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. 2024 Mar 7;4(3):281–291. doi: 10.1021/acsphyschemau.3c00063

Unraveling the Stability of Layered Intercalation Compounds through First-Principles Calculations: Establishing a Linear Free Energy Relationship with Aqueous Ions

Naoto Kawaguchi †,*, Kiyou Shibata †,‡, Teruyasu Mizoguchi †,‡,*
PMCID: PMC11117722  PMID: 38800725

Abstract

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Layered intercalation compounds, where atoms or molecules (intercalants) are inserted into layered materials (hosts), hold great potential for diverse applications. However, the lack of a systematic understanding of stable host–intercalant combinations poses challenges in materials design due to the vast combinatorial space. In this study, we performed first-principles calculations on 9024 compounds, unveiling a novel linear regression equation based on the principle of hard and soft acids and bases. This equation, incorporating the intercalant ion formation energy and ionic radius, quantitatively reveals the stability factors. Additionally, employing machine learning, we predicted regression coefficients from host properties, offering a comprehensive understanding and a predictive model for estimating the intercalation energy. Our work provides valuable insights into the energetics of layered intercalation compounds, facilitating targeted materials design.

Keywords: first-principles calculation, intercalation, layered intercalation compounds, principle of hard and soft acids and bases, stability

1. Introduction

Layered intercalation compounds, which have a structure in which atoms or molecules (intercalants) are inserted into layered compounds (hosts), have been extensively studied because of their characteristic physical properties and the wide variety of synthetic methods available. Due to their ability to intercalate/deintercalate ions and molecules,1,2 they are being investigated for applications in energy storage, and various properties resulting from their two-dimensional nature, such as superconductivity,3−5 spin glass,6 and topological electronic states,7 have also been studied. Other novel phenomena have also been reported, such as the change in host electrowetting response8 and manipulation of magnetism9 due to molecule intercalation. As for synthesis methods, in addition to the general solid-phase, vapor-phase, ion-exchange, and electrochemical insertion methods, a wide variety of synthetic techniques such as zerovalent metal intercalation,10 liquid alloy,11 molten salt,12 molecular beam epitaxy, and chemical vapor deposition methods13 have been studied in recent years, and various new materials have been synthesized. However, there is no systematic understanding of which combinations of hosts and intercalants are stable, and thus, it is not straightforward to search for new layered intercalation compounds from a vast number of combinations.

In recent years, comprehensive first-principles calculations have been performed in the field of computational science to search for substances in inorganic compounds,14 and attempts to synthesize substances considered stable from these calculations have been widely conducted in various fields, such as cathode materials for Li-ion secondary batteries,15 solid electrolytes for all-solid-state Li-ion secondary batteries,16 and semiconductors.17 Furthermore, databases of materials including virtual structures constructed by first-principles calculations based on density functional theory (DFT),18,19 such as the Materials Project20 and the Open Quantum Materials Database,21,22 cover the formation energy, Ef, an indicator of stability. The stability of materials with various structures is now widely discussed. These databases have also been used to develop various materials.23,24 In addition, there are databases specialized for specific structures, such as 2D materials25−27 and perovskites,28 and a data infrastructure called NOMAD,29 where materials databases can be easily uploaded by users. Thus, it can be said that data-driven material development using databases is very active. As software for DFT calculations, there are various codes such as CASTEP,30 the Vienna Ab initio Simulation Package (VASP),31−35 and Quantum ESPRESSO.36,37 Among them, the VASP code is one of the most widely used simulation codes to build the databases due to its versatility and high computational reliability.

In addition, the use of machine learning has been investigated to search for stable new materials, and there have been many attempts to predict the stability of inorganic compounds using new descriptors such as the Coulomb matrix38 and the orbital-field matrix.39,40 However, these simulations and predictions are, in many cases, difficult to handle in a generic and quantitative manner to determine what is contributing to the stability of a compound. Similarly, the importance of computational stability discussions has been recognized in layered intercalation compounds as well,41 and while there have been searches limited to specific hosts, such as the self-intercalation from calculations in transition metal dichalcogenides (TMDs)42 and the search for stable graphite intercalation compounds (GICs) we reported,43 universal factors for the stable host–guest combinations have yet to be extracted.

As a new perspective for the stability of the layered intercalation compounds, we focused on the principle of hard and soft acids and bases (HSAB),44,45 which is primarily used in complex chemistry to explain that hard acids tend to form ionic bonds with hard bases, while soft acids tend to form covalent bonds with soft bases due to the spread of electron clouds. The HSAB principle has been widely employed in complex chemistry to understand the stable ligand–central atom combinations, and various quantitative indices have been proposed, such as the chemical softness (η) introduced by Parr and Pearson.46 There are few reports where the HSAB principle has been used for understanding crystalline systems. For example, in binary ionic crystalline materials, the value of η calculated from two elements and the sum of their ionic radius have been utilized to quantitatively evaluate lattice energy.47 However, this idea is applicable only to the binary materials, and most research of the stability quantification using the HSAB principle is limited to the complexes. Nevertheless, considering the intercalant as the complex center and the host as the ligand, the relationship between the two is similar, and the importance of a covalent electron density distribution around the intercalant has been emphasized through the systematic simulation of GICs.48,49 Thus, we believe that the concept of the HSAB principle could be applicable to understanding the stability of layered intercalation compounds as well.

Based on the background described above, in this study, we conducted systematic first-principles calculations on various layered intercalation compounds with different intercalants to calculate their structures and energies, creating a database. While databases specialized for layered structures, such as 2D materials, exist,25−27 this study is the first to establish a database specifically for the layered intercalation compounds. Notably, our database is distinctive not only in its coverage of stable compounds with high synthesizability but also in its comprehensive calculation of less stable compounds. This approach allows for a thorough examination of the underlying physics, facilitating discussions on factors influencing both stability and instability. Next, we attempted to identify the factors contributing to the stability of layered intercalation compounds from the perspective of the HSAB principle. As a result, we discovered that the intercalation energy required for intercalation of layered intercalation compounds, obtained through the first-principles calculations, can be linearly regressed from the following two physical properties: (1) the standard Gibbs free energy of formation of the intercalant ion and (2) the ionic radius of the intercalant. This relationship is captured by a simple regression equation derived from the HSAB principle. Through this study, we have successfully extracted fundamental principles that provide valuable guidance for the efficient design of layered intercalation compounds within a vast combinatorial space. Our findings suggest potential advancements in diverse applications, and we anticipate the possibility of synthesizing new layered intercalation compounds based on this model.

2. Methodology

2.1. Preparation of Crystal Structures of Layered Intercalation Compounds

Seven types of structures and compositions were selected as hosts, C, AX2, A2X2, and A2Z, and their crystal structures are shown in Figure 1, where A represents all elements except lanthanides and actinides, X represents elements in groups 13–17, and Z represents C or N. In order to perform accurate regression, stable convergence of energy and structure calculations is required for various layered intercalation compounds. However, the interlayer compounds containing lanthanides and actinides have poor convergence in the calculations and are an obstacle to creating a high-quality database; thus, they had to be excluded in this study. Figure 1 (a) shows graphite, the host of typical layered intercalation compounds, GICs, and the five crystal structures of GICs experimentally reported to date are shown in Figure S1. Figure 1 (b) and (c) shows the structures with the composition AX2, with an octahedral structure and a triangular prismatic structure, respectively. Figure 1(d–f) represents structures with the composition A2X2 (relative to the composition of the intercalant, one). Figure 1(d–f) shows rock-salt, anti-PbO, and PbO structures, respectively. The difference between Figure 1(e,f) is whether the outer layer of the two constituent elements is anionic or cationic, and in this study, the distinction is made by the electronegativity (Allred-Rochow’s scale)50 of the two elements. Figure S4 shows the crystal structures of these host compounds. Figure 1(g) shows a layered material with the composition ZA2 (Z = C, N) with an octahedral structure. This crystal structure can be regarded as a termination-free structure of a substance called MXene. The intercalated crystal structures of this host are shown in Figure S5, which is known as the MAX phase.

Figure 1.

Figure 1

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Crystal structures and compositions treated as hosts in this study visualized by VESTA.51

As intercalants, the elements colored in Figure 2 were selected. These elements were chosen based on the availability of standard Gibbs free energy of ion formation and effective ionic radius data extracted from the references,52−56 excluding lanthanides and actinides for the same reason mentioned above. Elements in blue are more likely to become cations when hydrated, while those in red are more likely to become anions.

Figure 2.

Figure 2

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Elements were treated as intercalants. The elements represented in blue become cations, while those represented in red become anions when they are hydrated.

The crystal structures of the layered intercalation compounds were created based on these structures and elements. The method is shown in Figure 3. For substances other than GICs, compounds with the crystal structures shown in Figures S2–S5 were screened by the compositional formula and space group from the Materials Project,20 a comprehensive database of inorganic compounds. Subsequently, only substances that had been reported experimentally were extracted and substances with the same host and stacking were excluded. Subsequently, intercalants M were removed from the structures of the layered intercalation compounds, and the layered compound structures shown in Figure 1 were created as hosts. Then, first-principles calculations were performed on the hosts, and those structures that could keep layered structures were adopted as hosts, and only the layered intercalation compounds with these hosts were extracted. Note that the layered compounds obtained here as hosts include virtual compounds. For the GICs, we selected the five structures reported in Figure S1, yielding a total of 188 layered intercalation compounds, and by changing the intercalant to the 48 elements shown in Figure 2, we created 9024 structures of layered intercalation compounds. Thus, from a practical perspective, the structures were created by varying the intercalant using layered intercalation compounds with well-known host structures that have been experimentally reported as the parent materials.

Figure 3.

Figure 3

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Flowchart of making layered intercalation compounds.

2.2. First-Principles Calculations

First-principles calculations were performed on the obtained layered intercalation compounds and host-only structures. Structural relaxations through simulations based on DFT18,19 were performed on the initial structures using the plane-wave basis projector augmented wave method57 implemented in the VASP code.31−35 For the simulation of the layered compounds, van der Waals dispersion (vdW) forces have to be implemented in the simulation.58 To consider the vdW interaction, we systematically tested various vdW density functional methods59−63 for the GICs as the reference, confirming the reproducibility of crystal structures and the validity of the formation energies. The results are listed in Table S1. Consequently, we selected the rev-vdW-DF2 method proposed by Hamada,62 which was implemented using the algorithm of Román-Pérez and Soler64 because both errors were the lowest.

Spin-polarized calculations were performed, but the spin–orbit interaction was not considered. For primitive cell calculations, the Brillouin zone was sampled by odd-number k-point meshes with spacing less than 0.25 Å–1, using the Monkhorst–Pack scheme.65 The electron wave functions were expanded in plane waves up to a kinetic energy cutoff of 650 eV, and the self-consistent field convergence energy was set to 10–4 eV. Full structural relaxations of the cell volume and atomic positions were performed until the residual forces on the ions converged to below 0.05 eV/Å. Subsequently, the cell volume and atomic positions were fixed, and the total energies were calculated using the tetrahedron method with Blöchl corrections.66 This computation condition is considered to be accurate enough for all materials in this study for discussing the stability of layered intercalation compounds.

Although the convergence energy of the self-consistent field (10–4 eV) is not very strict, we adopted this value to converge the calculation in a realistic time for creating an exhaustive database. To confirm the accuracy of the present simulation, we performed additional calculations for M-NiO2 (O4 structure in Figure S2) and M-NbSe2 (T4 structure in Figure S3) with convergence energies set to 10–6 eV (namely 2 orders of magnitude stricter than the normal condition) and compared the results, as shown in Figure S6. Based on the fact that there was no significant difference in the total energies, it can be concluded that the present condition is accurate enough for the present study.

2.3. Estimation of Intercalation Energy

The intercalation energy Eint was calculated as the energy required for intercalation using eq 1

2.3. 1

where Etot(M – Host), Etot(M), and Etot(Host) are the calculated total energies of the layered intercalation compound, the standard state of the intercalant, and the host, respectively. The unit of Eint is eV/formula unit (f.u.). Eint can be interpreted as the reaction energy between the intercalant and host, allowing for a discussion of the stability of the interlayer compound. While a negative value of Eint does not imply that the reaction proceeds because the host is often a virtual structure, all hosts in our constructed database have been experimentally reported as a part of stable layered intercalation compounds with one or more intercalants. Therefore, if their Eint values are lower than those of the experimentally reported compounds, they could potentially be synthesized through topochemical reactions such as ion exchange. Essentially, Eint enables a discussion of the relative stability of various interlayer compounds from different host and intercalant combinations.

This calculation also allows for the determination of the average voltage associated with intercalation,67 which is crucial for energy material applications. Additionally, by replacing Etot(Host) with ∑Etot(Host-elements), where Etot(Host-elements) represents the total energy of the standard state of the element constructing the host, eq 1 becomes the formation energy (Ef) of the layered intercalation compounds. A negative Ef value suggests that the reaction may proceed from the standard state of elements. In addition to Eint, Ef is also shown in the Supporting Information.

3. Results

The objective of this study is to establish a new index for the stability of layered intercalation compounds. Considering the intercalant as the complex center and the host as the ligand, layered intercalation compounds are similar to complexes. We explored the possibility of applying the discussion on the stability of complex compounds. Various quantitative formulas, including the HSAB principle, have been proposed for the determination of the stability of complex compounds.68−70 Among them, Xu et al. reported a highly quantitative regression equation, eq 2, for the reaction energy of complex compounds71

3. 2

where R is the gas constant, T is the temperature, KML represents the stability constants of the metal complex ML, ΔG°f,Mn+ is the standard Gibbs free energy of formation of Mn+, rMn+ is the ionic radius of Mn+, ΔG°s,Mn+ is the standard Gibbs free energy of dissolution of the aqueous ion Mn+, and α*ML, β*ML, γ*ML, and δ*ML are ligand-specific coefficients. In this equation, 2.303 RT logKML represents the negative value of the reaction energy of the metal complex ML (−ΔG°r,ML), represented by the chemical equation M + L → ML. It was proposed that α*ML ΔG°f,Mn+ represents metal–ligand HSAB interactions, β*MLrMn+ represents ionic size effects, and ΔG°f,Mn+ is the “natural indices for the chemical hardness/softness”, referred to as “acid softness”. As a similar approach, limited to divalent cations, D.A. Sverjensky et al. reported that the energy of formation of inorganic crystalline solid substances can be described by the following linear regression eq 3(72)

3. 3

where ΔG°f,MvX is the standard Gibbs free energy of formation for crystalline solids, ΔG°n,M2+ is the nondissolved component of the standard Gibbs free energy of formation of M2+ (ΔG°n,M2+ = ΔG°f,M2+ – ΔG°s,M2+), and αMvX, βMvX, and bMvX are regression coefficients specific to crystalline solids.

Based on these regression equations, we considered the intercalation energy Eint. As a result, we developed eq 4 as a new regression equation that incorporates HSAB-like interactions and size effects

3. 4

where ΔG°f,Mn and rMn are the standard Gibbs free energy of the Mn ion and the ionic radii of the Mn ion including positive and negative for n, respectively, and αM-Host, βM-Host, and γM-Host are the regression coefficients specific to the layered intercalation compounds with the same host and stacking structure obtained as a result of the screening in Figure 3. These values are determined for each of them.

To apply this equation, it is necessary to consider the combination of an anion-like (base-like) host for cationic intercalants and a cation-like (acid-like) host for anionic intercalants. Therefore, we classified the hosts according to the electronegativity of their constituent elements as follows: graphite in Figure 1(a) is classified as both acid-like and base-like, i.e., an amphoteric host; hosts in Figure 1(b–e), where the elements coordinating to the intercalant are highly electronegative, are classified as base-like hosts; and hosts in Figure 1(f,g), where the opposite configuration of Figure 1(b–e) is observed, are classified as acid-like hosts. We then performed host-specific regressions for the 41 cation intercalants with 169 base-like hosts and 7 anion intercalants with 24 acid-like hosts, resulting in a total of 193 regressions using 7097 data.

To confirm the validity of our regression model, the values of the adjusted coefficient of determination (Adj. R2) for each variable combination and the sorted p-values calculated in the F-statistic test are shown in Figure 4(a,b). The regression results of the previously proposed model with eqs 2 and 3 were also compared.

Figure 4.

Figure 4

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Sorted values of (a) Adj. R2 and (b) p-values in the F-statistic test in each regression model and examples of regression results of (c) highest Adj. R2, (d) highest Adj. R2 in the base-like host, (e) moderately Adj. R2, and (f) lowest Adj. R2 among eq 4 regressions.

It is evident that eq 4 demonstrates the best performance in terms of both Adj. R2 and p-value. Particularly noteworthy is the p-value, where only eq 4 satisfies the criterion of p-value <0.05, signifying a significance level exceeding 95%, in all regressions. Its regression performance is higher than that of eq 2, which involves a regression using three variables. This superiority underscores the effectiveness of incorporating 1/rMn as the Coulomb energy term.

Figure 4(c–f) illustrates the regression results of eq 4 with different accuracies and hosts, specifically, (A) the regression with the highest Adj. R2, (B) the regression with the highest Adj. R2 in the base-like host, (C) the regression with medium Adj. R2, and (D) the regression with the lowest Adj. R2, indicated by arrows in Figure 4 (a). Even in the regression result with the lowest Adj. R2, the mean absolute error (MAE) is not considerably large as shown in Figure 4 (f). It appears that the small Adj. R2 is due to the narrower energy range of the Eint distribution. This indicates that the performance of regression using eq 4 can capture the overall trend of stability even in the worst case.

All regression results for each of the 6929 data of cation intercalants and base-like hosts and 168 data of anions and acid-like hosts are presented in Figure 5(a,b), respectively. Both plots display the R2 and MAE for the entire model calculated from all predicted values in eq 4, confirming the validity of the regression equation with a high linearity. In other words, in layered intercalation compounds, as in complex compounds, the compatibility between the host and intercalant can be understood by considering HSAB interactions and size effects (coulombic interactions).

Figure 5.

Figure 5

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All results of the liner regressions by eq 4. (a) Cation intercalants and base-like hosts. (b) Anion intercalants and acid-like hosts.

For comparison, the same plot for eqs 2 and 3 is provided in Figures S7 and S8, respectively. The values of αM-Host, βM-Host, and γM-Host for each layered intercalation compound with the same host and stacking, along with the substances reported for each of them, are listed in the Supporting Information.

4. Discussion

As described above, regression results were obtained using eq 2 proposed by Xu et al. for complexes, eq 3 proposed by Sverhebsky et al. for inorganic crystals of divalent cations, and eq 4 proposed by us based on them. It is evident that eq 4 exhibits the best regression performance for the 7,097 layered intercalation compounds calculated in this study. We then discuss the physical meaning of the optimal regression result in eq 4.

Based on previous studies, the first term αM-Host ΔG°f, Mn represents the HSAB-like interaction as in eq 2, while the second term βM-Host /rMn represents the size effect, distinct from eqs 2 and 3. Since this term involves the inverse of the ionic radius, it is considered to incorporate coulombic energy. These terms can be interpreted as the energy change due to electron transfer and electrostatic energy due to coulombic force. In this context, the regression coefficients αM-Host, βM-Host, and γM-Host can be considered the HSAB quantitative index for the host, the size effect quantitative index for the host, and the correction constant unique to each host, respectively.

To explore the relationship between these coefficients and regression eq 4 and to obtain a physical insight into the factors determining the stability of layered intercalation compounds, we attempted a decomposition of the intercalation process and energy, as illustrated in Figure 6.

Figure 6.

Figure 6

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Decomposition of the intercalation process of a layered intercalation compound (M-Host) into distinct steps, accompanied by energy considerations and its presumed correlation with eq 4.

Edecohesion, M is the decohesion energy of the intercalant M from the standard state, Ebinding, Host is the binding energy of the layered structure host, Eelectron transfer is the electron (ne–, n including positive and negative) transfer energy from the intercalant to the host, Ebinding, M-Host is the binding energy of the M-Host, and Estraining, Host is the strain energy of the Host.

These decomposed energy components can be classified into three groups by colors: blue; M decohesion and electronic interaction, red; electrostatic Coulomb energy, and green; M-Host-dependent values, and they correspond to αM-Host ΔG°f,Mn, βM-Host /rMn, and γM-Host in eq 4, respectively, as shown in Figure 6.

For example, the combination of the decohesion process of standard M and charge transfer process is analogous to the process by which M in the standard state ionized to form (hydrated) ions; it is reasonable that Edecohesion + Eelectrontransfer correlates with ΔG°f,Mn, as the blue part in the Figure 6, which represents the standard production energy of hydrated ions. In the same manner, second and third terms in eq 4 can be attributed to the decomposition process as shown in Figure 6, red and green parts, indicating that eq 4 and the terms are physically reasonable.

On the other hand, to predict the stability of the layered intercalation compounds solely from the intercalant–host combination before simulation and experimentation, determination of αM-Host, βM-Host, and γM-Host is necessary. These values are the host-dependent factors, and we investigated whether αM-Host, βM-Host, and γM-Host can be predicted from the compositional and physical properties of the host.

We examined regression by random forest regression,73 a machine learning algorithm that predicts an objective variable while checking the importance of descriptors, using the scikit-learn library.74 As a result of examining descriptors for various hosts, we succeeded in predicting them using four descriptors for each regression (eight descriptors in total). Figure 7(a–c) shows the regression results for αM-Host, βM-Host, and γM-Host, respectively. Figure 7(d–f) shows the numbers of each descriptor used for prediction and the results of the permutation importance analysis. Figure 7(g) shows the details of each descriptor number. All data are split into 80% train data and 20% test data, and a random forest model trained on the train data is used to validate against the test set. Detailed condition for the random forest regression and the values of the descriptors are described in the Supporting Information.75

Figure 7.

Figure 7

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Results of the random forest regression. Correlation of the observed and predicted values of (a) αM-Host, (b) βM-Host, and (c) αM-Host. The descriptor numbers of random forest regression and the results of permutation importance analysis for (d) αM-Host prediction, (e) βM-Host prediction, and (f) γM-Host prediction. (g) Detailed list of each descriptor.

In addition, the generalization performance of each model was evaluated by fivefold cross-validation, and the results are shown in Table 1. While there are some variations in R2 for αM-Host and γM-Host, the generalization performance is good for 193 sets of regression coefficients.

Table 1. Results of Fivefold Cross-Validation.

target   1 2 3 4 5 mean
αM-Host test R2 0.90 0.66 0.79 0.88 0.63 0.77
train R2 0.93 0.94 0.93 0.94 0.95 0.94
βM-Host test R2 0.93 0.87 0.94 0.93 0.95 0.92
train R2 0.96 0.98 0.98 0.97 0.98 0.97
γM-Host test R2 0.96 0.84 0.88 0.59 0.84 0.83
train R2 0.96 0.97 0.97 0.98 0.97 0.97
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Looking at the permutation importance of each model, it can be seen that the value of (1) formal valence of the atom coordinating to the intercalant is the most important descriptor. This value is considered to contain the basic information about whether the host is acid-like or base-like, and since it directly contacts the intercalant, it is reasonable to say that it greatly affects the compatibility with the intercalant. For βM-Host, (5) the formal valence of the host is also important, which is consistent to the meanings of the second term of eq 4, the coulombic interaction. For αM-Host and βM-Host, the contribution of (2) the coordination number to intercalants tends to be high. This reflects the geometric information around the intercalant. Actually, other important factors for αM-Host and βM-Host, (3) and (6), are commonly related to the radius of the coordinating atoms. The last important descriptor for αM-Host is (4) weighted average of first ionization energies of the elements constituting the host, which is considered to incorporate the effect of electron transfer as shown in Figure 6. As for γM-Host, (7) binding energy of the host, (6) ionic radius of the coordination atom, and (8) area per intercalant are the important descriptors, which also show that the model successfully incorporates the effects of Ebinding, Host and Estraining, Host as shown in Figure 6.

Finally, the comparison of Eint calculated by eq 4 with the predicted αM-Host, βM-Host, and γM-Host for the compounds in the test data of Figure 7 and that by DFT is shown in Figure 8. Although R2 is not high (0.68), eq 4 and parameters have the potential to predict the Eint with the accuracy of 0.75 eV/f.u.

Figure 8.

Figure 8

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Comparison of Eint calculated by DFT and predicted by regression eq 4 with predicted regression coefficients from random forest regression.

We have also confirmed that Eint can be predicted by machine learning methods, although the physics cannot be interpreted as well as the regression model that we have developed. The results are shown in Figure S9 in the Supporting Information. Figure S9 (a) shows the results of random forest regression using two intercalant properties (ΔG°f,Mn and rMn) and eight host properties (shown in Figure 7) as descriptors by random forest, and Figure S9 (b) shows the results of prediction using Crystal Graph Convolutional Neural Networks (CGCNN).76 It can be seen that both methods can predict Eint with good accuracy. However, these models lack physical support and are not validated with respect to extrapolative application to unknown material systems. This stands in contrast to our regression model, which relies on a simple and physically reasonable formulation. Through this study, we succeeded in extracting the underlying physics to estimate the intercalation energy only from two intercalant properties and eight host-derived descriptors by random forest and regression equations without the first-principles calculations.

5. Conclusions

We constructed a database of layered intercalation compounds and successfully developed a regression equation to predict the intercalation energy of layered intercalation compounds based on two properties of the intercalant: ΔG°f,Mn and the inverse of rMn. We investigated the coefficients for the equation, demonstrating their prediction using a machine learning approach. This enables the estimation of intercalation energy without first-principles calculations.

Acknowledgments

The authors thank Dr. Hiraku Ogino of the National Institute of Advanced Industrial Science and Technology for the discussions about applying the HSAB principle for crystalline inorganic materials. The authors also thank Prof. Shunsuke Yagi and Prof. Takanari Ouchi in the University of Tokyo for the discussions about the possibility of synthesis of the new layered intercalation compounds.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsphyschemau.3c00063.

  • Structures of layered intercalation compounds, comparison of total energy in different energy convergence thresholds, results of regression in other models, prediction of Eint by the machine learning methods, comparison of the vdW correction methods, values of ΔG°f,Mn and rMn of intercalant, and conditions of random forest regression (PDF)

  • Values of Eint and Ef of all layered intercalation compounds, Adj. R2, αM-Host, βM-Host, and γM-Host of each layered intercalation compounds with the same host and stacking, and value of descriptors for random forest regressions (XLSX)

Author Contributions

The article was written through contributions of all authors. All authors have given approval to the final version of the article. CRediT: Naoto Kawaguchi conceptualization, data curation, formal analysis, investigation, methodology, visualization, writing-original draft; Kiyou Shibata conceptualization, methodology, resources, supervision, writing-review & editing; Teruyasu Mizoguchi conceptualization, funding acquisition, methodology, project administration, resources, software, supervision, writing-review & editing.

This study was supported by the Ministry of Education, Culture, Sports, Science and Technology (MEXT) (grant no. 19H00818 and 19H05787) and the special fund (Tenkai) by the Institute of Industrial Science, the University of Tokyo.

The authors declare the following competing financial interest(s): The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Naoto Kawaguchi reports financial support was provided by Resonac Corporation.

Supplementary Material

pg3c00063_si_001.pdf (1.2MB, pdf)
pg3c00063_si_002.xlsx (614.1KB, xlsx)

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