predicted to be metallic and 6 of them were confirmed to be metallic by the calculations based on semilocal DFT. Dou et al. ¹⁸⁶ established a database containing experimentally measured conductivity of 224 MOFs and trained ML models based on the database. These models were subsequently applied to predict the conductivity of the MOFs in the QMOF database, identifying CuTTPD as a candidate with a predicted conductivity of 10^−3.3 S/cm. They synthesized CuTTPD and measured the conductivity (10^−5.77 S/cm) which is close to the prediction¹⁸⁶. Furthermore, they employed SHAP values to identify the influence factors of conductivity, which revealed that the number of hydrogen bond donors (HBD) and the acid dissociation constant (pKa) were the most significant descriptors influencing conductivity¹⁸⁶. Notably, these descriptors have been rarely considered in the study of conductive MOFs¹⁸⁶.

As for stability, Moghadam et al. ¹⁸⁷ conducted high-throughput molecular simulations on a dataset of 3385 MOFs to calculate their mechanical properties and trained ANN using this dataset, enabling rapid and accurate prediction of the MOF bulk modulus. Based on the dataset, certain topologies, high coordination numbers, shorter linkers, and smaller pore sizes are found to contribute to greater mechanical stability¹⁸⁷. Batra et al. ¹⁸⁸ developed a dataset containing water stability data for 207 MOFs and trained classification models. Their analysis revealed that the number of cyclic divalent nodes (MQNs30) and six-membered rings (MQNs36) were key descriptors influencing water stability¹⁸⁸. In particular, MOFs exhibited high water stability when MQN36 was less than 0.04 and MQN30 exceeded 0.01. Subsequently, Zhang et al. ¹⁸⁹ constructed a more extensive dataset comprising 1133 MOFs with water stability information. Their study identified critical factors affecting water stability, such as high surface area and narrow pore size, metal with high atomic mass and radius, linker with high connectivity degree, and electronegativity variation. The trained model was subsequently applied to the ARC-MOF database, identifying 129,661 MOFs with potential water stability^165,189.

Conclusions and Perspectives

Herein, we give an overview of applying DFT and ML in predicting the properties of MOFs to screen and design high-performance MOFs for EES systems. Our discussion focuses on the conductivity, stability, and redox activity of MOFs which are essential for the performance of the MOF-based electrode materials. Based on DFT calculations, we discuss the mechanisms of charge transport, strategies for improving conductivity, chemical and mechanical stability, and the processes and mechanisms of redox reactions. Additionally, we give an overview of ML workflow to efficiently screen MOFs for EES systems. Specifically, we discussed the database, descriptors, and models developed for the applications of ML in screening MOFs.

It is worth noting that current calculated structures of MOFs are typically idealized as perfect crystals, whereas experimentally synthesized MOFs are often polycrystalline. This discrepancy leads to inconsistencies between calculated and experimental results. Therefore, future research should focus on adjusting calculated MOF structures to better reflect their actual forms, while experimental efforts should aim to synthesize single-crystal MOFs to investigate their intrinsic conductive mechanisms.

3D MOFs generally exhibit high specific surface areas and more accessible redox-active sites. However, 3D conductive MOFs are relatively rare, as the most effective methods for enhancing conductivity—extended conjugation and through-space approaches—are challenging to incorporate into 3D structures¹⁹⁰. Identifying more conductive 3D MOFs through high-throughput calculations and ML is essential to explore the factors influencing conductivity and to elucidate the conductive mechanisms.

The customizable structures of MOFs enable them to achieve higher energy densities, making them promising for energy storage applications. For instance, Cu-THQ (THQ = benzoquinoid), when employed as a cathode material for Li-ion batteries, demonstrated a high reversible capacity of 387 mAh g⁻¹, surpassing the theoretical capacities of many transition metal compounds¹²⁴. Similarly, 2D Ni-MOF nanofilaments, when used as anode materials for Li-ion batteries, achieved a remarkable specific capacity of 719 mAh g⁻¹ at 1 A g⁻¹, exceeding the theoretical energy density of graphite¹⁹¹. While these advancements underscore the potential of MOFs for higher energy densities compared to standard materials, their lower cycling stability poses a significant limitation for practical applications²². Furthermore, achieving high stability seems to conflict with the requirement for high conductivity because the strong coordination bonds, typically designed based on the HSAB theory, tend to localize electrons, resulting in low conductivity or even insulating behavior¹⁰². Thus, simultaneously incorporating high conductivity, high stability, and high redox activity in MOF-based materials remains a key challenge.

Rather than screening for MOFs, designing MOF structures tailored for specific functionalities is more desirable. Achieving this goal requires a deep understanding of the relationship between MOF structure and functionality. While advancements in ML have improved predictive accuracy, they have often come at the expense of interpretability, turning the structure-function relationship into a black box³⁴. This challenge presents a promising avenue for future research: developing explainable ML methods to better elucidate these relationships. Integrating domain knowledge of MOFs into ML models offers an effective approach to enhancing both model performance and interpretability^192,193,194.