# Fileset

[takahara-et-al-2024-toward-the-atomic-level-analysis-of-ground-state-electronic-structures-of-solid-materials-via.pdf](https://mdr.nims.go.jp/filesets/fc4789c7-e738-4821-9a44-14642f1ca119/download)

## Creator

Izumi Takahara, [Fumihiko Uesugi](https://orcid.org/0000-0003-3346-4218), [Koji Kimoto](https://orcid.org/0000-0002-3927-0492), Kiyou Shibata, Teruyasu Mizoguchi

## Rights

[Creative Commons BY Attribution 4.0 International](https://creativecommons.org/licenses/by/4.0/)

## Other metadata

[Toward the Atomic-Level Analysis of Ground-State Electronic Structures of Solid Materials via Prediction from Core-Loss Spectra: A Computational Study in Si](https://mdr.nims.go.jp/datasets/f985fead-b571-4be9-8096-a52da0bb8065)

## Fulltext

Toward the Atomic-Level Analysis of Ground-State Electronic Structures of Solid Materials via Prediction from Core-Loss Spectra: A Computational Study in SiToward the Atomic-Level Analysis of Ground-State ElectronicStructures of Solid Materials via Prediction from Core-Loss Spectra:A Computational Study in SiIzumi Takahara,* Fumihiko Uesugi, Koji Kimoto, Kiyou Shibata, and Teruyasu Mizoguchi*Cite This: J. Phys. Chem. C 2024, 128, 13500−13507 Read OnlineACCESS Metrics & More Article Recommendations *sı Supporting InformationABSTRACT: Local electronic structure in the ground state is essential for understanding thestability and properties of materials. Core-loss spectroscopy using electron or X-ray providesinsights into the local electronic structure, but directly observable information is limited to thepartial density of state (PDOS) of the conduction band at the excited state. To overcome thislimitation, we developed a machine learning (ML) approach by creating a database of Si-K core-lossspectra and corresponding ground-state PDOS for various silicon structures. Using this database, weconstructed an ML model capable of predicting the atom-specific ground-state PDOS of the valenceand conduction bands from Si-K edges. Our model demonstrated the ability of the ML to extractthe complex correlation between ground-state PDOS and Si-K edges. This study provides crucialinsights into achieving atomic-level analysis of ground-state electronic structures, paving the way fora deeper understanding of stability and properties of materials.■ INTRODUCTIONUnderstanding the local electronic structure is essential forcomprehending the structures and properties of materials. Oneof the approaches to access the local electronic structure is thedensity functional theory (DFT)1,2 calculations, where we cananalyze the relationship between the atomic and electronicstructures in detail. Furthermore, by constructing machinelearning (ML) models on DFT data, we can rapidly predictand analyze the electronic structure from the correspondingatomic structures.3−5 For instance, the prediction of theelectronic structure of silicon from local structure has beenreported,3 but when one wants to experimentally analyze theelectronic structure, it is difficult to fully determine the atomicstructure, making predictions based on the atomic structurechallenging. Moreover, it is desirable to directly extractinformation about the electronic structure from the measure-ment data without going through the process of structuredetermination. Among various characterization techniquespromising for this purpose, core−electron spectroscopy,specifically electron energy loss near edge structure (ELNES)and X-ray absorption near-edge structure (XANES), stands outas a powerful method.6,7 ELNES and XANES capturetransitions of core electrons to conduction bands, therebyproviding insights into the electronic states of specific atoms.This enables the extraction of elemental and chemicalinformation on the atom through the spectrum analysis, suchas fingerprint verification and first-principles simulations basedon DFT.7−9 Previous studies have utilized ELNES for atomic-level elemental mapping, oxidization-state mapping, andchemical-bonding mapping, establishing it as a powerfulanalytical tool for characterizing local states.10−13 Moreover,XANES provides exceptional detection sensitivity andtemporal resolution, enabling the investigation of chemicalreactions in battery materials and beyond.14,15On the other hand, the ELNES/XANES spectroscopicmethod has a significant limitation. The ELNES/XANESreflects the excitation of core electrons to the conductionbands, which is a process that generates core holes andconsequently shifts electron orbitals toward lower energylevels. This implies that the orbitals involved in transitions arenot in their ground state but in their excited state, making theELNES/XANES spectral shapes reflect the DOS of theconduction band in the excited state. Furthermore, since theelectronic transition obeys the selection rule of dipoletransitions, the change in an orbital’s angular momentumnumber is limited to Δl = ± 1. Therefore, the ELNES/XANESdoes not provide information on all orbitals but yields onlylimited PDOS related to the specific orbitals. In other words, itis not possible to obtain the electronic structure of both thevalence and conduction bands for all orbitals in the groundstate directly from the ELNES/XANES, while the ground-stateelectronic structure is more crucial for understanding thestability and properties of the materials.Traditionally, to obtain information on the electronic states,including both the valence and conduction bands at theReceived: April 30, 2024Revised: July 3, 2024Accepted: July 5, 2024Published: August 2, 2024Articlepubs.acs.org/JPCC© 2024 The Authors. Published byAmerican Chemical Society13500https://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−13507This article is licensed under CC-BY 4.0Downloaded via NATL INST FOR MATLS SCIENCE (NIMS) on September 9, 2024 at 02:11:19 (UTC).See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Izumi+Takahara"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Fumihiko+Uesugi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Koji+Kimoto"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kiyou+Shibata"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Teruyasu+Mizoguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/showCitFormats?doi=10.1021/acs.jpcc.4c02818&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?goto=articleMetrics&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?goto=recommendations&?ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?goto=supporting-info&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=tgr1&ref=pdfhttps://pubs.acs.org/toc/jpccck/128/32?ref=pdfhttps://pubs.acs.org/toc/jpccck/128/32?ref=pdfhttps://pubs.acs.org/toc/jpccck/128/32?ref=pdfhttps://pubs.acs.org/toc/jpccck/128/32?ref=pdfpubs.acs.org/JPCC?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://pubs.acs.org?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://pubs.acs.org/JPCC?ref=pdfhttps://pubs.acs.org/JPCC?ref=pdfhttps://acsopenscience.org/researchers/open-access/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/https://creativecommons.org/licenses/by/4.0/ground state from ELNES/XANES, it has been necessary tocompare the experimental spectra with theoretically simulatedspectra or reference spectra followed by further analysisthrough theoretical calculations. On the other hand, in recentyears, the effectiveness of employing ML techniques inmaterials characterization has been demonstrated.16 ML hasalso increasingly been utilized in extracting information fromELNES/XANES spectra, with methods reported for directlypredicting atomic structure and material properties fromELNES/XANES.17−25 Furthermore, it has recently beenreported that it is possible to predict the electronic structureof organic molecules in their ground state from C-K edgeELNES/XANES.26Building upon prior research employing ML methods, weaim to develop an ML-model to predict the atom-specificelectronic structure of all orbitals in their ground state for solidmaterials from ELNES/XANES, toward the realization ofatomic-level analysis of ground-state electronic structures. Inthis study, we focus on the Si-K edge of Si. Si is anindispensable material in industrial applications despite itssimplicity, and understanding the electronic structure with ahigh spatial resolution is of great importance. In Si, theexcitation energy of a core electron from the 1s orbital to theconduction bands is large, and the Si-K edge is located around1850 eV. It is known that the magnitude of excitation energycorrelates with the locality of the information obtained byEELS, and higher excitation energy results in the higher spatialresolution at which the signal can be acquired. Therefore,compared to other typical edges that appear at lower energies,such as the Si-L23 edge, the use of the Si-K edge is expected toenable the atomic-level analysis of ground-state electronicstructures. In order to theoretically investigate the feasibility,we constructed a database of Si-K ELNES/XANES and thecorresponding ground-state PDOS for various structures of Siby using DFT simulations. Utilizing this database, wedeveloped an ML model based on a one-dimensionalconvolutional neural network to predict the ground-statePDOS from the Si-K edge. Si-K edge involves the excitation ofthe 1s core electron to the p-orbitals of the conduction band,thus providing the p-orbitals of the conduction band at theexcited state. We demonstrate that an ML model can capturethe complex correlation between Si-K edge and the ground-state PDOS, thereby enabling the prediction of PDOS for notonly transition-allowed p-orbitals but also transition-prohibiteds-orbitals, not only of conduction band but also of the valenceband. Additionally, by conducting a comparison with templatematching, we demonstrate the utility of our ML basedapproach.■ METHODOLOGYThe data sets for ELNES/XANES and the correspondingground-state PDOS were all generated using first-principlescalculations based on DFT.1,2 First, we retrieved all thestructures of Si registered on the Materials Project,27 whichresulted in 41 structures. Using the “SpaceGroupAnalyzer”class in the “pymatgen.symmetry” package,28 we searched forthe primitive cell across all these structures and thenenumerated all the inequivalent Si sites in all the Si structures,identifying 655 Si sites. To address the scarcity of data, dataaugmentation was conducted in an on-the-f ly manner,ultimately yielding data for 1,405 Si sites. Detailed procedurefor the data augmentation process is provided in theSupporting Information B.For all the Si sites, the Si-K edge and the correspondingground-state PDOS were calculated using the CASTEP29 codeand the OptaDOS30 code. For the relaxation of electronicstructures, the plane-wave basis pseudopotential method wasemployed as implemented in the CASTEP code, and theexchange-correlation interactions were approximated usingGGA-PBE.31 The cutoff-energy for the plane-wave expansionwas set to 500 eV. In the calculation of ELNES/XANES, thecore-hole effect was considered by generating the pseudopo-tentials with a full core-hole, and the supercell approach wasemployed to eliminate the influence of interactions betweencore-holes.8 Reflecting the bond distance between Si atoms,supercells with lattice constants larger than 10 Å were used forthe calculation of the Si-K edge. A k-point density of 0.03 Å−1was used for the calculation of both the Si-K ELNES/XANESand the ground-state PDOS. The transition energy of Si-KELNES/XANES can be calculated separately based on thetotal energy difference between the ground-state and excited-state simulations, but for the prediction of the ground-statePDOS in this study, all the spectra were shifted to theirspectral onset to be zero. In other words, the prediction wasconducted solely based on their spectral features.All the calculated Si-K ELNES/XANES and ground-statePDOS were broadened by a Gaussian function with a standarddeviation of 0.5 eV. The Si-K ELNES/XANES spectra werecompiled into the database as 200-dimensional vectors with aresolution of 0.1 eV spanning from −1 to 19 eV relative to theFermi level, while the ground-state PDOS spectra were storedin the database as 300-dimensional vectors with a resolution of0.1 eV spanning from −15 to 15 eV.We constructed an ML model using the database builtthrough DFT simulations to predict atomic-level ground-statePDOS of a Si atom, including both valence and conductionbands, from the input Si-K ELNES/XANES. Given thedifficulty in determining the absolute intensity of ELNES/XANES spectra in actual experiments, we normalized eachinput Si-K ELNES/XANES spectrum to have a maximumintensity of 1.0. The ML model is based on a one-dimensionalconvolutional neural network, designed to directly predict theground-state PDOS about s- and p-orbitals separately from theoutput layer using the Si-K ELNES/XANES as the input. Thedetailed model architecture is described in SupportingInformation C. The data was split into training, validation,and test sets with a ratio of 6:2:2.■ RESULTSIn Figure 1, we show the result of the prediction for Si with adiamond-type structure, which is a representative crystalstructure of Si. Here, the data for the diamond-type Si hasbeen allocated to the test data set. Figure 1a shows the DFT-simulated ground-state PDOS of the Si atom in the diamond-type Si, where the gray dotted line corresponds to the PDOSrelated to the s-orbitals and the gray solid line corresponds tothat about p-orbitals. The yellow solid line represents the sumof them. In the valence band, three main peaks can beobserved. The peak highlighted with a yellow background onthe lowest energy side is primarily composed of s-orbitals. Thesecond peak consists of hybridized s- and p-orbitals, and thethird peak is primarily composed of p-orbitals. In theconduction band, a strong peak composed of p- and s-orbitalscan be observed at the onset.Figure 1b shows the DFT-simulated Si-K edge for a Si atomin diamond-type Si. Since the Si-K edge corresponds to theThe Journal of Physical Chemistry C pubs.acs.org/JPCC Articlehttps://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−1350713501https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c02818/suppl_file/jp4c02818_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c02818/suppl_file/jp4c02818_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c02818/suppl_file/jp4c02818_si_001.pdfpubs.acs.org/JPCC?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-astransitions of core electrons to the p-orbitals of the conductionband in the excited state due to the electric dipole selectionrule, the spectral shape of the Si-K edge is believed to reflectthe PDOS associated with p-orbitals of the conduction band inthe excited state. Generally, in the case of the Si-K edge, twoprominent peaks can be observed: a strong peak near the onsetand another peak around 13 eV, as indicated by blue hatches inFigure 1b.Figure 1c shows the predicted ground state PDOS from theSi-K edge, where the yellow solid line represents the ground-truth ground-state PDOS and the black dotted line representsthe predicted PDOS by the ML model. Despite the Si-K edgereflecting the p-PDOS of the conduction band in the excitedstate, PDOS in the ground state was accurately predicted bythe model. Furthermore, the valence band PDOS about s-orbitals in the ground state (yellow hatched area), which isconsidered to have little relevance to the conduction band p-orbitals, was also predicted successfully.Figure 2 shows the prediction results for the entire test dataset. In Figure 2a, all of the test data were sorted with the meansquared error (MSE) between the ground-truth PDOS and theML-predicted PDOS. Figure 2b shows the prediction result forthe data indicated by ‘A’ in Figure 2a, which corresponds to thedata showing the best prediction accuracy among the entiretest data, and the local coordination environment around thecorresponding excited atom. Here, the yellow solid linerepresents the ground-truth PDOS, while the black dottedline represents the predicted PDOS. Additionally, in theillustration depicting the local coordination environment, theexcited Si atoms are colored gold, while the surrounding SiFigure 1. (a) Ground-state PDOS of the valence and conductionbands of Si in diamond-type Si calculated by DFT simulation. (b)DFT-simulated Si-K edge in diamond-type Si, where two main peakscan be observed. (c) Result of predicting the ground-state PDOSincluding both the valence band (VB) and conduction band (CB) ofSi atom from the Si-K edge. Fermi level (EF) was aligned to be 0 eV.Figure 2. Result of prediction for the entire test data set. (a) Sortedmean squared error (MSE) for all the test data. (b) Result exhibitingthe highest prediction accuracy among the test data andcorresponding local coordination environment around the excitedatom (gold). (c) Result corresponding to the top 33% predictionaccuracy among the entire test data. (d) Result with top 67%prediction accuracy and (e) worst prediction accuracy.The Journal of Physical Chemistry C pubs.acs.org/JPCC Articlehttps://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−1350713502https://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig1&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig2&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig2&ref=pdfpubs.acs.org/JPCC?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asatoms are shown in white. The results corresponding to thetop 33%, 67%, and the worst predictions are shown in Figure2c−e, respectively.The data set includes various crystal structures of Si besidesdiamond-type Si, resulting in a variety of spectral shapes for theSi-K edge and the corresponding ground-state PDOS. Fromthe results in Figure 2b−e, it can be observed that the ground-state PDOS of both valence and conduction bands, includingthe spectral shapes near the Fermi level, were generallypredicted. In the results of Figure 2e, the MSE is large, which iscaused by the similarity in the shape of the Si-K edge, while theshape of the ground state PDOS differs. The details of theresult with low accuracy are described in SupportingInformation A.■ DISCUSSIONWe have confirmed the ability to predict ground state PDOSfrom the Si-K edge across the entire test data set. To explorewhich regions of the Si-K edge, namely, how large energy rangefrom the spectral threshold, are crucial for achieving highpredictability, we assessed the accuracy of predicting ground-state PDOS while varying the range of the Si-K edge used asinput. The results are listed in Figure 3. As depicted in Figure3a, the range of Si-K edge from −1 to 19 eV was initiallydivided into four sections with 5 eV windows: −1 to 4, 4 to 9,9 to 14, and 14 to 19 eV. The 0 eV corresponds to the spectralonset for each spectrum. Subsequently, we examined thechange in the prediction accuracy of the ground state PDOSwhen incrementally expanding the input Si-K region by 5 eV.Resulting changes in the prediction accuracy are shown inFigure 3b. Here, the observation that the MSE of p-PDOS isconsistently larger than that of s-PDOS can be attributed to theground-state PDOS exhibiting a larger component of p-orbitalsthan s-orbitals, as can be found in Figure 1a. From Figure 3b, itcan be observed that progressively expanding the input Si-Kedge region results in a decrease in the MSE for both s-PDOSand p-PDOS, indicating an enhancement in predictability.However, it can also be observed that additionally includingthe spectral region from 14 to 19 eV as input does notcontribute to the improvement in prediction accuracy. Thismeans that, when predicting the ground-state PDOS in therange of −15−15 eV with respect to the Fermi level, the regionfrom the onset of the Si-K edge to 14 eV is more critical. It hasbeen known that the excited electronic structure tends to belocalized to the excited atom, resulting in a shift of PDOStoward the lower energy sides compared to the ground statedue to the formation of a core-hole. Therefore, it is reasonablethat the spectral feature in the lower energy part of ELNES/XANES is more important for PDOS prediction.As mentioned above, we observed a trend of improvedprediction accuracy with an increasing input range. Toinvestigate how each region of the Si-K edge contributes tothis improvement, we examined the prediction accuracy of theground-state PDOS when each 5 eV region of the Si-K edgewas used as an independent input. The results are shown inFigure 3c. From these results, it is evident that higherprediction accuracy in terms of MSE is achieved when usingthe 4−14 eV region rather than the rising region of the Si-Kedge for both s-PDOS and p-PDOS predictions. Furthermore,the highest prediction accuracy for p-PDOS was observedwhen utilizing the 4−9 eV region, while the highest predictionaccuracy for s-PDOS was achieved with the 9−14 eV region.As explained in more detail later, the Si-K edge in the region of4−9 eV contains the most useful information for predicting thep-PDOS near the Fermi level, while the Si-K edge in the regionof 9−14 eV contains the most beneficial information forpredicting valence-band s-PDOS. In the regions on the lowerenergy side of 14−19 eV, higher prediction accuracy wasobtained regardless of which region is used, and there is nosignificant change in MSE when using the Si-K edge of eachregion. On the other hand, as can be seen from Figure 3b, theMSE significantly decreased by expanding the region. Thissuggests that each region of the Si-K edge contains informationon different characteristics.To investigate how each region of the Si-K edge contributesto the decrease in the MSE of the ground-state PDOS, theground state PDOS was divided into four regions afterpredicting the PDOS across the entire region from the Si-Kedge, and the prediction accuracy for each region wasexamined. As illustrated in Figure 4a, the 30 eV region fromFigure 3. (a) Input Si-K edge spectrum, which covers a region of 20eV, was divided into four sections, each with a range of 5 eV. (b)Change in the MSE as the input region is progressively increased byincrements of 5 eV. (c) Variation in the MSE when each 5 eV regionis used as an independent input.The Journal of Physical Chemistry C pubs.acs.org/JPCC Articlehttps://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−1350713503https://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c02818/suppl_file/jp4c02818_si_001.pdfhttps://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c02818/suppl_file/jp4c02818_si_001.pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig3&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig3&ref=pdfpubs.acs.org/JPCC?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as−15 to 15 eV was divided into four regions, each spanning 7.5eV. Here, regions 1 and 2 correspond to the valence band,while regions 3 and 4 correspond to the conduction band.Although the data set used in this work includes PDOSs withvarious spectral shapes, as an overall trend, characteristic peaksof s-PDOS can be observed in region below −7.5 eV (region1) and that of p-PDOS can be observed in region from −7.5 to7.5 eV (regions 2 and 3).Figure 4b,c shows the relationship between the input rangeof Si-K edge and the prediction accuracy for each region of s-PDOS and p-PDOS, respectively. The s-PDOS mainly consistsof valence band contributions, i.e., regions 1 and 2, and itsdirect information should be absent in the Si-K edge due to theselection rule. It can be observed that the prediction accuracyof such s-PDOS is slightly changed by the spectral region, andthe highest accuracy for these regions is achieved when usingthe Si-K edge from 9 to 14 eV. As previously mentioned inFigure 3c, the highest prediction accuracy for the s-PDOS wasachieved by utilizing the Si-K edge in the 9−14 eV. Those tworesults indicate that the 9 to 14 eV region encompassesvaluable information for predicting s-orbitals throughout theentire valence band. At the present time, the underlying reasonfor this cannot be elucidated. However, as discussed in Figure1b, there are two peaks at the Si-K edge, and it is implied thatthe second peak around 13 eV may contain valuableinformation beneficial for predicting the s-orbital in the groundstate.The prediction accuracy for the p-PDOS across the differentregions differs from that for the s-PDOS. The p-PDOSprimarily exhibits high electronic density of states at the upperedge of the valence band, namely, region 2, and at the loweredge of the conduction band, namely, region 3. Focusing onregion 3, which is the lower edge of the conduction band, it isconfirmed that high prediction accuracy can be achieved whenusing the Si-K edge with −1 to 9 eV. This seems natural whenconsidering that Si-K edge reflects the p-orbitals of theconduction band in excited states, and there exists at leastsome correlation with the p-orbitals of the conduction band inthe ground state. In contrast, for region 2, similar to the casewith the s-PDOS, it is found that the highest predictionaccuracy is also achieved when using the Si-K edge with 9 to 14eV. This implies that the information related to thehybridization of s- and p-orbitals is primarily contained withinthe 9 to 14 eV range. Upon a comprehensive examination of allregions, it can be found that the Si-K edge in the energy rangeof 4−9 eV provides high prediction accuracy for p-PDOS inboth region 2 and region 3.The Si-K edge is thought to reflect the p-orbital PDOS ofthe conduction band in the excited state. Since the electronicstructures of Si atoms are affected by the hybridization of s-and p-orbitals, the Si-K edge is considered to containinformation related to the hybridization to some extent. Theresults shown in Figure 4 suggest the existence of energy bandscontaining information related to hybridization and that theML model successfully extracts information related to thehybridization, allowing the prediction of not only the p-orbitalsin the conduction band but also s-orbitals in the valence band.In this study, we employed an ML model to predict theground-state PDOS from the Si-K edge. To verify theeffectiveness of using ML models, a comparison was conductedwith an alternative method, which is template matching. Intemplate matching, given a specific Si-K edge, the methodinvolves searching the training data for the Si-K edge that isclosest to the given one. The ground state PDOScorresponding to the spectrum of the closest match is thenutilized as the prediction result. The comparison of the resultsfrom predictions made by the ML model and those madethrough template matching is shown in Figure 5. Here, in thisstudy, MSE is used as the metric for measuring the similarity ofthe Si-K edge in template matching.In Figure 5b, the values on the horizontal axis correspond tothe MSE between the target Si-K edge and the Si-K edge,matched by template matching. Also, the value on the verticalaxis represents the difference between MSE:=MSE MSE(Matched) MSE(ML predicted)Figure 4. (a) After predicting ground-state PDOS across the entireregion by varying the input regions, the ground-state PDOS wassegmented into four distinct areas (regions 1 to region 4).Subsequently, the prediction accuracy within each of these areaswas investigated. (b) Variation in prediction accuracy for the ground-state PDOS concerning s-orbitals within each specified region, inresponse to the variation in the input Si-K edge spectral region. (c)Result for the ground-state PDOS about p-orbitals.The Journal of Physical Chemistry C pubs.acs.org/JPCC Articlehttps://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−1350713504https://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig4&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig4&ref=pdfpubs.acs.org/JPCC?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-aswhere MSE (Matched) represents the MSE between theground-truth PDOS and the PDOS predicted by templated-matching, and the MSE (ML predicted) represents the MSEbetween the ground-truth PDOS and that predicted by theML. When ΔMSE values are positive, indicating higherprediction accuracy achieved with ML, they are representedby purple dotes. Conversely, when ΔMSE values are negative,indicating higher prediction accuracy achieved with template-matching, they are represented by orange dots. In addition,histograms are displayed in the Figure 5a.The histogram in Figure 5a reveals that in a large portion ofcases ΔMSE is positive, revealing that higher predictionaccuracy is achieved with the ML model. Furthermore, twopoints can be found from Figure 5b. First, the absolute value ofΔMSE tends to be smaller when it is negative, whereas thelarger absolute value is often obtained when ΔMSE is positive,indicating that while template matching can be alternative toML models in some cases, ML generally leads to higherprediction accuracy than the template matching. The secondpoint is that when the MSE of the Si-K edge is large, indicatingthat it is difficult to find spectra with similar shapes within thedatabase, the ΔMSE tends to be positive. This clearly indicatesthat the ML becomes more effective when there are no similarspectra in the database. Thus, compared to template matching,the utilization of ML models has generally been shown to beeffective.Finally, to investigate the applicability of our approach toexperimental spectra, we input the experimental Si-K edge ofdiamond-type Si into the ML model. Figure 6a shows theDFT-calculated Si-K edge of diamond-type Si, and Figure 6bshows the corresponding DFT-calculated ground-state PDOS.Here, calculated spectra were broadened by a Gaussianfunction with a standard deviation of 1.2 eV to match theenergy resolution of the experimentally obtained spectrum.The experimental spectrum was obtained using an aberrationcorrected STEM (JEOL ARM200CF) with a cold-type fieldemission electron source operated at 200 kV, with an EELSspectrometer (Gatan Quantum system) with an energydispersion of 0.25 eV/channel. The spectrum was obtainedfrom a single crystal of [110] oriented pure Si. In Figure 6c, weshow the experimentally obtained Si-K edge of diamond-typeSi. Compared to the DFT-calculated Si-K edge, it can be foundthat the experimental spectrum contains noise, and the secondpeak around 10−15 eV is obscured and cannot be observed.Figure 6d shows the result of prediction from the Si-K edge.Here, the yellow solid line corresponds to the DFT-calculatedground-state PDOS of diamond-type Si and the black dottedline corresponds to the ground-state PDOS predicted by theML model trained using the spectra with the broadening widthof 1.2 eV. The overall shapes of the two PDOSs are similar, butthere are differences in the DOS especially near the Fermilevel. Figure 6e shows the experimental Si-K edge in Figure 6csmoothed using a Savitzky-Golay filter with a filter window sizeof 40 and a polynomial order of 3, and Figure 6f shows theground-state PDOS predicted from the smoothed spectrum.Compared to the case using an unsmoothed spectrum, there isa slight change in the spectral shape, but the spectral featurenear the Fermi level still differs from the DFT-calculatedground-state PDOS. These results suggest that whether peaksFigure 5. Comparison of predictions using ML vs. template matching.The values on the horizontal axis correspond to the MSE between theoriginal ELNES/XANES and the ELNES/XANES matched bytemplate matching, which is denoted as MSE (ELNES/XANES).(a) Cases where ML performed better compared to templatematching are shown in the purple histogram, while the cases wheretemplate matching exhibits better accuracy are represented by theorange histogram. (b) Relationship between the differences in MSE ofPDOS prediction by ML and MSE of PDOS prediction by templatematching, and MSE (ELNES/XANES). The purple dots indicate thatpredictions made by ML exhibited higher prediction accuracy, whilethe orange dots signify those predictions made through templatematching showed higher prediction accuracy.Figure 6. (a) DFT-calculated Si-K edge of diamond-type Si. (b) DFT-calculated ground-state PDOS of Si in diamond-type Si. (c)Experimentally obtained Si-K edge of diamond-type Si. (d)Ground-state PDOS predicted from the experimental Si-K edge ofdiamond-type Si. (e) Smoothed experimental Si-K edge of diamond-type Si. (f) Ground-state PDOS predicted from the smoothedexperimental Si-K edge of diamond-type Si.The Journal of Physical Chemistry C pubs.acs.org/JPCC Articlehttps://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−1350713505https://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig5&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig6&ref=pdfhttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?fig=fig6&ref=pdfpubs.acs.org/JPCC?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-asare properly observed in the spectrum has a greater impact onthe validity of prediction rather than whether noise smoothinghas been performed. Therefore, to better apply to experimentalspectra, it is considered necessary to address the factors thatcontribute to peak obscuration and to improve the energyresolution of Si-K edge observations.In this study, we theoretically examined the predictability ofthe atomic-level electronic structures at the ground state fromELNES/XANES, focusing on the Si-K edge of Si. It wassuggested that by training an ML model to learn thecorrelation between ELNES/XANES and the PDOS of thevalence and conduction bands at the ground state, it is possibleto predict the electronic structure at the ground state includingthe valence band from ELNES/XANES. The insights obtainedin this study are expected to be in part transferable to the Kedges of elements with electronic structure similar to Si, suchas the C-K edge. As in the case of Si, C tends to formhybridized orbitals, and it is expected that the ground-statePDOS, including not only p-orbitals but also s-orbitals, can bepredicted from the C-K edge. On the other hand, oxides tendto form more ionic bonds, and the PDOS of O in oxides,unlike in the case of Si and C, has a larger DOS only in valenceband. Investigating the applicability of this approach to systemswhere the correlation between the valence and conductionbands is less apparent is an interesting direction for futureresearch.■ CONCLUSIONSIn conclusion, we have developed an ML model capable ofpredicting atom-specific ground-state PDOS of a Si atom fromthe corresponding Si-K ELNES/XANES. This demonstrationhas shown the feasibility of predicting PDOS for both thevalence and conduction bands, including both s- and p- orbitalsin the ground state of silicon atoms, from the Si-K edge, whichis traditionally thought to reflect the conduction band PDOSof p-orbitals in the excited state. We discovered that theinformation within the energy region of the Si-K edge varies,with the area near the rising edge being particularly effectivefor predicting p-orbitals of the conduction band, which isbelieved to be directly correlated with the Si-K edge.Additionally, the energy region just beyond the rising edgewas proved to be effective for predicting the s- and p-orbitals ofthe valence band in the ground state. This region is consideredto contain information related to the hybridization of s- and p-orbitals, suggesting that ML models can capture such complexcorrelations.Finally, the effectiveness of ML models was confirmedthrough comparison with template matching. Consequently,the ML models are confirmed to be particularly advantageousover template matching when the database lacks similar shapesof the Si-K edge.Through this study, we have demonstrated the prediction ofatom-specific ground-state PDOS from ELNES/XANES with afocus on silicon. Expanding this technique to encompass morecomplex materials and experimental spectra is anticipated tonot only facilitate the realization of atomic-level analysis ofground-state electronic structures but also to deepen ourunderstanding on the stability and properties of materials.■ ASSOCIATED CONTENT*sı Supporting InformationThe Supporting Information is available free of charge athttps://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818.Analysis on the results with low prediction accuracy,detailed procedure for data set augmentation, anddetailed model architecture (PDF)■ AUTHOR INFORMATIONCorresponding AuthorsIzumi Takahara − Institute of Industrial Science, TheUniversity of Tokyo, Tokyo 153-8505, Japan; orcid.org/0009-0004-6022-1945; Email: kougen@iis.u-tokyo.ac.jpTeruyasu Mizoguchi − Institute of Industrial Science, TheUniversity of Tokyo, Tokyo 153-8505, Japan; orcid.org/0000-0003-3712-7307; Email: teru@iis.u-tokyo.ac.jpAuthorsFumihiko Uesugi − Research Network and Facility ServicesDivision, National Institute for Materials Science, Tsukuba305-0044, JapanKoji Kimoto − Center for Basic Research on Materials,National Institute for Materials Science, Tsukuba 305-0044,Japan; orcid.org/0000-0002-3927-0492Kiyou Shibata − Institute of Industrial Science, The Universityof Tokyo, Tokyo 153-8505, Japan; orcid.org/0000-0002-0639-5408Complete contact information is available at:https://pubs.acs.org/10.1021/acs.jpcc.4c02818NotesThe authors declare no competing financial interest.■ ACKNOWLEDGMENTSThis work was supported by MEXT/JSPS, KAKENHI (GrantNumbers JP19H05787, JP24K08016, JP24KJ0939) and JST,CREST (Grant Number JP-MJCR1993). This study waspartially supported by NEDO (New Energy and IndustrialTechnology Development Organization), Japan. We acknowl-edge Mr. Poyen Chen at the University of Tokyo for fruitfuldiscussion on the present study. I.T. was supported by theProgram for Leading Graduate Schools (MERIT-WINGS).■ REFERENCES(1) Hohenberg, P.; Kohn, W. Inhomogeneous Electron Gas. Phys.Rev. 1964, 136 (3B), B864−B871.(2) Kohn, W.; Sham, L. J. Self-Consistent Equations IncludingExchange and Correlation Effects. Phys. Rev. 1965, 140 (4A), A1133−A1138.(3) Ben Mahmoud, C.; Anelli, A.; Csányi, G.; Ceriotti, M. Learningthe Electronic Density of States in Condensed Matter. Phys. Rev. B2020, 102 (2), No. 235130.(4) Chandrasekaran, A.; Kamal, D.; Batra, R.; Kim, C.; Chen, L.;Ramprasad, R. Solving the Electronic Structure Problem withMachine Learning. npj Comput. Mater. 2019, 5 (1), No. 22.(5) Fung, V.; Ganesh, P.; Sumpter, B. G. Physically InformedMachine Learning Prediction of Electronic Density of States. Chem.Mater. 2022, 34 (11), 4848−4855.(6) Ikeno, H.; Mizoguchi, T. Basics and Applications of ELNESCalculations. Microscopy 2017, 66 (5), 305−327.(7) Tanaka, I.; Mizoguchi, T.; Yamamoto, T. XANES and ELNES inCeramic Science. J. Am. Ceram. Soc. 2005, 88 (8), 2013−2029.(8) Mizoguchi, T.; Tanaka, I.; Gao, S.-P.; Pickard, C. J. First-Principles Calculation of Spectral Features, Chemical Shift andAbsolute Threshold of ELNES and XANES Using a Plane WavePseudopotential Method. J. Phys.: Condens. Matter 2009, 21 (10),No. 104204.The Journal of Physical Chemistry C pubs.acs.org/JPCC Articlehttps://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−1350713506https://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?goto=supporting-infohttps://pubs.acs.org/doi/suppl/10.1021/acs.jpcc.4c02818/suppl_file/jp4c02818_si_001.pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Izumi+Takahara"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0009-0004-6022-1945https://orcid.org/0009-0004-6022-1945mailto:kougen@iis.u-tokyo.ac.jphttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Teruyasu+Mizoguchi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0003-3712-7307https://orcid.org/0000-0003-3712-7307mailto:teru@iis.u-tokyo.ac.jphttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Fumihiko+Uesugi"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://pubs.acs.org/action/doSearch?field1=Contrib&text1="Koji+Kimoto"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-3927-0492https://pubs.acs.org/action/doSearch?field1=Contrib&text1="Kiyou+Shibata"&field2=AllField&text2=&publication=&accessType=allContent&Earliest=&ref=pdfhttps://orcid.org/0000-0002-0639-5408https://orcid.org/0000-0002-0639-5408https://pubs.acs.org/doi/10.1021/acs.jpcc.4c02818?ref=pdfhttps://doi.org/10.1103/PhysRev.136.B864https://doi.org/10.1103/PhysRev.140.A1133https://doi.org/10.1103/PhysRev.140.A1133https://doi.org/10.1103/PhysRevB.102.235130https://doi.org/10.1103/PhysRevB.102.235130https://doi.org/10.1038/s41524-019-0162-7https://doi.org/10.1038/s41524-019-0162-7https://doi.org/10.1021/acs.chemmater.1c04252?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.chemmater.1c04252?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1093/jmicro/dfx033https://doi.org/10.1093/jmicro/dfx033https://doi.org/10.1111/j.1551-2916.2005.00547.xhttps://doi.org/10.1111/j.1551-2916.2005.00547.xhttps://doi.org/10.1088/0953-8984/21/10/104204https://doi.org/10.1088/0953-8984/21/10/104204https://doi.org/10.1088/0953-8984/21/10/104204https://doi.org/10.1088/0953-8984/21/10/104204pubs.acs.org/JPCC?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as(9) Mizoguchi, T.; Tanaka, I.; Yoshioka, S.; Kunisu, M.; Yamamoto,T.; Ching, W. Y. First-Principles Calculations of ELNES and XANESof Selected Wide-Gap Materials: Dependence on Crystal Structureand Orientation. Phys. Rev. B 2004, 70 (4), No. 045103.(10) Kimoto, K.; Asaka, T.; Nagai, T.; Saito, M.; Matsui, Y.;Ishizuka, K. Element-Selective Imaging of Atomic Columns in aCrystal Using STEM and EELS. Nature 2007, 450 (7170), 702−704.(11) Bosman, M.; Keast, V. J.; García-Muñoz, J. L.; D’Alfonso, A. J.;Findlay, S. D.; Allen, L. J. Two-Dimensional Mapping of ChemicalInformation at Atomic Resolution. Phys. Rev. Lett. 2007, 99 (8),No. 086102.(12) Tan, H.; Turner, S.; Yücelen, E.; Verbeeck, J.; Van Tendeloo,G. 2D Atomic Mapping of Oxidation States in Transition MetalOxides by Scanning Transmission Electron Microscopy and ElectronEnergy-Loss Spectroscopy. Phys. Rev. Lett. 2011, 107 (10),No. 107602.(13) Bugnet, M.; Ederer, M.; Lazarov, V. K.; Li, L.; Ramasse, Q. M.;Löffler, S.; Kepaptsoglou, D. M. Imaging the Spatial Distribution ofElectronic States in Graphene Using Electron Energy-Loss Spectros-copy: Prospect of Orbital Mapping. Phys. Rev. Lett. 2022, 128 (11),No. 116401.(14) Cuisinier, M.; Cabelguen, P.-E.; Evers, S.; He, G.; Kolbeck, M.;Garsuch, A.; Bolin, T.; Balasubramanian, M.; Nazar, L. F. SulfurSpeciation in Li−S Batteries Determined by Operando X-RayAbsorption Spectroscopy. J. Phys. Chem. Lett. 2013, 4 (19), 3227−3232.(15) Iglesias-Juez, A.; Chiarello, G. L.; Patience, G. S.; Guerrero-Pérez, M. O. cy�XAS,XANES. Can. J. Chem. Eng. 2022, 100 (1), 3−22.(16) Houhou, R.; Bocklitz, T. Trends in Artificial Intelligence,Machine Learning, and Chemometrics Applied to Chemical Data.Anal. Sci. Adv. 2021, 2 (3−4), 128−141.(17) Timoshenko, J.; Lu, D.; Lin, Y.; Frenkel, A. I. SupervisedMachine-Learning-Based Determination of Three-Dimensional Struc-ture of Metallic Nanoparticles. J. Phys. Chem. Lett. 2017, 8 (20),5091−5098.(18) Kiyohara, S.; Tsubaki, M.; Liao, K.; Mizoguchi, T. QuantitativeEstimation of Properties from Core-Loss Spectrum via NeuralNetwork. J. Phys. Mater. 2019, 2 (2), No. 024003.(19) Zheng, C.; Chen, C.; Chen, Y.; Ong, S. P. Random ForestModels for Accurate Identification of Coordination Environmentsfrom X-Ray Absorption Near-Edge Structure. Patterns (N Y) 2020, 1(2), No. 100013.(20) Kiyohara, S.; Mizoguchi, T. Radial Distribution Function fromX-Ray Absorption near Edge Structure with an Artificial NeuralNetwork. J. Phys. Soc. Jpn. 2020, 89 (10), No. 103001.(21) Kikumasa, K.; Kiyohara, S.; Shibata, K.; Mizoguchi, T.Quantification of the Properties of Organic Molecules Using Core-loss Spectra as Neural Network Descriptors. Adv. Intell. Syst. 2022, 4(1), No. 2100103.(22) Mizoguchi, T.; Kiyohara, S. Machine Learning Approaches forELNES/XANES. Microscopy 2020, 69 (2), 92−109.(23) Guda, A. A.; Guda, S. A.; Martini, A.; Kravtsova, A. N.; Algasov,A.; Bugaev, A.; Kubrin, S. P.; Guda, L. V.; Šot, P.; van Bokhoven, J. A.;Copéret, C.; Soldatov, A. V. Understanding X-Ray Absorption Spectraby Means of Descriptors and Machine Learning Algorithms. npjComput. Mater. 2021, 7 (1), No. 203.(24) Carbone, M. R.; Yoo, S.; Topsakal, M.; Lu, D. Classification ofLocal Chemical Environments from X-Ray Absorption Spectra UsingSupervised Machine Learning. Phys. Rev. Mater. 2019, 3 (3),No. 033604.(25) Torrisi, S. B.; Carbone, M. R.; Rohr, B. A.; Montoya, J. H.; Ha,Y.; Yano, J.; Suram, S. K.; Hung, L. Random Forest Machine LearningModels for Interpretable X-Ray Absorption near-Edge StructureSpectrum-Property Relationships. npj Comput. Mater. 2020, 6 (1),No. 109.(26) Chen, P.-Y.; Shibata, K.; Hagita, K.; Miyata, T.; Mizoguchi, T.Prediction of the Ground-State Electronic Structure from Core-LossSpectra of Organic Molecules by Machine Learning. J. Phys. Chem.Lett. 2023, 14 (20), 4858−4865.(27) Jain, A.; Ong, S. P.; Hautier, G.; Chen, W.; Richards, W. D.;Dacek, S.; Cholia, S.; Gunter, D.; Skinner, D.; Ceder, G.; Persson, K.A. Commentary: The Materials Project: A Materials GenomeApproach to Accelerating Materials Innovation. APL Mater. 2013, 1(1), No. 011002.(28) Togo, A.; Tanaka, I. Spglib: A Software Library for CrystalSymmetry Search. arXiv [cond-mat.mtrl-sci], 2018. http://arxiv.org/abs/1808.01590.(29) Clark, S. J.; Segall, M. D.; Pickard, C. J.; Hasnip, P. J.; Probert,M. I. J.; Refson, K.; Payne, M. C. First Principles Methods UsingCASTEP. Zeitschrift für Kristallographie - Crystalline Materials 2005,220 (5−6), 567−570.(30) Morris, A. J.; Nicholls, R. J.; Pickard, C. J.; Yates, J. R.OptaDOS: A Tool for Obtaining Density of States, Core-Level andOptical Spectra from Electronic Structure Codes. Comput. Phys.Commun. 2014, 185 (5), 1477−1485.(31) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized GradientApproximation Made Simple. Phys. Rev. Lett. 1996, 77 (18), 3865−3868.The Journal of Physical Chemistry C pubs.acs.org/JPCC Articlehttps://doi.org/10.1021/acs.jpcc.4c02818J. Phys. Chem. C 2024, 128, 13500−1350713507https://doi.org/10.1103/PhysRevB.70.045103https://doi.org/10.1103/PhysRevB.70.045103https://doi.org/10.1103/PhysRevB.70.045103https://doi.org/10.1038/nature06352https://doi.org/10.1038/nature06352https://doi.org/10.1103/PhysRevLett.99.086102https://doi.org/10.1103/PhysRevLett.99.086102https://doi.org/10.1103/PhysRevLett.107.107602https://doi.org/10.1103/PhysRevLett.107.107602https://doi.org/10.1103/PhysRevLett.107.107602https://doi.org/10.1103/PhysRevLett.128.116401https://doi.org/10.1103/PhysRevLett.128.116401https://doi.org/10.1103/PhysRevLett.128.116401https://doi.org/10.1021/jz401763d?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/jz401763d?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/jz401763d?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1002/cjce.24291https://doi.org/10.1002/ansa.202000162https://doi.org/10.1002/ansa.202000162https://doi.org/10.1021/acs.jpclett.7b02364?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.jpclett.7b02364?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.jpclett.7b02364?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1088/2515-7639/ab0b68https://doi.org/10.1088/2515-7639/ab0b68https://doi.org/10.1088/2515-7639/ab0b68https://doi.org/10.1016/j.patter.2020.100013https://doi.org/10.1016/j.patter.2020.100013https://doi.org/10.1016/j.patter.2020.100013https://doi.org/10.7566/JPSJ.89.103001https://doi.org/10.7566/JPSJ.89.103001https://doi.org/10.7566/JPSJ.89.103001https://doi.org/10.1002/aisy.202270004https://doi.org/10.1002/aisy.202270004https://doi.org/10.1093/jmicro/dfz109https://doi.org/10.1093/jmicro/dfz109https://doi.org/10.1038/s41524-021-00664-9https://doi.org/10.1038/s41524-021-00664-9https://doi.org/10.1103/PhysRevMaterials.3.033604https://doi.org/10.1103/PhysRevMaterials.3.033604https://doi.org/10.1103/PhysRevMaterials.3.033604https://doi.org/10.1038/s41524-020-00376-6https://doi.org/10.1038/s41524-020-00376-6https://doi.org/10.1038/s41524-020-00376-6https://doi.org/10.1021/acs.jpclett.3c00142?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1021/acs.jpclett.3c00142?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-ashttps://doi.org/10.1063/1.4812323https://doi.org/10.1063/1.4812323http://arxiv.org/abs/1808.01590http://arxiv.org/abs/1808.01590https://doi.org/10.1524/zkri.220.5.567.65075https://doi.org/10.1524/zkri.220.5.567.65075https://doi.org/10.1016/j.cpc.2014.02.013https://doi.org/10.1016/j.cpc.2014.02.013https://doi.org/10.1103/PhysRevLett.77.3865https://doi.org/10.1103/PhysRevLett.77.3865pubs.acs.org/JPCC?ref=pdfhttps://doi.org/10.1021/acs.jpcc.4c02818?urlappend=%3Fref%3DPDF&jav=VoR&rel=cite-as