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ArticleMarch 28, 2024

Band Alignment of Oxides by Learnable Structural-Descriptor-Aided Neural Network and Transfer Learning
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Shin Kiyohara*
Shin Kiyohara
Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, R3-7, 4259 Nagatsuta, Midori-ku, Yokohama 226-8501, Japan
Institute for Materials Research, Tohoku University, 2-2-1 Katahira, Aoba-ku, Sendai 980-8577, Japan
*Email: [email protected]
More by Shin Kiyohara
https://orcid.org/0000-0003-2890-5760
Yoyo Hinuma
Yoyo Hinuma
Department of Energy and Environment, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan
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https://orcid.org/0000-0003-2272-1178
Fumiyasu Oba*
Fumiyasu Oba
Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, R3-7, 4259 Nagatsuta, Midori-ku, Yokohama 226-8501, Japan
MDX Research Center for Element Strategy, International Research Frontiers Initiative, Tokyo Institute of Technology, SE-6, 4259 Nagatsuta, Midori-ku, Yokohama 226-8501, Japan
*Email: [email protected]
More by Fumiyasu Oba
https://orcid.org/0000-0001-7178-5333

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Journal of the American Chemical Society

Cite this: J. Am. Chem. Soc. 2024, 146, 14, 9697–9708

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https://doi.org/10.1021/jacs.3c13574

Published March 28, 2024

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Abstract

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The band alignment of semiconductors, insulators, and dielectrics is relevant to diverse material properties and device structures utilizing their surfaces and interfaces. In particular, the ionization potential and electron affinity are fundamental quantities that describe surface-dependent band-edge positions with respect to the vacuum level. Their accurate and systematic determination, however, demands elaborate experiments or simulations for well-characterized surfaces. Here, we report machine learning for the band alignment of nonmetallic oxides using a high-throughput first-principles calculation data set containing about 3000 oxide surfaces. Our neural network accurately predicts the band positions for relaxed surfaces of binary oxides simply by using the information on bulk structures and surface termination planes. Moreover, we extend the model to naturally include multiple-cation effects and transfer it to ternary oxides. The present approach enables the band alignment of a vast number of solid surfaces, thereby opening the way to a systematic understanding and materials screening.

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You are free to share(copy and redistribute) this article in any medium or format and to adapt(remix, transform, and build upon) the material for any purpose, even commercially within the parameters below:
- Creative Commons (CC): This is a Creative Commons license.
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This summary highlights only some of the key features and terms of the actual license. It is not a license and has no legal value. Carefully review the actual license before using these materials.

Introduction

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The ionization potential (IP) and electron affinity (EA) of a nonmetallic solid are defined as the energy levels of the valence band maximum (VBM) and conduction band minimum (CBM) with respect to the vacuum level, respectively. They show not only how easily an electron is released or accepted but also information about the relative band positions of materials. Such band alignments or lineups play crucial roles in our understanding, design, and development of materials and devices utilizing surfaces and heterointerfaces, including photocatalysts, (1−3) photovoltaics, (4−6) and all other heterostructured electronic and optoelectronic devices. (7−13) The lattice mismatch, local atomic structure, and charge transfer should also be considered for depicting complete band alignments at heterointerfaces; nevertheless, IPs and EAs are fundamental information for designing interfacial functionalities in addition to surface-related properties. (7)

The IPs and EAs of solids involve contributions of surface dipole moments. Thus, they significantly depend on the atomic and electronic structures in the vicinity of the surfaces and therefore on the surface orientation and composition. (14−16) Computationally, first-principles calculations have successfully quantified IPs and EAs. (15−23) Separate calculations of bulk and surface systems are performed in a typical procedure for the evaluation of IPs and EAs. Bulk calculations offer VBM and CBM positions with respect to a reference level; surface calculations offer the differences between the vacuum and reference levels, which include the surface dipole contributions to electrostatic potentials. IPs and EAs are then obtained by the alignment of the bulk and surface reference levels.

However, an accurate and high-throughput evaluation of IPs and EAs is not straightforward because both processes are time-consuming. Density functional theory calculations using standard local and semilocal functionals produce large errors in the VBM and CBM positions, requiring us to use more elaborate and computationally demanding approaches, e.g., hybrid functionals including nonlocal exchange contributions and GW approximations based on many-body perturbation theory. (15−20,24,25) Surfaces have both macroscopic and microscopic degrees of freedom, namely, the surface orientation as given by Miller indices and the location of the termination plane. Substantial reconstruction from ideal structures also takes place at some surfaces, (26−33) which can significantly affect band positions as reported for perovskite oxides and TiO₂. (32,33) Therefore, even one material has a large variety of surface atomic structures, and systematic evaluation of their IPs and EAs requires huge amounts of computation.

Recently, machine learning has been widespread in materials science. Virtual screening based on machine learning is an efficient way to explore new materials with desired functions, where a surrogate model enables us to virtually predict material properties. (34−39) In particular, theoretical calculations can generate comparatively large data sets that are prerequisites for constructing accurate surrogate models. Previous studies have reported successful materials screening for various properties by machine learning in combination with theoretical calculations. (35−38,40−44)

In this article, we present a regression model based on an artificial neural network (ANN) using the smooth overlap of atom positions (SOAPs) (45) as input descriptors to predict the IPs and EAs of nonmetallic oxides (see Figure 1). First-principles calculations based on a non-self-consistent dielectric-dependent hybrid functional approach (21) allow for the accurate and efficient evaluation of the IPs and EAs of about 3000 binary and ternary oxide surfaces. The ANN model constructed using this data set accurately predicts the IPs and EAs of binary oxides despite the model using the information before structural relaxation at surfaces as the input, namely, bulk crystal structures and surface termination planes of the oxides of interest. Moreover, we enable the ANN model to be applied to ternary oxides by developing “learnable” SOAPs, which can incorporate atom species varieties while keeping low descriptor dimensions.

Figure 1. Schematic of prediction of IPs and EAs in nonmetallic solids by theoretical calculations and machine learning. The theoretical calculations from first principles typically use a combination of surface and bulk models to evaluate the energy difference between the vacuum level and the VBM (IP) or CBM (EA). Our ANN predicts the IPs and EAs of relaxed surfaces by simply inputting the information on the bulk crystal structure and the surface index and termination plane.

Results and Discussion

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High-Throughput First-Principles Calculations of IPs and EAs of Binary Oxides

Figure 2a shows distributions of the theoretical IPs and EAs in the binary oxide data set for 2195 nonpolar surfaces; all IP and EA values can be found in the Supporting Information. Here, we focus on nonpolar surfaces because the modeling of polar surfaces requires the consideration of system- and environment-dependent charge-compensation mechanisms (26,27,46) and therefore their high-throughput calculations are not straightforward. The horizontal axis in Figure 2a is the constituent cation species, each of which contains various surfaces of several polymorphs. We find the tendency that the IP and EA values depend largely on the cation species, although the variety in the crystal and surface atomic structures leads to deviations of ∼ ±1 eV from their average values. The calculated IPs and EAs for selected surfaces are shown with available experimental values in Figure 2b. Although the IPs and EAs are, by nature, rather sensitive to the detailed structures and conditions of the experimentally investigated surfaces, reasonable agreement between the experiment and theory is recognized overall. The non-self-consistent dielectric-dependent hybrid functional approach taken here also well-reproduces the experimental IPs and EAs of group IV, III–V, and II–VI semiconductor surfaces. (21) These comparisons with the experimental results demonstrate the accuracy of our high-throughput surface calculation data.

Figure 2. Distribution of theoretical IPs and EAs of binary oxides and comparison with experiments. (a) Upper panel shows the distribution of the IPs and EAs of the respective binary oxides. Orange and green dots are IPs and EAs, respectively. Cross and circle symbols are Tasker’s type I and II surfaces, (64) respectively. The bottom panel is the number of surfaces, where yellow and dark blue bars are types I and II, respectively. (b) Theoretical IPs and EAs versus reported experimental values for selected binary oxides. The upper edges of the pale orange bars and the lower edges of the light green bars are calculated VBMs and CBMs with respect to the vacuum level (set at 0 eV), respectively. The orange and green solid lines are experimentally reported IPs and EAs, respectively; the dashed lines are derived by combining experimental IPs or EAs and experimental band gaps. The experimental data are taken from refs (70and71) for MgO, refs (72and73) for Al₂O₃, ref (74) for TiO₂, ref (75) for V₂O₅, ref (76) for Cu₂O, refs (77–79) for ZnO, refs (80and81) for Ga₂O₃, ref (82) for MoO₃, refs (83and84) for Ag₂O, refs (85and86) for In₂O₃, ref (87) for CeO₂, ref (83) for Ta₂O₅, and ref (88) for WO₃. The surface orientations have not been presented in the experimental reports for V₂O₅, Cu₂O, MoO₃, Ag₂O, In₂O₃, Ta₂O₅, and WO₃. Therefore, all theoretical IPs and EAs of binary oxides with the indicated space groups are depicted in the figure. Note that there are many types of surfaces for V₂O₅, MoO₃, and Ta₂O₅, and the bars for each surface are extremely narrow.

Construction of ANN Models

Using the binary oxide data set, we constructed the ANN (hereinafter called simple-ANN) as shown in Figure 3a. The SOAP descriptors, which sophisticatedly include structural information such as the bond length, bond angle, and coordination number, (45) are evaluated for unrelaxed surfaces and inputted in the first layer to describe the IPs and EAs at relaxed surfaces. The SOAPs in this study were preprocessed as follows. When multiple elements are included in a system, the concatenations of the SOAPs based on the elemental pairs (hereinafter called element-pair SOAPs) are generally used for describing atomic structures in a system (47) as shown in the bottom left panel of Figure 4. Here, we consider 41 atom species simultaneously. Thus, the element-pair SOAPs have several tens of thousands of dimensions because SOAPs of a pair of elements have several tens to several hundreds of dimensions. To reduce the number of descriptor dimensions and prevent overfitting, we dealt with the 40 cation species as the same species when calculating SOAPs and oxygen as an anion, resulting in calculating the SOAPs of three pairs, namely, cation–cation, cation–anion, and anion–anion combinations (hereinafter called cation–anion-pair SOAPs), as shown in the bottom center panel of Figure 4. The cation–anion-pair SOAPs were calculated on each atom site in a system while the IP and EA need one-to-one correspondence with a system. Thus, we averaged the cation–anion-pair SOAPs in a system for inputs. Assuming that the information about the vicinity of the surfaces is critical to the IPs and EAs, we extracted the surface-region atoms by the scheme developed in ref (48) and averaged their SOAPs. More details of the architecture of the simple-ANN and SOAPs are described in “Machine Learning: SOAP Descriptors” and “Procedures for Regression” in Methods. The best combinations of n_max and l_max, which are hyperparameters for SOAPs (see “Machine Learning: SOAP Descriptors” in Methods), are 3 and 7 based on root mean squared errors (RMSEs) and 5 and 3 based on mean absolute errors (MAEs), respectively (see Figure S1). Hereinafter, we show the results for n_max and l_max of 5 and 3, respectively; the other case is shown in Table S1. It should be noted that the results do not depend much on the combinations of n_max and l_max.

Figure 3. Architecture of ANNs. (a) Simple-ANN, (b) ANN w/AL, and (c) ANN w/L-SOAP. Each circle in the figure is a node where the input and output are scalars. Edges between nodes in two adjacent layers are fully connected but omitted for easy visualization.

Figure 4. Schematic of conventional and learnable SOAP descriptors. The element-pair SOAPs (bottom left panel) are concatenations of the SOAPs of each elemental pair; the cation–anion-pair SOAPs (bottom center panel) are concatenations of three pairs, namely, cation–cation, cation–anion, and anion–anion combinations; and L-SOAPs (bottom right panel) have element-based learnable weights, which are automatically adjusted during ANN training.

Figure 5a,b show the predicted IPs and EAs of the training data (gray dots) and test data (orange and green dots), respectively. Most of the data points are located near the diagonal lines, which means that the IPs and EAs predicted by the ANN are considerably close to the corresponding theoretical values from first-principles calculations. The coefficient of determination (R²), RMSE, and MAE of the test data are 0.90, 0.31, and 0.22 eV for the IPs and 0.90, 0.32, and 0.23 eV for the EAs, respectively. The high prediction accuracy indicates that the ANN model has learned to differentiate the cation species through structural information, even though elemental information is not explicitly given. In addition, the errors are much smaller than the aforementioned distributions of the IPs and EAs for each cation species in the data set, which indicates proper learning of the surface structure dependence. It is noteworthy that our ANN model can also learn and predict surface energies at the level of accuracy shown in Table S2, enabling us to screen out unstable or unreasonable surfaces without explicit first-principles calculations.

Figure 5. Theoretical and predicted IPs and EAs using simple-ANN and ANN w/AL. (a) IPs and (b) EAs obtained by first-principles calculations versus those predicted by the simple-ANN. (c) IPs and (d) EAs by first-principles calculations versus those predicted by the ANN w/AL. The orange or green and gray dots represent the test and training data, respectively. (e) Atom-site weights from the attention layer in the IP and EA prediction of a (001) surface of Sb₂O₃ whose space group is *Pccn* (index is 20 in Table S3). The frame indicates the surface supercell where the upper vacant region corresponds to the vacuum layer. Larger and smaller circles are the Sb and O atoms, respectively. The weights are represented by the shades of the atom colors: blue for Sb and pink for O. The weights are normalized so that the largest weight is one.

Although the simple-ANN model shows valuable prediction accuracy, it has a disadvantage; that is, it equally weights surface-region atoms in a system when averaging their SOAPs. To overcome this disadvantage and further enhance the prediction accuracy, we introduced an attention layer into our ANN architecture. (49,50) Figure 3b shows the ANN architecture with an attention layer (hereinafter called ANN w/AL). In contrast to the simple-ANN model, cation–anion-pair SOAPs of a system are inputted into the ANN without averaging and then averaged after passing through the inserted attention layer just before the output layer. The attention layer outputs a scalar value, and afterward, the value is input into a softmax function. Thus, each SOAP in a system has a weight, the sum of which is one. The transformed cation–anion-pair SOAPs are multiplied with the weights, averaged, and finally input into the output layer. As shown in Figures 5c,d, the prediction accuracy is evidently improved by introducing the attention layer, with an R² of 0.90, RMSE of 0.29 eV, and MAE of 0.21 eV for the IPs, and 0.93, 0.27, and 0.19 eV, respectively, for the EAs.

Furthermore, the ANN w/AL can automatically estimate the magnitude of the impact of each atom site on the IPs and EAs. Figure 5e exemplifies this feature for the case of a (001) surface of Sb₂O₃ (space group: Pccn). The IP prediction clearly shows the higher importance of the antimony and oxygen atoms in the vicinity of the surface, while the halves of the antimony atoms on the surface are especially relevant to the EA. The weight profiles of some other binary oxides are shown in Figure S2. The profiles depend on the oxides and the IP or EA but have features common to the surfaces of the same oxides. Generally, the atoms on the second layers from the surfaces tend to have the smallest weights and the IPs put more importance on the surface atoms than the EAs.

Extension of SOAPs and Application to Ternary Oxides

Next, we focus on ternary systems. Figure 6a shows the theoretical IPs and EAs for 718 ternary oxide surfaces, with respect to the constituent cation species. The distributions of IPs and EAs are much larger than those in the binary systems partly because of the inclusion of multiple cation species in the ternary systems, as well as differences in the crystal and surface structures between the binary and ternary systems.

Figure 6. Distribution of theoretical IPs and EAs of ternary oxides and prediction accuracy of transfer learning. (a) Distribution of theoretical IPs and EAs. Ternary oxides include two cation species, and the same data points are shown at both cation species. The other details are the same as those for Figure 2a. (b,c) Prediction accuracy of transfer learning for IPs and EAs, respectively. The filled and open symbols are the results of the ANN w/L-SOAP and the ANN w/AL, respectively. The horizontal axis is the ratio of the ternary data for training to all ternary data.

In the element-pair SOAPs, information about elements can be explicitly incorporated by concatenation of the SOAPs of each elemental pair (see bottom left panel of Figure 4), but this results in several thousands of dimensions in multispecies systems (see “Machine Learning: SOAP Descriptors” in Methods). The cation–anion-pair SOAPs have manageable dimensions but cannot differentiate cations in a system, which may be crucial for the ternary systems. Hence, we developed element-based learnable-weighted SOAPs (L-SOAPs), which have sufficient information about atomic species despite the considerably small number of dimensions. The details of the L-SOAPs are described in “Machine Learning: SOAP Descriptors” in Methods.

The new architecture of the ANN with L-SOAP (hereinafter called ANN w/L-SOAP) showed an R² of 0.90, RMSE of 0.31 eV, and MAE of 0.23 eV for the IPs, and 0.91, 0.29, and 0.21 eV, respectively, for the EAs of the binary systems; this is comparable to the accuracy of the ANN w/AL. It is noteworthy that the L-SOAP has only one-third of the number of dimensions of the cation–anion-pair SOAP. The number of dimensions of element-pair SOAPs rapidly increases with the number of atomic species, whereas the L-SOAP keeps the same number of dimensions. This feature of the ANN w/L-SOAP model is a great advantage for dealing with multiple-element systems.

The trained model, however, cannot be directly applied to ternary systems, unlike the simple-ANN and the ANN w/AL models, because multiple-cation effects (eq 10 in Methods) are not learned from the binary systems. Thus, we trained the models using the binary oxide data set and afterward retrained them using the ternary oxide data set. In other words, we performed transfer learning from the binary systems to the ternary systems, where all the learning parameters in the ANN w/AL were retrained using the ternary oxide data set. The ratio of the ternary data for training to all ternary data was set at 10, 30, 50, and 70%, where the residues were used as test data. The effectiveness of “transferring” is shown in Figure S3. A clear improvement in the prediction accuracy is found for transfer learning compared with learning from scratch.

Figure 6b shows the performance of the IP prediction with an n_max of 5 and l_max of 3; see Figure S4 for the parity plots and Figure S5 for the case of an n_max of 3 and l_max of 7. For comparison, the results of the transferred ANN w/AL are included in Figure 6. The ANN w/L-SOAP and the ANN w/AL exhibit almost the same levels of performance in all the ratios of training and test data. The IPs relate to the VBMs, in which oxygen 2p-orbitals are the major components in most binary oxides. This fact also applies to the ternary oxides although the weak multiple-cation effects on the VBMs exist. Because the ANN w/L-SOAP mainly learns cation–cation interactions here, both of the ANNs show similar performances regarding the IPs.

We now move on to the prediction of the EAs. The main components of the CBMs are cation orbitals that are system-dependent. Because an accurate prediction of the EAs requires learning such CBM characters, one expects that the ANN w/AL, which cannot explicitly incorporate the effects of the variety of cations, would be inaccurate. Indeed, the ANN w/AL shows considerably poor accuracy when the ratio of the training data is 10% (Figure 6c). On the other hand, the ANN w/L-SOAP is clearly more accurate at the same training/test data ratio. Surprisingly, the performance of the ANN w/L-SOAP at the 10% ratio is almost equal to that of the ANN w/AL at the 70% ratio, and the performance at the 70% ratio is comparable to that of the IPs, indicating the successful incorporation of the multiple-cation effects during training. Thus, the ANN w/L-SOAP in combination with transfer learning makes accurate and systematic prediction of both IPs and EAs of ternary systems feasible.

Conclusions

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Our high-throughput first-principles calculations based on the non-self-consistent dielectric-dependent hybrid functional approach have enabled the construction of a large data set of IPs and EAs for 2195 binary and 718 ternary oxide surfaces. The accuracy of the calculated IPs and EAs has been confirmed by comparison with available experimental values for the selected binary oxides as shown in Figure 2b. Using the data set, we constructed the simple-ANN model to predict the IPs and EAs of the binary oxides. The cation–anion-pair SOAPs were used to describe surface atomic structures before structural relaxation, by simply inputting the crystal structures and surface termination planes. The IPs and EAs of relaxed surfaces were accurately predicted using the SOAP structural descriptors even though elemental information was not explicitly given. Furthermore, introducing an attention layer to the simple-ANN model allows for automatically determining relevant atoms in surface regions and enhancing the prediction performance. This feature of the attention layer can collaterally help us to analyze chemical and physical origins of target properties. Finally, we extended the SOAPs to transfer the model to the ternary oxides by introducing the element-based learnable weights to the calculation of the SOAPs and by connecting this process to the ANN w/AL. This transfer learning model based on the ANN w/L-SOAP was able to incorporate the small effects of the cations on the VBMs with the small data set in the IP prediction. Moreover, apparent improvement was demonstrated regarding the EA prediction, indicating that diverse cation effects on the CBMs were well incorporated.

The ANN w/L-SOAP developed here enables the band alignment of a vast number of metal oxide surfaces, which is fundamental to the design of various materials and devices. Moreover, it is not restricted to the prediction of surface properties of metal oxides but can be naturally applied to other multicomponent systems and other properties in the same way as crystal graph convolutional neural networks. (38) Thus, we believe that our new model paves the way for the high-throughput prediction of diverse materials and properties.

Methods

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Screening of First-Principles Calculation Data: Binary Oxides

The binary oxides considered in this work are listed in Table S3. The table contains 134 nonmetallic oxides whose band structures are formally constructed by fully occupied or empty atomic orbitals, including 41 types of atom species. To cover a wide variety of stable and metastable polymorphs, experimentally determined crystal structures of binary oxides were used as prototypes, and the cations of the prototypes were substituted with isovalent cations. The details of the cation substitution procedures are described in ref (51).

We excluded the oxides without the special isometry that nonpolar slabs should have. (52) In addition, we screened out binary oxides with rather narrow theoretical band gaps using criteria of band gaps smaller than 0.1 eV and ion-clamped static dielectric constants larger than 20, resulting in the 127 binary oxides with cation species other than those in the parentheses in Table S3. Then, we generated 3383 nonpolar surface models for the 127 binary oxides with relatively small Miller indices as listed in Table S3. To exclude unreasonable surface structures, we selected surfaces that were smoothly optimized during first-principles calculations and those with surface energies higher than 0 J/m². In addition, we excluded the outliers in surface energy, which did not fulfill the following inequality

E_{s u r f a c e, m e a n} - 3 \times E_{s u r f a c e, s t d} < E_{s u r f a c e} < E_{s u r f a c e, m e a n} + 3 \times E_{s u r f a c e, s t d}

(1)

where E_surface is the surface energy of the objective surface, and E_surface,mean and E_surface,std are the mean and standard deviations of the surface energies, respectively, in which the surfaces are generated from the common bulk system to the objective surface, resulting in the data set with 2195 binary oxide surfaces for machine learning.

Ternary Oxides

We screened and collected ternary oxide data from the Materials Project database (53) in the following manner: (1) extract the most stable binary oxides of A and B, where A and B are any of the 40 cation elements; (2) draw a convex hull of the formation energies of A–B ternary oxides with respect to the A binary oxide and the B binary oxide; (3) select the ternary oxides on the convex hull; and (4) exclude the ternary oxides without the special isometry and with band gaps smaller than 0.1 eV. We then evaluated the band gaps using non-self-consistent dielectric-dependent hybrid functional calculations and screened the ternary oxides in the same way as the binary oxides. We obtained 344 ternary oxides through these processes. Then, we made the nonpolar surface models, where the maximum Miller indices were set to be 2. These surfaces were screened in the same way as the binary cases, resulting in 718 ternary oxide surface data.

First-Principles Calculations of Band Positions

IPs and EAs are estimated as follows (16)

I P = (ε_{v a c}^{s u r f a c e} - ε_{r e f}^{s u r f a c e, f a r}) - (ε_{V B M}^{b u l k} - ε_{r e f}^{b u l k})

(2)

E A = (ε_{v a c}^{s u r f a c e} - ε_{r e f}^{s u r f a c e, f a r}) - (ε_{C B M}^{b u l k} - ε_{r e f}^{b u l k})

(3)

where

ε_{v a c}^{s u r f a c e}

and

ε_{r e f}^{s u r f a c e, f a r}

are the vacuum level and the electrostatic reference level in the bulk-like region far from the surface, respectively. These quantities are obtained by calculations using surface supercells, each of which is composed of a slab of an oxide and a vacuum layer.

ε_{V B M}^{b u l k}

ε_{C B M}^{b u l k}

, and

ε_{r e f}^{b u l k}

are the VBM, CBM, and electrostatic reference levels in the corresponding bulk model, respectively. These three values are obtained by calculations using bulk primitive cells.

Computational Procedures for Bulk Systems

The calculations were performed using the projector augmented-wave (PAW) method (54) as implemented in the Vienna ab initio simulation package (VASP). (55,56) The

ε_{V B M}^{b u l k}

and

ε_{C B M}^{b u l k}

were calculated by the approach reported in ref (21). In this scheme, the nonlocal exchange mixing parameter in the full-range hybrid functional of the Perdew–Burke–Ernzerhof (PBE0) form (57,58) is set to be the inverse of the ion-clamped static dielectric constant of the system. (59,60) The PBE functional tuned for solids (PBEsol) (61) was used for the semilocal part of the hybrid functional. Non-self-consistent hybrid functional calculations (21,62) were performed on top of PBEsol with Hubbard U corrections to localized orbitals (63) to simultaneously attain low computational cost and high accuracy. This approach is particularly advantageous in the high-throughput evaluation of IPs and EAs as it allows for the direct alignment of the bulk hybrid functional eigenvalues with the vacuum levels in surface supercells obtained using PBEsol(+U) through the common electrostatic reference levels. (21) For the reference level

ε_{r e f}^{b u l k}

, we used the averaged local potentials at the oxygen sites.

PBEsol(+U) was used for obtaining optimized structures, static dielectric constants, and wave functions for the non-self-consistent dielectric-dependent hybrid functional calculations. The means of the diagonal elements of the ion-clamped static dielectric tensors obtained using the random phase approximation were taken to determine the values of the nonlocal exchange mixing parameter for respective systems.

Computational Procedures for Surfaces

We focus on high-throughput calculations of nonpolar surfaces in this study because specific treatments are necessary for modeling polar surfaces as mentioned above. We prepared slab models for nonpolar surfaces of Tasker’s types I and II (64) for the binary and ternary oxides. Their maximum Miller indices were set to be those listed in Table S3 for binary oxides and 2 for ternary oxides. Each slab model has a slab layer thicker than 20 Å and a vacuum layer thicker than 15 Å, which are large enough for the electrostatic potential to converge sufficiently. (21) The convergence test results of IPs, EAs, and surface energies with respect to the vacuum and slab layer thicknesses are shown for selected systems in Figure S6. The slab models were automatically created using the code developed in ref (52). The surfaces were structurally relaxed with their lattice constants fixed by using PBEsol(+U).

ε_{v a c}^{s u r f a c e}

was estimated as the electrostatic potential at the midpoint of the vacuum layer, and

ε_{r e f}^{s u r f a c e, f a r}

was taken to be the average of the local potentials of the oxygen sites around the midpoint of the slab layer.

Computational Details

The PAW data set used in the calculations is detailed in Table S4. The plane-wave cutoff energy was set to 520 eV for the bulk structure optimization, including lattice parameter relaxation, and 400 eV for the other calculations with the lattice parameters fixed. The k-point mesh spacings for structure optimization were set to be smaller than 0.2 Å^–1 and reduced to be less than 0.1 Å^–1 in the calculations of the ion-clamped static dielectric tensors. The band path for estimating the VBM and CBM of each bulk system was generated using SeeK-path. (65,66) Hubbard U corrections were applied to localized orbitals by using the parameters listed in Table S4.

Machine Learning: SOAP Descriptors

For input descriptors to describe surface atomic configurations, we employed SOAPs, which are often used to construct machine learning potentials and analyze complicated systems. (67,68) In SOAPs, the positions of atoms labeled with Z (usually atomic species) are smeared with three-dimensional Gaussian functions as

ρ^{Z} (r) = \sum_{i}^{| Z |} e^{- \frac{1}{2 σ^{2}} | r - R_{i} |}

(4)

where R_i is the position of the i-th atom surrounding r. |Z| is the number of atoms labeled Z within the cutoff radius and σ is a standard deviation of the Gaussian function. The summation of the smeared atom positions is then expanded by linear combinations of radial basis functions with a cutoff radius and spherical harmonics considering the local point of interest. The coefficients are defined as

c_{n l m}^{Z} = ∭_{R^{3}} d V g_{n} (| r |) Y_{l m} (θ, ϕ) ρ^{Z} (r)

(5)

where g_n and Y_lm are radial basis functions and spherical harmonics, respectively. The former generally depends on location r from the center and the latter on polar angle θ and azimuth ϕ in the polar coordinates around the center. n is the degree of the radial basis function; l and m are the degree and order of the spherical harmonics, respectively. The partial power spectrum vector is defined as

p_{n n^{'} l}^{Z_{1} Z_{2}} = π \sqrt{\frac{8}{2 l + 1}} \sum_{m} c_{n l m}^{Z_{1}} c_{n^{'} l m}^{Z_{2}}

(6)

where Z₁ and Z₂ are the symbols of elements. The element-pair and cation–anion-pair SOAPs were obtained on the basis of these procedures by using the DScribe code. (47)

In the L-SOAP, atomic positions are not separately considered for every atom species, unlike the usual SOAP procedure. Instead, we weighted the broadened atomic positions in eq 4 on every atom as

ρ (r) = \sum_{i}^{N} w_{i} e^{- \frac{1}{2 σ^{2}} | r - R_{i} |}

(7)

where w_i is its weight and N is the number of atoms within the cutoff radius. The bottom right panel of Figure 4 shows the schematic of the L-SOAP. Here, we replaced the Gaussian function in eq 7 with the delta function for easy calculation, resulting in changing the operation of integration in eq 5 to a summation as

c_{n l m} = \sum_{i}^{N} g_{n} (| r_{i} |) Y_{l m} (θ_{i}, ϕ_{i}) w_{i}

(8)

We connected the L-SOAPs to the ANN w/AL (see Figure 3c), which enables the model to learn the weights w_i in eq 8 during training. Atomic species described by one-hot vectors are encoded at an embedding layer to atomic feature vectors as

v_{i} = W_{e m b} x_{i}

(9)

where x_i is a one-hot vector of an i-th atom in a system for describing its atomic species. W_emb is a weight matrix for encoding the one-hot vectors into the feature vectors v_i. Here, the dimensions of the feature vectors were set to 32. Then, the weights for the L-SOAPs in eq 8 are calculated as

w_{i} = f (v_{c e n t e r}, v_{i}, | r_{i} |)

(10)

where v_center is the atomic feature vector of the centered atom and v_i is that of the atom located at |r_i| from the center. The function f is a simple neural network with two hidden layers. The coefficients and SOAPs are then calculated according to eqs 6 and 8. The rest of the processes are the same as those for the ANN w/AL.

SOAPs are typically inputted into a kernel function; however, we used nonkernel SOAPs, namely, the partial power spectrum vector in this study. The maxima of n (n_max) and l (l_max) for the radial basis functions and spherical harmonics were surveyed in combinations 3, 5, and 7. The cutoff radius for the radial basis functions was fixed to 7.0 Å and the standard deviation of the Gaussian function in eqs 4 and 7 was set at 1.0 Å. The relatively large cutoff radius was used to include the surface effects in the SOAPs for atoms on layers below the surfaces, thereby improving prediction accuracy. For instance, a smaller cutoff radius of 5.0 Å in the Simple-NN for the IP prediction shows an MAE of 0.38 eV for the test data, which is clearly less accurate than the case of 7.0 Å, 0.23 eV.

Procedures for Regression

Among various regression techniques, we selected ANNs for predicting IPs and EAs in this study because they offer flexible architecture, automatic extraction of relevant surface-region atoms, as described in Results and Discussion, and transferability to other systems.

The simple-ANN shown in Figure 3a has a typical architecture with input, hidden, and output layers. The input vectors are averaged SOAPs of a system. Its hyperparameters, e.g., the number of hidden layers, are listed in Table S5. The rectified linear unit was used as an activation function, and the dropout rate was fixed at 0.5 in hidden layers that were not linked with the output layer.

The data sets used in the regression were divided into training, validation, and test data sets with a ratio of 8:1:1, where we did not care about the distribution of the cation species in respective data sets. Fivefold cross validation using the validation data sets was performed for tuning the hyperparameters of the ANNs. We used backpropagation based on the Adam scheme (69) to optimize all the learning parameters in the network, thereby minimizing the mean squared errors between the model outputs and the training targets. The learning rate for the optimization was 0.001, and the maximum epoch was 200. The training was terminated when the prediction accuracy of the validation data was converged to be almost constant as exemplified by the IP learning curve for the simple-NN in Figure S7. All of the training converged well within 200 epochs.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.3c13574.

RMSE and MAE of all the considered combinations of the SOAP hyperparameters; profile of the weights from the attention layer; transfer learning versus learning from scratch; theoretical and predicted IPs and EAs for the ternary data sets; convergence of IPs, EAs, and surface energies; learning curve for IPs; prediction accuracies; 134 prototypical binary oxides and surface orientation; PAW datasets and Hubbard U parameters; and hyperparameters of the simple-ANN (PDF)
Theoretical IPs and EAs of the 2195 binary and 718 ternary oxide surfaces and related properties. Database contains the index, system (binary or ternary), chemical formula, space group number, Miller index, surface energy, IP, EA, and band gap (bulk) (XLSX)
Supercells before and after structural optimization for the 2195 binary and 718 ternary oxide surfaces (ZIP)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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Corresponding Authors
- Shin Kiyohara - Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, R3-7, 4259 Nagatsuta, Midori-ku, Yokohama 226-8501, Japan; Institute for Materials Research, Tohoku University, 2-2-1 Katahira, Aoba-ku, Sendai 980-8577, Japan; https://orcid.org/0000-0003-2890-5760; Email: [email protected]
- Fumiyasu Oba - Laboratory for Materials and Structures, Institute of Innovative Research, Tokyo Institute of Technology, R3-7, 4259 Nagatsuta, Midori-ku, Yokohama 226-8501, Japan; MDX Research Center for Element Strategy, International Research Frontiers Initiative, Tokyo Institute of Technology, SE-6, 4259 Nagatsuta, Midori-ku, Yokohama 226-8501, Japan; https://orcid.org/0000-0001-7178-5333; Email: [email protected]
Author
- Yoyo Hinuma - Department of Energy and Environment, National Institute of Advanced Industrial Science and Technology (AIST), 1-8-31 Midorigaoka, Ikeda, Osaka 563-8577, Japan; https://orcid.org/0000-0003-2272-1178
Notes
The authors declare no competing financial interest.

Acknowledgments

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This work was supported by JSPS KAKENHI (grant nos. JP20J00773, JP20H00302, and JP23K13811), KISTEC Project, MEXT Data Creation and Utilization Type Material Research and Development Project (grant no. JPMXP1122683430), and JST CREST (grant no. JPMJCR17J2), Japan. The computing resources of Academic Center for Computing and Media Studies at Kyoto University and Research Institute for Information Technology at Kyushu University were used for this work.

References

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Hinuma, Yoyo; Gruneis, Andreas; Kresse, Georg; Oba, Fumiyasu
Physical Review B: Condensed Matter and Materials Physics (2014), 90 (15), 155405/1-155405/16, 16 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
The band lineup, or alignment, of semiconductors is investigated via first-principles calcns. based on d. functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technol. importance. Band alignments are detd. using the valence and conduction band offsets from heterointerface calcns., the ionization potential (IP) and electron affinity (EA) from surface calcns., and the valence band max. and conduction band min. relative to the branch point energy, or charge neutrality level, from bulk calcns. The performance of various approxns. to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, and the GW approxn. with and without vertex corrections in the screened Coulomb interaction, is assessed using the GWΓ1 approxn. as a ref., where first-order vertex corrections are included in the self-energy. The exptl. IPs, EAs, and band offsets are well reproduced by GWΓ1 for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the GW approxn. is almost on par with GWΓ1 as far as relative band positions are concerned. The band alignments based on av. interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calcd. interfacial band offsets with small mean abs. errors of both ∼0.1eV, indicating a good overall transitivity of the band offsets. The alignment based on IPs from selected nonpolar surfaces performs comparably well in the prediction of band offsets at most of the considered interfaces. The max. errors are, however, as large as 0.3, 0.4, and 0.7 eV for the alignments based on the av. band offsets, branch point energies, and IPs, resp. This margin of error should be taken into account when performing materials screening using these alignments.
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Chen, W.; Pasquarello, A. Band-Edge Positions in GW: Effects of Starting Point and Self-Consistency. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90 (16), 165133, DOI: 10.1103/PhysRevB.90.165133
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Moses, P. G.; Miao, M.; Yan, Q.; Van de Walle, C. G. Hybrid Functional Investigations of Band Gaps and Band Alignments for AlN, GaN, InN, and InGaN. J. Chem. Phys. 2011, 134 (8), 084703, DOI: 10.1063/1.3548872
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Hybrid functional investigations of band gaps and band alignments for AlN, GaN, InN, and InGaN
Moses, Poul Georg; Miao, Maosheng; Yan, Qimin; Van de Walle, Chris G.
Journal of Chemical Physics (2011), 134 (8), 084703/1-084703/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Band gaps and band alignments for AlN, GaN, InN, and InGaN alloys are studied using d. functional theory with the with the Heyd-Scuseria-Ernzerhof {HSE06} XC functional. The band gap of InGaN alloys as a function of In content is calcd. and a strong bowing at low In content is found, described by bowing parameters 2.29 eV at 6.25% and 1.79 eV at 12.5%, indicating the band gap cannot be described by a single compn.-independent bowing parameter. Valence-band maxima (VBM) and conduction-band min. (CBM) are aligned by combining bulk calcns. with surface calcns. for nonpolar surfaces. The influence of surface termination (1‾100) m-plane or (11‾20) a-plane is thoroughly studied. For the relaxed surfaces of the binary nitrides the difference in electron affinities between m- and a-plane is <0.1 eV. The abs. electron affinities strongly depend on the choice of XC functional. However, relative alignments are less sensitive to the choice of XC functional. In particular, relative alignments may be calcd. based on Perdew-Becke-Ernzerhof surface calcns. with the HSE06 lattice parameters. For InGaN the VBM is a linear function of In content and the majority of the band-gap bowing is located in the CBM. Based on the calcd. electron affinities the authors predict that InGaN will be suited for H2O splitting up to 50% In content. (c) 2011 American Institute of Physics.
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Komsa, H.-P.; Broqvist, P.; Pasquarello, A. Alignment of Defect Levels and Band Edges through Hybrid Functionals: Effect of Screening in the Exchange Term. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (20), 205118, DOI: 10.1103/PhysRevB.81.205118
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Alignment of defect levels and band edges through hybrid functionals: Effect of screening in the exchange term
Komsa, Hannu-Pekka; Broqvist, Peter; Pasquarello, Alfredo
Physical Review B: Condensed Matter and Materials Physics (2010), 81 (20), 205118/1-205118/12CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We investigate how various treatments of exact exchange affect defect charge transition levels and band edges in hybrid functional schemes for a variety of systems. We distinguish the effects of long-range vs. short-range exchange and of local vs. nonlocal exchange. This is achieved by the consideration of a set of four functionals, which comprise the semilocal Perdew-Burke-Ernzerhof (PBE) functional, the PBE hybrid (PBE0), the Heyd-Scuseria-Ernzerhof (HSE) functional, and a hybrid derived from PBE0 in which the Coulomb kernel in the exact exchange term is screened as in the HSE functional but which, unlike HSE, does not include a local expression compensating for the loss of the long-range exchange. We find that defect levels in PBE0 and in HSE almost coincide when aligned with respect to a common ref. potential, due to the close total-energy differences in the two schemes. At variance, the HSE band edges detd. within the same alignment scheme are found to shift significantly with respect to the PBE0 ones: the occupied and the unoccupied states undergo shifts of about +0.4 eV and -0.4 eV, resp. These shifts are found to vary little among the materials considered. Through a rationale based on the behavior of local and nonlocal long-range exchange, this conclusion is generalized beyond the class of materials used in this study. Finally, we explicitly address the practice of tuning the band gap by adapting the fraction of exact exchange incorporated in the functional. When PBE0-like and HSE-like functionals are tuned to yield identical band gaps, their resp. results for the positions of defect levels within the band gap and for the band alignments at interfaces are found to be very close.
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Oba, F.; Kumagai, Y. Design and Exploration of Semiconductors from First Principles: A Review of Recent Advances. Appl. Phys. Express 2018, 11 (6), 060101, DOI: 10.7567/APEX.11.060101
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Hinuma, Y.; Kumagai, Y.; Tanaka, I.; Oba, F. Band Alignment of Semiconductors and Insulators Using Dielectric-Dependent Hybrid Functionals: Toward High-Throughput Evaluation. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 95 (7), 075302, DOI: 10.1103/PhysRevB.95.075302
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Butler, K. T.; Hendon, C. H.; Walsh, A. Electronic Chemical Potentials of Porous Metal–Organic Frameworks. J. Am. Chem. Soc. 2014, 136 (7), 2703– 2706, DOI: 10.1021/ja4110073
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Electronic Chemical Potentials of Porous Metal-Organic Frameworks
Butler, Keith T.; Hendon, Christopher H.; Walsh, Aron
Journal of the American Chemical Society (2014), 136 (7), 2703-2706CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
The binding energy of an electron in a material is a fundamental characteristic, which dets. a wealth of important chem. and phys. properties. For metal-org. frameworks this quantity is hitherto unknown. We present a general approach for detg. the vacuum level of porous metal-org. frameworks and apply it to obtain the first ionization energy for six prototype materials including zeolitic, covalent, and ionic frameworks. This approach for valence band alignment can explain observations relating to the electrochem., optical, and elec. properties of porous frameworks.
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Jacobs, R.; Booske, J.; Morgan, D. Understanding and Controlling the Work Function of Perovskite Oxides Using Density Functional Theory. Adv. Funct. Mater. 2016, 26 (30), 5471– 5482, DOI: 10.1002/adfm.201600243
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Understanding and controlling the work function of perovskite oxides using density functional theory
Jacobs, Ryan; Booske, John; Morgan, Dane
Advanced Functional Materials (2016), 26 (30), 5471-5482CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
Perovskite oxides contg. transition metals are promising materials in a wide range of electronic and electrochem. applications. However, neither their work function values nor an understanding of their work function physics have been established. Here, the work function trends of a series of perovskite (ABO3 formula) materials using d. functional theory are predicted, and show that the work functions of (001)-terminated AO- and BO2-oriented surfaces can be described using concepts of electronic band filling, bond hybridization, and surface dipoles. The calcd. range of AO (BO2) work functions are 1.60-3.57 eV (2.99-6.87 eV). An approx. linear correlation (R2 between 0.77 and 0.86 is found, depending on surface termination) between work function and position of the oxygen 2p band center, which correlation enables both understanding and rapid prediction of work function trends. Furthermore, SrVO3 is identified as a stable, low work function, highly conductive material. Undoped (Ba-doped) SrVO3 has an intrinsically low AO-terminated work function of 1.86 eV (1.07 eV). These properties make SrVO3 a promising candidate material for a new electron emission cathode for application in high power microwave devices, and as a potential electron emissive material for thermionic energy conversion technologies.
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Grüneis, A.; Kresse, G.; Hinuma, Y.; Oba, F. Ionization Potentials of Solids: The Importance of Vertex Corrections. Phys. Rev. Lett. 2014, 112 (9), 096401, DOI: 10.1103/PhysRevLett.112.096401
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Ping, Y.; Rocca, D.; Galli, G. Electronic Excitations in Light Absorbers for Photoelectrochemical Energy Conversion: First Principles Calculations Based on Many Body Perturbation Theory. Chem. Soc. Rev. 2013, 42 (6), 2437, DOI: 10.1039/c3cs00007a
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Deacon-Smith, D. E. E.; Scanlon, D. O.; Catlow, C. R. A.; Sokol, A. A.; Woodley, S. M. Interlayer Cation Exchange Stabilizes Polar Perovskite Surfaces. Adv. Mater. 2014, 26 (42), 7252– 7256, DOI: 10.1002/adma.201401858
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Setvin, M.; Reticcioli, M.; Poelzleitner, F.; Hulva, J.; Schmid, M.; Boatner, L. A.; Franchini, C.; Diebold, U. Polarity Compensation Mechanisms on the Perovskite Surface KTaO₃ (001). Science 2018, 359 (6375), 572– 575, DOI: 10.1126/science.aar2287
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Polarity compensation mechanisms on the perovskite surface KTaO3(001)
Setvin, Martin; Reticcioli, Michele; Poelzleitner, Flora; Hulva, Jan; Schmid, Michael; Boatner, Lynn A.; Franchini, Cesare; Diebold, Ulrike
Science (Washington, DC, United States) (2018), 359 (6375), 572-575CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
The stacking of alternating charged planes in ionic crystals creates a diverging electrostatic energy-a "polar catastrophe"-that must be compensated at the surface. We used scanning probe microscopies and d. functional theory to study compensation mechanisms at the perovskite potassium tantalate(KTaO3) (001) surface as increasing degrees of freedom were enabled. The as-cleaved surface in vacuum is frozen in place but immediately responds with an insulator-to-metal transition and possibly ferroelec. lattice distortions. Annealing in vacuum allows the formation of isolated oxygen vacancies, followed by a complete rearrangement of the top layers into an ordered pattern of KO and TaO2 stripes. The optimal soln. is found after exposure to water vapor through the formation of a hydroxylated overlayer with ideal geometry and charge.
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Enterkin, J. A.; Subramanian, A. K.; Russell, B. C.; Castell, M. R.; Poeppelmeier, K. R.; Marks, L. D. A Homologous Series of Structures on the Surface of SrTiO₃ (110). Nat. Mater. 2010, 9 (3), 245– 248, DOI: 10.1038/nmat2636
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Lazzeri, M.; Selloni, A. Stress-Driven Reconstruction of an Oxide Surface: The Anatase TiO₂ (001)-(1 × 4) Surface. Phys. Rev. Lett. 2001, 87 (26), 266105, DOI: 10.1103/PhysRevLett.87.266105
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Zhu, Q.; Li, L.; Oganov, A. R.; Allen, P. B. Evolutionary Method for Predicting Surface Reconstructions with Variable Stoichiometry. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87 (19), 195317, DOI: 10.1103/PhysRevB.87.195317
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Evolutionary method for predicting surface reconstructions with variable stoichiometry
Zhu, Qiang; Li, Li; Oganov, Artem R.; Allen, Philip B.
Physical Review B: Condensed Matter and Materials Physics (2013), 87 (19), 195317/1-195317/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We present a specially designed evolutionary algorithm for the prediction of surface reconstructions. This technique allows one to automatically explore stable and low-energy metastable configurations with variable surface atoms and variable surface unit cells through the whole chem. potential range. The power of evolutionary search is demonstrated by the efficient identification of diamond 2 × 1 (100) and 2 × 1 (111) surface reconstructions with a fixed no. of surface atoms and a fixed cell size. With further variation of surface unit cells, we study the reconstructions of the polar surface MgO (111). Expt. has detected an oxygen trimer (ozone) motif. We predict another version of this motif which can be thermodynamically stable in extreme oxygen-rich conditions. Finally, we perform a variable stoichiometry search for a complex ternary system: semipolar GaN (10‾11) with and without adsorbed oxygen. The search yields a counterintuitive reconstruction based on N3 trimers. These examples demonstrate that an automated scheme to explore the energy landscape of surfaces will improve our understanding of surface reconstructions. The method presented in this paper can be generally applied to binary and multicomponent systems.
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Wanzenböck, R.; Arrigoni, M.; Bichelmaier, S.; Buchner, F.; Carrete, J.; Madsen, G. K. H. Neural-Network-Backed Evolutionary Search for SrTiO₃ (110) Surface Reconstructions. Digital Discovery 2022, 1 (5), 703– 710, DOI: 10.1039/D2DD00072E
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Mochizuki, Y.; Sung, H.-J.; Gake, T.; Oba, F. Chemical Trends of Surface Reconstruction and Band Positions of Nonmetallic Perovskite Oxides from First Principles. Chem. Mater. 2023, 35 (5), 2047– 2057, DOI: 10.1021/acs.chemmater.2c03615
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Chemical Trends of Surface Reconstruction and Band Positions of Nonmetallic Perovskite Oxides from First Principles
Mochizuki, Yasuhide; Sung, Ha-Jun; Gake, Tomoya; Oba, Fumiyasu
Chemistry of Materials (2023), 35 (5), 2047-2057CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
An evolutionary algorithm search in combination with first-principles calcns. is performed to systematically predict the reconstructed surface structures of nonmetallic perovskite oxides. Four types of lowest-energy reconstruction patterns are obtained for the macroscopically stoichiometric (001) surfaces of NaTaO3, KTaO3, CaTiO3, SrTiO3, YAlO3, and LaAlO3 as representatives of A+B5+O3, A2+B4+O3, and A3+B3+O3 systems. We explain chem. trends in the surface energies and band positions of 10 perovskite oxides, addnl. including KNbO3, BaTiO3, BaZrO3, and LaGaO3, in terms of the at. environments at the outermost reconstructed surface layers. Regaining A-O (B-O) coordination nos. and bond lengths at the surfaces is found to stabilize the A2+B4+O3 and A3+B3+O3 (A+B5+O3) surfaces. Decreasing the coordination no. of cation A (B) leads to shallow (deep) valence band maxima and conduction band min. relative to the vacuum level. Our study provides general insights into the surface reconstruction and band alignment of nonmetallic perovskite oxides.
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Kim, S.; Sinai, O.; Lee, C.-W.; Rappe, A. M. Controlling Oxide Surface Dipole and Reactivity with Intrinsic Nonstoichiometric Epitaxial Reconstructions. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92 (23), 235431, DOI: 10.1103/PhysRevB.92.235431
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Stanev, V.; Oses, C.; Kusne, A. G.; Rodriguez, E.; Paglione, J.; Curtarolo, S.; Takeuchi, I. Machine Learning Modeling of Superconducting Critical Temperature. npj Comput. Mater. 2018, 4 (1), 29, DOI: 10.1038/s41524-018-0085-8
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Kiyohara, S.; Oda, H.; Miyata, T.; Mizoguchi, T. Prediction of Interface Structures and Energies via Virtual Screening. Sci. Adv. 2016, 2 (11), 1600746, DOI: 10.1126/sciadv.1600746
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Schütt, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Müller, K. R. SchNet – A Deep Learning Architecture for Molecules and Materials. J. Chem. Phys. 2018, 148 (24), 241722, DOI: 10.1063/1.5019779
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SchNet - A deep learning architecture for molecules and materials
Schuett, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Mueller, K.-R.
Journal of Chemical Physics (2018), 148 (24), 241722/1-241722/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chem. physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mech. interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chem. compd. space. Here, we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chem. space for mols. and materials, where our model learns chem. plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for mol. dynamics simulations of small mols. and perform an exemplary study on the quantum-mech. properties of C20-fullerene that would have been infeasible with regular ab initio mol. dynamics. (c) 2018 American Institute of Physics.
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Freeze, J. G.; Kelly, H. R.; Batista, V. S. Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists. Chem. Rev. 2019, 119 (11), 6595– 6612, DOI: 10.1021/acs.chemrev.8b00759
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Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists
Freeze, Jessica G.; Kelly, H. Ray; Batista, Victor S.
Chemical Reviews (Washington, DC, United States) (2019), 119 (11), 6595-6612CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
In silico catalyst design is a grand challenge of chem. Traditional computational approaches have been limited by the need to compute properties for an intractably large no. of possible catalysts. Recently, inverse design methods have emerged, starting from a desired property and optimizing a corresponding chem. structure. Techniques used for exploring chem. space include gradient-based optimization, alchem. transformations, and machine learning. Though the application of these methods to catalysis is in its early stages, further development will allow for robust computational catalyst design. This review provides an overview of the evolution of inverse design approaches and their relevance to catalysis. The strengths and limitations of existing techniques are highlighted, and suggestions for future research are provided.
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Xie, T.; Grossman, J. C. Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties. Phys. Rev. Lett. 2018, 120 (14), 145301, DOI: 10.1103/PhysRevLett.120.145301
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Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties
Xie, Tian; Grossman, Jeffrey C.
Physical Review Letters (2018), 120 (14), 145301CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
The use of machine learning methods for accelerating the design of cryst. materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either constrains the model to certain crystal types or makes it difficult to provide chem. insights. Here, we develop a crystal graph convolutional neural networks framework to directly learn material properties from the connection of atoms in the crystal, providing a universal and interpretable representation of cryst. materials. Our method provides a highly accurate prediction of d. functional theory calcd. properties for eight different properties of crystals with various structure types and compns. after being trained with 104 data points. Further, our framework is interpretable because one can ext. the contributions from local chem. environments to global properties. Using an example of perovskites, we show how this information can be utilized to discover empirical rules for materials design.
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Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine Learning for Molecular and Materials Science. Nature 2018, 559 (7715), 547– 555, DOI: 10.1038/s41586-018-0337-2
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Machine learning for molecular and materials science
Butler, Keith T.; Davies, Daniel W.; Cartwright, Hugh; Isayev, Olexandr; Walsh, Aron
Nature (London, United Kingdom) (2018), 559 (7715), 547-555CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
Here we summarize recent progress in machine learning for the chem. sciences. We outline machine-learning techniques that are suitable for addressing research questions in this domain, as well as future directions for the field. We envisage a future in which the design, synthesis, characterization and application of mols. and materials is accelerated by artificial intelligence.
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Kang, S.; Jeong, W.; Hong, C.; Hwang, S.; Yoon, Y.; Han, S. Accelerated Identification of Equilibrium Structures of Multicomponent Inorganic Crystals Using Machine Learning Potentials. npj Comput. Mater. 2022, 8 (1), 108, DOI: 10.1038/s41524-022-00792-w
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Shen, C.; Li, T.; Zhang, Y.; Xie, R.; Long, T.; Fortunato, N. M.; Liang, F.; Dai, M.; Shen, J.; Wolverton, C. M.; Zhang, H. Accelerated Screening of Ternary Chalcogenides for Potential Photovoltaic Applications. J. Am. Chem. Soc. 2023, 145 (40), 21925– 21936, DOI: 10.1021/jacs.3c06207
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Hwang, S.; Jung, J.; Hong, C.; Jeong, W.; Kang, S.; Han, S. Stability and Equilibrium Structures of Unknown Ternary Metal Oxides Explored by Machine-Learned Potentials. J. Am. Chem. Soc. 2023, 145 (35), 19378– 19386, DOI: 10.1021/jacs.3c06210
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Stability and Equilibrium Structures of Unknown Ternary Metal Oxides Explored by Machine-Learned Potentials
Hwang, Seungwoo; Jung, Jisu; Hong, Changho; Jeong, Wonseok; Kang, Sungwoo; Han, Seungwu
Journal of the American Chemical Society (2023), 145 (35), 19378-19386CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
Extensive crystal structure prediction methods, accelerated by machine-learned potentials, were used to study these untapped chem. spaces. The authors examine 181 ternary metal oxide systems, encompassing most cations except for partially filled 3d or f shells, and det. their lowest-energy crystal structures with representative stoichiometry derived from prevalent oxidn. states or recommender systems. Forty-five ternary oxide systems contg. stable compds. against decompn. into binary or elemental phases, the majority of which incorporate noble metals, were discovered. Comparisons with other theor. databases highlight the strengths and limitations of informatics-based material searches.
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Kim, M.; Yeo, B. C.; Park, Y.; Lee, H. M.; Han, S. S.; Kim, D. Artificial Intelligence to Accelerate the Discovery of N₂ Electroreduction Catalysts. Chem. Mater. 2020, 32 (2), 709– 720, DOI: 10.1021/acs.chemmater.9b03686
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Artificial Intelligence to Accelerate the Discovery of N2 Electroreduction Catalysts
Kim, Myungjoon; Yeo, Byung Chul; Park, Youngtae; Lee, Hyuck Mo; Han, Sang Soo; Kim, Donghun
Chemistry of Materials (2020), 32 (2), 709-720CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
The development of catalysts for the electrochem. N2 redn. reaction (NRR) with a low limiting potential and high faradaic efficiency is highly desirable but remains challenging. Here, to achieve acceleration, the authors develop and report a slab graph convolutional neural network (SGCNN), an accurate and flexible machine learning (ML) model that is suited for probing surface reactions in catalysis. With a self-accumulated database of 3040 surface calcns. at the d.-functional-theory (DFT) level, SGCNN predicted the binding energies, ranging over 8 eV, of five key adsorbates (H, N2, N2H, NH, NH2) related to NRR performance with a mean abs. error (MAE) of only 0.23 eV. SGCNN only requires the low-level inputs of elemental properties available in the periodic table of elements and connectivity information of constituent atoms; thus, accelerations can be realized. Via a combined process of SGCNN-driven predictions and DFT verifications, four novel catalysts in the L12 crystal space, including V3Ir(111), Tc3Hf(111), V3Ni(111), and Tc3Ta(111), are proposed as stable candidates that likely exhibit both a lower limiting potential and higher faradaic efficiency in the NRR, relative to the ref. Mo(110). The ML work combined with a statistical data anal. reveals that catalytic surfaces with an av. d-orbital occupation between 4 and 6 could lower the limiting potential and potentially overcome the scaling relation in the NRR.
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Chen, C.; Ong, S. P. A Universal Graph Deep Learning Interatomic Potential for the Periodic Table. Nat. Comput. Sci. 2022, 2 (11), 718– 728, DOI: 10.1038/s43588-022-00349-3
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A universal graph deep learning interatomic potential for the periodic table
Chen Chi; Ong Shyue Ping
Nature computational science (2022), 2 (11), 718-728 ISSN:.
Interatomic potentials (IAPs), which describe the potential energy surface of atoms, are a fundamental input for atomistic simulations. However, existing IAPs are either fitted to narrow chemistries or too inaccurate for general applications. Here we report a universal IAP for materials based on graph neural networks with three-body interactions (M3GNet). The M3GNet IAP was trained on the massive database of structural relaxations performed by the Materials Project over the past ten years and has broad applications in structural relaxation, dynamic simulations and property prediction of materials across diverse chemical spaces. About 1.8 million materials from a screening of 31 million hypothetical crystal structures were identified to be potentially stable against existing Materials Project crystals based on M3GNet energies. Of the top 2,000 materials with the lowest energies above the convex hull, 1,578 were verified to be stable using density functional theory calculations. These results demonstrate a machine learning-accelerated pathway to the discovery of synthesizable materials with exceptional properties.
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Bartók, A. P.; Kondor, R.; Csányi, G. On Representing Chemical Environments. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87 (18), 184115, DOI: 10.1103/PhysRevB.87.184115
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On representing chemical environments
Bartok, Albert P.; Kondor, Risi; Csanyi, Gabor
Physical Review B: Condensed Matter and Materials Physics (2013), 87 (18), 184115/1-184115/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
We review some recently published methods to represent at. neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave nos. are used to expand the at. neighborhood d. function. Using the example system of small clusters, we quant. show that this expansion needs to be carried to higher and higher wave nos. as the no. of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.
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Dulub, O.; Diebold, U.; Kresse, G. Novel Stabilization Mechanism on Polar Surfaces: ZnO (0001)-Zn. Phys. Rev. Lett. 2003, 90 (1), 016102, DOI: 10.1103/PhysRevLett.90.016102
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Himanen, L.; Jäger, M. O. J.; Morooka, E. V.; Canova, F. F.; Ranawat, Y. S.; Gao, D. Z.; Rinke, P.; Foster, A. S. DScribe: Library of Descriptors for Machine Learning in Materials Science. Comput. Phys. Commun. 2020, 247, 106949, DOI: 10.1016/j.cpc.2019.106949
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DScribe: Library of descriptors for machine learning in materials science
Himanen, Lauri; Jager, Marc O. J.; Morooka, Eiaki V.; Federici Canova, Filippo; Ranawat, Yashasvi S.; Gao, David Z.; Rinke, Patrick; Foster, Adam S.
Computer Physics Communications (2020), 247 (), 106949CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
DScribe is a software package for machine learning that provides popular feature transformations ("descriptors") for atomistic materials simulations. DScribe accelerates the application of machine learning for atomistic property prediction by providing user-friendly, off-the-shelf descriptor implementations. The package currently contains implementations for Coulomb matrix, Ewald sum matrix, sine matrix, Many-body Tensor Representation (MBTR), Atom-centered Symmetry Function (ACSF) and Smooth Overlap of Atomic Positions (SOAP). Usage of the package is illustrated for two different applications: formation energy prediction for solids and ionic charge prediction for atoms in org. mols. The package is freely available under the open-source Apache License 2.0. Program Title: DScribeProgram Files doi:http://dx.doi.org/10.17632/vzrs8n8pk6.1Licensing provisions: Apache-2.0Programming language: Python/C/C++Supplementary material: Supplementary Information as PDFNature of problem: The application of machine learning for materials science is hindered by the lack of consistent software implementations for feature transformations. These feature transformations, also called descriptors, are a key step in building machine learning models for property prediction in materials science. Soln. method: We have developed a library for creating common descriptors used in machine learning applied to materials science. We provide an implementation the following descriptors: Coulomb matrix, Ewald sum matrix, sine matrix, Many-body Tensor Representation (MBTR), Atom-centered Symmetry Functions (ACSF) and Smooth Overlap of Atomic Positions (SOAP). The library has a python interface with computationally intensive routines written in C or C++. The source code, tutorials and documentation are provided online. A continuous integration mechanism is set up to automatically run a series of regression tests and check code coverage when the codebase is updated.
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Hinuma, Y.; Kamachi, T.; Hamamoto, N. Algorithm for Automatic Detection of Surface Atoms. Trans. Mater. Res. Soc. Jpn. 2020, 45 (4), 115– 120, DOI: 10.14723/tmrsj.45.115
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Algorithm for automatic detection of surface atoms
Hinuma, Yoyo; Kamachi, Takashi; Hamamoto, Nobutsugu
Transactions of the Materials Research Society of Japan (2020), 45 (4), 115-120CODEN: TMRJE3; ISSN:1382-3469. (Materials Research Society of Japan)
Automated identification of surface atoms is very convenient when, for instance, finding atoms that may desorb from a catalyst surface. The proposed algorithm for automated identification is based on the geometry of atom positions and quantifies the solid angle of "open space" around an atom. The solid angle is 2π sr for a prototypical surface atom, while the angle would be larger than 2π sr for a step edge atom, slightly larger than π sr for a surface atom at the foot of a step, and much smaller than π sr for a subsurface atom. The algorithm is expected to accelerate anal. of surface defects of slabs and nanoparticles and contribute to, for example, catalyst design.
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Goodall, R. E. A.; Lee, A. A. Predicting Materials Properties without Crystal Structure: Deep Representation Learning from Stoichiometry. Nat. Commun. 2020, 11 (1), 6280, DOI: 10.1038/s41467-020-19964-7
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Predicting materials properties without crystal structure: deep representation learning from stoichiometry
Goodall, Rhys E. A.; Lee, Alpha A.
Nature Communications (2020), 11 (1), 6280CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
Machine learning has the potential to accelerate materials discovery by accurately predicting materials properties at a low computational cost. However, the model inputs remain a key stumbling block. Current methods typically use descriptors constructed from knowledge of either the full crystal structure - therefore only applicable to materials with already characterised structures - or structure-agnostic fixed-length representations hand-engineered from the stoichiometry. We develop a machine learning approach that takes only the stoichiometry as input and automatically learns appropriate and systematically improvable descriptors from data. Our key insight is to treat the stoichiometric formula as a dense weighted graph between elements. Compared to the state of the art for structure-agnostic methods, our approach achieves lower errors with less data.
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Wang, A. Y. T.; Kauwe, S. K.; Murdock, R. J.; Sparks, T. D. Compositionally Restricted Attention-Based Network for Materials Property Predictions. npj Comput. Mater. 2021, 7 (1), 77, DOI: 10.1038/s41524-021-00545-1
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Hinuma, Y.; Hayashi, H.; Kumagai, Y.; Tanaka, I.; Oba, F. Comparison of Approximations in Density Functional Theory Calculations: Energetics and Structure of Binary Oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96 (9), 094102, DOI: 10.1103/PhysRevB.96.094102
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Hinuma, Y.; Kumagai, Y.; Oba, F.; Tanaka, I. Categorization of Surface Polarity from a Crystallographic Approach. Comput. Mater. Sci. 2016, 113, 221– 230, DOI: 10.1016/j.commatsci.2015.11.042
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Categorization of surface polarity from a crystallographic approach
Hinuma, Yoyo; Kumagai, Yu; Oba, Fumiyasu; Tanaka, Isao
Computational Materials Science (2016), 113 (), 221-230CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)
With ab initio codes that employ three-dimensional periodic boundary conditions, the slab-and-vacuum model has proven invaluable for the derivation of energetic, atomistic, and electronic properties of materials. Within this approach, polar and nonpolar slabs require different levels of treatment, as any polar instability must be compensated on a case-by-case basis in the former. This article proposes an efficient algorithm based on isometries to identify whether a slab with the given surface orientation would be intrinsically polar, and if not, to obtain information on where to cleave the bulk crystal to obtain a stoichiometric nonpolar slab and whether reconstruction is necessary to generate a stoichiometric slab that is not polar.
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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 Genome Approach to Accelerating Materials Innovation. APL Mater. 2013, 1 (1), 011002, DOI: 10.1063/1.4812323
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Commentary: The Materials Project: A materials genome approach to accelerating materials innovation
Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy; Chen, Wei; Richards, William Davidson; Dacek, Stephen; Cholia, Shreyas; Gunter, Dan; Skinner, David; Ceder, Gerbrand; Persson, Kristin A.
APL Materials (2013), 1 (1), 011002/1-011002/11CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
Accelerating the discovery of advanced materials is essential for human welfare and sustainable, clean energy. In this paper, we introduce the Materials Project (www.materialsproject.org), a core program of the Materials Genome Initiative that uses high-throughput computing to uncover the properties of all known inorg. materials. This open dataset can be accessed through multiple channels for both interactive exploration and data mining. The Materials Project also seeks to create open-source platforms for developing robust, sophisticated materials analyses. Future efforts will enable users to perform rapid-prototyping'' of new materials in silico, and provide researchers with new avenues for cost-effective, data-driven materials design. (c) 2013 American Institute of Physics.
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Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50 (24), 17953– 17979, DOI: 10.1103/PhysRevB.50.17953
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Projector augmented-wave method
Blochl
Physical review. B, Condensed matter (1994), 50 (24), 17953-17979 ISSN:0163-1829.
There is no expanded citation for this reference.
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Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54 (16), 11169– 11186, DOI: 10.1103/PhysRevB.54.11169
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Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
Kresse, G.; Furthmueller, J.
Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59 (3), 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
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From ultrasoft pseudopotentials to the projector augmented-wave method
Kresse, G.; Joubert, D.
Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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Perdew, J. P.; Ernzerhof, M.; Burke, K. Rationale for Mixing Exact Exchange with Density Functional Approximations. J. Chem. Phys. 1996, 105 (22), 9982– 9985, DOI: 10.1063/1.472933
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Rationale for mixing exact exchange with density functional approximations
Perdew, John P.; Ernzerhof, Matthias; Burke, Kieron
Journal of Chemical Physics (1996), 105 (22), 9982-9985CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
D. functional approxns. for the exchange-correlation energy ExcDFA of an electronic system are often improved by admixing some exact exchange Ex: Exc ≈ ExcDFA + (1/n)(Ex - ExDFA). This procedure is justified when the error in ExcDFA arises from the λ = 0 or exchange end of the coupling-const. integral ∫01dλ Exc,λDFA. We argue that the optimum integer n is approx. the lowest order of Goerling-Levy perturbation theory which provides a realistic description of the coupling-const. dependence Exc,λ in the range 0 ≤ λ ≤ 1, whence n ≈ 4 for atomization energies of typical mols. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second-order perturbation theory with the generalized gradient approxn.
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Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110 (13), 6158– 6170, DOI: 10.1063/1.478522
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Toward reliable density functional methods without adjustable parameters: the PBE0 model
Adamo, Carlo; Barone, Vincenzo
Journal of Chemical Physics (1999), 110 (13), 6158-6170CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
We present an anal. of the performances of a parameter free d. functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amt. of exact exchange. The results obtained for structural, thermodn., kinetic and spectroscopic (magnetic, IR and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chem. and condensed matter physics.
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Skone, J. H.; Govoni, M.; Galli, G. Self-Consistent Hybrid Functional for Condensed Systems. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89 (19), 195112, DOI: 10.1103/PhysRevB.89.195112
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Gerosa, M.; Bottani, C. E.; Caramella, L.; Onida, G.; Di Valentin, C.; Pacchioni, G. Electronic Structure and Phase Stability of Oxide Semiconductors: Performance of Dielectric-Dependent Hybrid Functional DFT, Benchmarked against GW Band Structure Calculations and Experiments. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91 (15), 155201, DOI: 10.1103/PhysRevB.91.155201
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Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100 (13), 136406, DOI: 10.1103/PhysRevLett.100.136406
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Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gabor I.; Vydrov, Oleg A.; Scuseria, Gustavo E.; Constantin, Lucian A.; Zhou, Xiaolan; Burke, Kieron
Physical Review Letters (2008), 100 (13), 136406/1-136406/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
Popular modern generalized gradient approxns. are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of d. gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approxn. that improves equil. properties of densely packed solids and their surfaces.
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Tran, F. On the Accuracy of the Non-Self-Consistent Calculation of the Electronic Structure of Solids with Hybrid Functionals. Phys. Lett. A 2012, 376 (6–7), 879– 882, DOI: 10.1016/j.physleta.2012.01.022
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Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57 (3), 1505– 1509, DOI: 10.1103/PhysRevB.57.1505
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Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P.
Physical Review B: Condensed Matter and Materials Physics (1998), 57 (3), 1505-1509CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
By taking better account of electron correlations in the 3d shell of metal ions in Ni oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin d. functional theory.
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Tasker, P. W. The Stability of Ionic Crystal Surfaces. J. Phys. C Solid State Phys. 1979, 12 (22), 4977– 4984, DOI: 10.1088/0022-3719/12/22/036
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The stability of ionic crystal surfaces
Tasker, P. W.
Journal of Physics C: Solid State Physics (1979), 12 (22), 4977-84CODEN: JPSOAW; ISSN:0022-3719.
For ionic crystals with a dipole moment in the repeat unit perpendicular to the surface, the lattice sums of the electrostatic energy diverge and the calcd. surface energy is infinite. The cause of this divergence is demonstrated and the surfaces of ionic or partly ionic materials are classified into 3 types. Type 1 is neutral with equal nos. of anions and cations on each plane, whereas type 2 is charged, but there is no dipole moment perpendicular to the surface because of the sym. stacking sequence. Both these surfaces have modest surface energies and are stable with only limited relaxations of the surface ions. The type 3 surface is charged and has a dipole moment in the repeat unit perpendicular to the surface and this surface can only be stabilized by substantial reconstruction.
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Hinuma, Y.; Pizzi, G.; Kumagai, Y.; Oba, F.; Tanaka, I. Band Structure Diagram Paths Based on Crystallography. Comput. Mater. Sci. 2017, 128, 140– 184, DOI: 10.1016/j.commatsci.2016.10.015
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Band structure diagram paths based on crystallography
Hinuma, Yoyo; Pizzi, Giovanni; Kumagai, Yu; Oba, Fumiyasu; Tanaka, Isao
Computational Materials Science (2017), 128 (), 140-184CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)
Systematic and automatic calcns. of the electronic band structure are a crucial component of computationally-driven high-throughput materials screening. An algorithm, for any crystal, to derive a unique description of the crystal structure together with a recommended band path is indispensable for this task. The electronic band structure is typically sampled along a path within the first Brillouin zone including the surface in reciprocal space. Some points in reciprocal space have higher site symmetries and/or have higher constraints than other points regarding the electronic band structure and therefore are likely to be more important than other points. This work categorizes points in reciprocal space according to their symmetry and provides recommended band paths that cover all special wavevector (k-vector) points and lines necessarily and sufficiently. Points in reciprocal space are labeled such that there is no conflict with the crystallog. convention. The k-vector coeffs. of labeled points, which are located at Brillouin zone face and edge centers as well as vertices, are derived based on a primitive cell compatible with the crystallog. convention, including those with axial ratio-dependent coordinates. Furthermore, we provide an open-source implementation of the algorithms within our SeeK-path python code, to allow researchers to obtain k-vector coeffs. and recommended band paths in an automated fashion. Finally, we created a free online service to compute and visualize the first Brillouin zone, labeled k-points and suggested band paths for any crystal structure, that we made available at http://www.materialscloud.org/tools/seekpath/.
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Togo, A.; Tanaka, I. Spglib: A Software Library for Crystal Symmetry Search. arXiv 2018, arXiv:1808.01590, [cond-mat.mtrl-sci] DOI: 10.48550/arXiv.1808.01590
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Bartók, A. P.; Kermode, J.; Bernstein, N.; Csányi, G. Machine Learning a General-Purpose Interatomic Potential for Silicon. Phys. Rev. X 2018, 8 (4), 041048, DOI: 10.1103/PhysRevX.8.041048
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Machine Learning a General-Purpose Interatomic Potential for Silicon
Bartok, Albert P.; Kermode, James; Bernstein, Noam; Csanyi, Gabor
Physical Review X (2018), 8 (4), 041048CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
The success of first-principles electronic-structure calcn. for predictive modeling in chem., solid-state physics, and materials science is constrained by the limitations on simulated length scales and timescales due to the computational cost and its scaling. Techniques based on machine-learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the phys. relevant space of configurations remains a challenging goal. Here, we present a Gaussian approxn. potential for silicon that achieves this milestone, accurately reproducing d.-functional-theory ref. results for a wide range of observable properties, including crystal, liq., and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calcns. such as finite-temp. phase-boundary lines, self-diffusivity in the liq., formation of the amorphous by slow quench, and dynamic brittle fracture, all of which are very expensive with a first-principles method. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qual. est. of the potential's accuracy for a given at. configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interat. potential that comprehensively describes a material on the at. scale and serves as a template for the development of such models in the future.
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De, S.; Bartók, A. P.; Csányi, G.; Ceriotti, M. Comparing Molecules and Solids across Structural and Alchemical Space. Phys. Chem. Chem. Phys. 2016, 18 (20), 13754– 13769, DOI: 10.1039/C6CP00415F
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Comparing molecules and solids across structural and alchemical space
De, Sandip; Bartok, Albert P.; Csanyi, Gabor; Ceriotti, Michele
Physical Chemistry Chemical Physics (2016), 18 (20), 13754-13769CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
Evaluating the (dis)similarity of cryst., disordered and mol. compds. is a crit. step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural similarity metric is crucial for classifying structures, searching chem. space for better compds. and materials, and driving the next generation of machine-learning techniques for predicting the stability and properties of mols. and materials. In the last few years several strategies have been designed to compare at. coordination environments. In particular, the smooth overlap of at. positions (SOAPs) has emerged as an elegant framework to obtain translation, rotation and permutation-invariant descriptors of groups of atoms, underlying the development of various classes of machine-learned inter-at. potentials. Here we discuss how one can combine such local descriptors using a regularized entropy match (REMatch) approach to describe the similarity of both whole mol. and bulk periodic structures, introducing powerful metrics that enable the navigation of alchem. and structural complexities within a unified framework. Furthermore, using this kernel and a ridge regression method we can predict atomization energies for a database of small org. mols. with a mean abs. error below 1 kcal mol-1, reaching an important milestone in the application of machine-learning techniques for the evaluation of mol. properties.
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Jaouen, T.; Jézéquel, G.; Delhaye, G.; Lépine, B.; Turban, P.; Schieffer, P. Work Function Shifts, Schottky Barrier Height, and Ionization Potential Determination of Thin MgO Films on Ag (001). Appl. Phys. Lett. 2010, 97 (23), 232104, DOI: 10.1063/1.3525159
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Work function shifts, Schottky barrier height, and ionization potential determination of thin MgO films on Ag(001)
Jaouen, T.; Jezequel, G.; Delhaye, G.; Lepine, B.; Turban, P.; Schieffer, P.
Applied Physics Letters (2010), 97 (23), 232104/1-232104/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
The electronic band structure and the work function of MgO thin films epitaxially grown on Ag(001) were investigated using x-ray and UPS for various oxide thicknesses. The deposition of thin MgO films on Ag(001) induces a strong diminution in the metal work function. The p-type Schottky barrier height is const. at 3.85 ± 0.10 eV above 2 MgO monolayers and the exptl. value of the ionization potential is 7.15 ± 0.15 eV. Our results are well consistent with the description of the Schottky barrier height in terms of the Schottky-Mott model cor. by an MgO-induced polarization effect. (c) 2010 American Institute of Physics.
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Electronic spectrum and ultraviolet optical properties of crystalline magnesium oxide
Roessler, David M.; Walker, William Charles
Physical Review (1967), 159 (3), 733-8CODEN: PHRVAO; ISSN:0031-899X.
The electronic spectrum of single-crystal MgO, i.e., the real (ε1) and imaginary (ε2) parts of the dielec. response, has been obtained over the region 5-28 ev. from normal-incidence reflectance spectra. Measurements were made on freshly cleaved crystals over the entire region at 295°K. and at 5-11.5 ev. and 77°K. Structure in ε2 was observed near 7.7, 10.8, 13.3, 16.8, 17.3, and 20.5 ev. The first peak, which was a doublet with components at 7.69 ± 0.01 and 7.76 ± 0.01 ev., was attributed to the Γ3/2 and Γ1/2 spin-orbit split exciton. A Lorentzian fit to the exciton components gave oscillator strengths of 0.035 and 0.017 per mol., resp. Subtraction of the exciton structure from the remaining interband structure gave a direct interband edge at 7.77 ± 0.01 ev. A large plasma peak was observed in the energy-loss function near 22 ev., in agreement with recent energy-loss expts. The remaining structure was attributed to interband transitions and will be discussed in terms of recent pseudopotential band-structure calcns. 24 references.
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Transition Metal Oxides for Organic Electronics: Energetics, Device Physics and Applications
Meyer, Jens; Hamwi, Sami; Kroeger, Michael; Kowalsky, Wolfgang; Riedl, Thomas; Kahn, Antoine
Advanced Materials (Weinheim, Germany) (2012), 24 (40), 5408-5427CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
A review. During the last few years, transition metal oxides (TMO) such as molybdenum tri-oxide (MoO3), vanadium pent-oxide (V2O5) or tungsten tri-oxide (WO3) were extensively studied because of their exceptional electronic properties for charge injection and extn. in org. electronic devices. These unique properties led to the performance enhancement of several types of devices and to a variety of novel applications. TMOs were used to realize efficient and long-term stable p-type doping of wide band gap org. materials, charge-generation junctions for stacked org. light emitting diodes (OLED), sputtering buffer layers for semi-transparent devices, and org. photovoltaic (OPV) cells with improved charge extn., enhanced power conversion efficiency and substantially improved long term stability. Energetics in general play a key role in advancing device structure and performance in org. electronics; however, the literature provides a very inconsistent picture of the electronic structure of TMOs and the resulting interpretation of their role as functional constituents in org. electronics. With this review the authors intend to clarify some of the existing misconceptions. An overview of TMO-based device architectures ranging from transparent OLEDs to tandem OPV cells is also given. Various TMO film deposition methods are reviewed, addressing vacuum evapn. and recent approaches for soln.-based processing. The specific properties of the resulting materials and their role as functional layers in org. devices are discussed.
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Work function, electron affinity and band bending of zinc oxide surfaces
Jacobi, K.; Zwicker, G.; Gutmann, A.
Surface Science (1984), 141 (1), 109-25CODEN: SUSCAS; ISSN:0039-6028.
(000‾1)O, (10‾10) and (0001) Zn faces of ZnO were prepd. by Ar-ion bombardment and annealing at 700 K ((000‾1) and (0001)) and 825 K (10‾10). Work function, electron affinity and band bending were evaluated by using angle-resolved UPS. All quantities show time-dependent changes specific for each face. These changes are interpreted by assuming O diffusion from the surface layer into near-surface bulk vacancies. This process initiates a redistribution of O-derived states at the valence band max.
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Schottky barrier height of Au on the transparent semiconducting oxide β-Ga2O3
Mohamed, M.; Irmscher, K.; Janowitz, C.; Galazka, Z.; Manzke, R.; Fornari, R.
Applied Physics Letters (2012), 101 (13), 132106/1-132106/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
The Schottky barrier height of Au deposited on (100) surfaces of n-type β-Ga2O3 single crystals was detd. by current-voltage characteristics and high-resoln. photoemission spectroscopy resulting in a common effective value of 1.04 ± 0.08 eV. Furthermore, the electron affinity of β-Ga2O3 and the work function of Au were detd. to be 4.00 ± 0.05 eV and 5.23 ± 0.05 eV, resp., yielding a barrier height of 1.23 eV according to the Schottky-Mott rule. The redn. of the Schottky-Mott barrier to the effective value was ascribed to the image-force effect and the action of metal-induced gap states, whereas extrinsic influences could be avoided. (c) 2012 American Institute of Physics.
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Kröger, M.; Hamwi, S.; Meyer, J.; Riedl, T.; Kowalsky, W.; Kahn, A. P-Type Doping of Organic Wide Band Gap Materials by Transition Metal Oxides: A Case-Study on Molybdenum Trioxide. Org. Electron. 2009, 10 (5), 932– 938, DOI: 10.1016/j.orgel.2009.05.007
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82
P-type doping of organic wide band gap materials by transition metal oxides: A case-study on Molybdenum trioxide
Kroger, Michael; Hamwi, Sami; Meyer, Jens; Riedl, Thomas; Kowalsky, Wolfgang; Kahn, Antoine
Organic Electronics (2009), 10 (5), 932-938CODEN: OERLAU; ISSN:1566-1199. (Elsevier B.V.)
A study on p-doping of org. wide band gap materials with Molybdenum trioxide using current transport measurements, UPS and inverse photoelectron spectroscopy is presented. When MoO3 is co-evapd. with 4,4'-Bis(N-carbazolyl)-1,1'-biphenyl (CBP), a significant increase in cond. is obsd., compared to intrinsic CBP thin films. This increase in cond. is due to electron transfer from the HOMO of the host mols. to very low lying unfilled states of embedded Mo3O9 clusters. The energy levels of these clusters are estd. by the energy levels of a neat MoO3 thin film with a work function of 6.86 eV, an electron affinity of 6.7 eV and an ionization energy of 9.68 eV. The Fermi level of MoO3-doped CBP and N,N'-bis(1-naphthyl)-N,N'-diphenyl-1,1'-biphenyl-4,4'-diamine (α-NPD) thin films rapidly shifts with increasing doping concn. towards the occupied states. Pinning of the Fermi level several 100 meV above the HOMO edge is obsd. for doping concns. higher than 2 mol% and is explained in terms of a Gaussian d. of HOMO states. We det. a relatively low dopant activation of ∼0.5%, which is due to Coulomb-trapping of hole carriers at the ionized dopant sites.
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Greiner, M. T.; Helander, M. G.; Tang, W.-M.; Wang, Z.-B.; Qiu, J.; Lu, Z.-H. Universal Energy-Level Alignment of Molecules on Metal Oxides. Nat. Mater. 2012, 11 (1), 76– 81, DOI: 10.1038/nmat3159
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Universal energy-level alignment of molecules on metal oxides
Greiner, Mark T.; Helander, Michael G.; Tang, Wing-Man; Wang, Zhi-Bin; Qiu, Jacky; Lu, Zheng-Hong
Nature Materials (2012), 11 (1), 76-81CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
Transition-metal oxides improve power conversion efficiencies in org. photovoltaics and are used as low-resistance contacts in org. light-emitting diodes and org. thin-film transistors. What makes metal oxides useful in these technologies is the fact that their chem. and electronic properties can be tuned to enable charge exchange with a wide variety of org. mols. Although it is known that charge exchange relies on the alignment of donor and acceptor energy levels, the mechanism for level alignment remains under debate. Here, we conclusively establish the principle of energy alignment between oxides and mols. We observe a universal energy-alignment trend for a set of transition metal oxides-representing a broad diversity in electronic properties-with several org. semiconductors. The trend demonstrates that, despite the variance in their electronic properties, oxide energy alignment is governed by one driving force: electron-chem. potential equilibration. Using a combination of simple thermodn., electrostatics and Fermi statistics we derive a math. relation that describes the alignment.
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Lei, Y.; Lu, X. The Decisive Effect of Interface States on the Photocatalytic Activity of the Silver(I) Oxide/Titanium Dioxide Heterojunction. J. Colloid Interface Sci. 2017, 492, 167– 175, DOI: 10.1016/j.jcis.2017.01.001
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Hohmann, M. V.; Ágoston, P.; Wachau, A.; Bayer, T. J. M.; Brötz, J.; Albe, K.; Klein, A. Orientation Dependent Ionization Potential of In₂O₃: A Natural Source for Inhomogeneous Barrier Formation at Electrode Interfaces in Organic Electronics. J. Phys.: Condens. Matter 2011, 23 (33), 334203, DOI: 10.1088/0953-8984/23/33/334203
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Orientation dependent ionization potential of In2O3: a natural source for inhomogeneous barrier formation at electrode interfaces in organic electronics
Hohmann, Mareike V.; Agoston, Peter; Wachau, Andre; Bayer, Thorsten J. M.; Broetz, Joachim; Albe, Karsten; Klein, Andreas
Journal of Physics: Condensed Matter (2011), 23 (33), 334203/1-334203/8CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
The ionization potentials of In2O3 films grown epitaxially by magnetron sputtering on Y-stabilized ZrO2 substrates with (100) and (111) surface orientation are detd. using photoelectron spectroscopy. Epitaxial growth is verified using x-ray diffraction. The obsd. ionization potentials, which directly affect the work functions, are in good agreement with ab initio calcns. using d. functional theory. While the (111) surface exhibits a stable surface termination with an ionization potential of ∼7.0 eV, the surface termination and the ionization potential of the (100) surface depend strongly on the oxygen chem. potential. With the given deposition conditions an ionization potential of ∼7.7 eV is obtained, which is attributed to a surface termination stabilized by oxygen dimers. This orientation dependence also explains the lower ionization potentials obsd. for In2O3 compared to Sn-doped In2O3 (ITO). Due to the orientation dependent ionization potential, a polycryst. ITO film will exhibit a laterally varying work function, which results in an inhomogeneous charge injection into org. semiconductors when used as electrode material. The variation of work function will become even more pronounced when oxygen plasma or UV-ozone treatments are performed, as an oxidn. of the surface is only possible for the (100) surface. The influence of the deposition technique on the formation of stable surface terminations is also discussed.
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Physical Review Letters (2008), 100 (16), 167402/1-167402/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
Bulk and surface sensitive x-ray spectroscopic techniques are applied in tandem to show that the valence band edge for In2O3 is found significantly closer to the bottom of the conduction band than expected from the widely quoted bulk band gap of 3.75 eV. First-principles theory shows that the upper valence bands of In2O3 exhibit a small dispersion and the conduction band min. is positioned at Γ. However, direct optical transitions give a minimal dipole intensity until 0.8 eV below the valence band max. The results set an upper limit on the fundamental band gap of 2.9 eV.
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Abstract
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Figure 1
Figure 1. Schematic of prediction of IPs and EAs in nonmetallic solids by theoretical calculations and machine learning. The theoretical calculations from first principles typically use a combination of surface and bulk models to evaluate the energy difference between the vacuum level and the VBM (IP) or CBM (EA). Our ANN predicts the IPs and EAs of relaxed surfaces by simply inputting the information on the bulk crystal structure and the surface index and termination plane.
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Figure 2
Figure 2. Distribution of theoretical IPs and EAs of binary oxides and comparison with experiments. (a) Upper panel shows the distribution of the IPs and EAs of the respective binary oxides. Orange and green dots are IPs and EAs, respectively. Cross and circle symbols are Tasker’s type I and II surfaces, (64) respectively. The bottom panel is the number of surfaces, where yellow and dark blue bars are types I and II, respectively. (b) Theoretical IPs and EAs versus reported experimental values for selected binary oxides. The upper edges of the pale orange bars and the lower edges of the light green bars are calculated VBMs and CBMs with respect to the vacuum level (set at 0 eV), respectively. The orange and green solid lines are experimentally reported IPs and EAs, respectively; the dashed lines are derived by combining experimental IPs or EAs and experimental band gaps. The experimental data are taken from refs (70and71) for MgO, refs (72and73) for Al₂O₃, ref (74) for TiO₂, ref (75) for V₂O₅, ref (76) for Cu₂O, refs (77–79) for ZnO, refs (80and81) for Ga₂O₃, ref (82) for MoO₃, refs (83and84) for Ag₂O, refs (85and86) for In₂O₃, ref (87) for CeO₂, ref (83) for Ta₂O₅, and ref (88) for WO₃. The surface orientations have not been presented in the experimental reports for V₂O₅, Cu₂O, MoO₃, Ag₂O, In₂O₃, Ta₂O₅, and WO₃. Therefore, all theoretical IPs and EAs of binary oxides with the indicated space groups are depicted in the figure. Note that there are many types of surfaces for V₂O₅, MoO₃, and Ta₂O₅, and the bars for each surface are extremely narrow.
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Figure 3
Figure 3. Architecture of ANNs. (a) Simple-ANN, (b) ANN w/AL, and (c) ANN w/L-SOAP. Each circle in the figure is a node where the input and output are scalars. Edges between nodes in two adjacent layers are fully connected but omitted for easy visualization.
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Figure 4
Figure 4. Schematic of conventional and learnable SOAP descriptors. The element-pair SOAPs (bottom left panel) are concatenations of the SOAPs of each elemental pair; the cation–anion-pair SOAPs (bottom center panel) are concatenations of three pairs, namely, cation–cation, cation–anion, and anion–anion combinations; and L-SOAPs (bottom right panel) have element-based learnable weights, which are automatically adjusted during ANN training.
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Figure 5
Figure 5. Theoretical and predicted IPs and EAs using simple-ANN and ANN w/AL. (a) IPs and (b) EAs obtained by first-principles calculations versus those predicted by the simple-ANN. (c) IPs and (d) EAs by first-principles calculations versus those predicted by the ANN w/AL. The orange or green and gray dots represent the test and training data, respectively. (e) Atom-site weights from the attention layer in the IP and EA prediction of a (001) surface of Sb₂O₃ whose space group is Pccn (index is 20 in Table S3). The frame indicates the surface supercell where the upper vacant region corresponds to the vacuum layer. Larger and smaller circles are the Sb and O atoms, respectively. The weights are represented by the shades of the atom colors: blue for Sb and pink for O. The weights are normalized so that the largest weight is one.
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Figure 6
Figure 6. Distribution of theoretical IPs and EAs of ternary oxides and prediction accuracy of transfer learning. (a) Distribution of theoretical IPs and EAs. Ternary oxides include two cation species, and the same data points are shown at both cation species. The other details are the same as those for Figure 2a. (b,c) Prediction accuracy of transfer learning for IPs and EAs, respectively. The filled and open symbols are the results of the ANN w/L-SOAP and the ANN w/AL, respectively. The horizontal axis is the ratio of the ternary data for training to all ternary data.
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References
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  16
  Band alignment of semiconductors from density-functional theory and many-body perturbation theory
  Hinuma, Yoyo; Gruneis, Andreas; Kresse, Georg; Oba, Fumiyasu
  Physical Review B: Condensed Matter and Materials Physics (2014), 90 (15), 155405/1-155405/16, 16 pp.CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  The band lineup, or alignment, of semiconductors is investigated via first-principles calcns. based on d. functional theory (DFT) and many-body perturbation theory (MBPT). Twenty-one semiconductors including C, Si, and Ge in the diamond structure, BN, AlP, AlAs, AlSb, GaP, GaAs, GaSb, InP, InAs, InSb, ZnS, ZnSe, ZnTe, CdS, CdSe, and CdTe in the zinc-blende structure, and GaN and ZnO in the wurtzite structure are considered in view of their fundamental and technol. importance. Band alignments are detd. using the valence and conduction band offsets from heterointerface calcns., the ionization potential (IP) and electron affinity (EA) from surface calcns., and the valence band max. and conduction band min. relative to the branch point energy, or charge neutrality level, from bulk calcns. The performance of various approxns. to DFT and MBPT, namely the Perdew-Burke-Ernzerhof (PBE) semilocal functional, the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional, and the GW approxn. with and without vertex corrections in the screened Coulomb interaction, is assessed using the GWΓ1 approxn. as a ref., where first-order vertex corrections are included in the self-energy. The exptl. IPs, EAs, and band offsets are well reproduced by GWΓ1 for most of the semiconductor surfaces and heterointerfaces considered in this study. The PBE and HSE functionals show sizable errors in the IPs and EAs, in particular for group II-VI semiconductors with wide band gaps, but are much better in the prediction of relative band positions or band offsets due to error cancellation. The performance of the GW approxn. is almost on par with GWΓ1 as far as relative band positions are concerned. The band alignments based on av. interfacial band offsets for all pairs of 17 semiconductors and branch point energies agree with explicitly calcd. interfacial band offsets with small mean abs. errors of both ∼0.1eV, indicating a good overall transitivity of the band offsets. The alignment based on IPs from selected nonpolar surfaces performs comparably well in the prediction of band offsets at most of the considered interfaces. The max. errors are, however, as large as 0.3, 0.4, and 0.7 eV for the alignments based on the av. band offsets, branch point energies, and IPs, resp. This margin of error should be taken into account when performing materials screening using these alignments.
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17. 17
  Chen, W.; Pasquarello, A. Band-Edge Positions in GW: Effects of Starting Point and Self-Consistency. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90 (16), 165133, DOI: 10.1103/PhysRevB.90.165133
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18. 18
  Moses, P. G.; Miao, M.; Yan, Q.; Van de Walle, C. G. Hybrid Functional Investigations of Band Gaps and Band Alignments for AlN, GaN, InN, and InGaN. J. Chem. Phys. 2011, 134 (8), 084703, DOI: 10.1063/1.3548872
  18
  Hybrid functional investigations of band gaps and band alignments for AlN, GaN, InN, and InGaN
  Moses, Poul Georg; Miao, Maosheng; Yan, Qimin; Van de Walle, Chris G.
  Journal of Chemical Physics (2011), 134 (8), 084703/1-084703/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Band gaps and band alignments for AlN, GaN, InN, and InGaN alloys are studied using d. functional theory with the with the Heyd-Scuseria-Ernzerhof {HSE06} XC functional. The band gap of InGaN alloys as a function of In content is calcd. and a strong bowing at low In content is found, described by bowing parameters 2.29 eV at 6.25% and 1.79 eV at 12.5%, indicating the band gap cannot be described by a single compn.-independent bowing parameter. Valence-band maxima (VBM) and conduction-band min. (CBM) are aligned by combining bulk calcns. with surface calcns. for nonpolar surfaces. The influence of surface termination (1‾100) m-plane or (11‾20) a-plane is thoroughly studied. For the relaxed surfaces of the binary nitrides the difference in electron affinities between m- and a-plane is <0.1 eV. The abs. electron affinities strongly depend on the choice of XC functional. However, relative alignments are less sensitive to the choice of XC functional. In particular, relative alignments may be calcd. based on Perdew-Becke-Ernzerhof surface calcns. with the HSE06 lattice parameters. For InGaN the VBM is a linear function of In content and the majority of the band-gap bowing is located in the CBM. Based on the calcd. electron affinities the authors predict that InGaN will be suited for H2O splitting up to 50% In content. (c) 2011 American Institute of Physics.
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  Komsa, H.-P.; Broqvist, P.; Pasquarello, A. Alignment of Defect Levels and Band Edges through Hybrid Functionals: Effect of Screening in the Exchange Term. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (20), 205118, DOI: 10.1103/PhysRevB.81.205118
  19
  Alignment of defect levels and band edges through hybrid functionals: Effect of screening in the exchange term
  Komsa, Hannu-Pekka; Broqvist, Peter; Pasquarello, Alfredo
  Physical Review B: Condensed Matter and Materials Physics (2010), 81 (20), 205118/1-205118/12CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We investigate how various treatments of exact exchange affect defect charge transition levels and band edges in hybrid functional schemes for a variety of systems. We distinguish the effects of long-range vs. short-range exchange and of local vs. nonlocal exchange. This is achieved by the consideration of a set of four functionals, which comprise the semilocal Perdew-Burke-Ernzerhof (PBE) functional, the PBE hybrid (PBE0), the Heyd-Scuseria-Ernzerhof (HSE) functional, and a hybrid derived from PBE0 in which the Coulomb kernel in the exact exchange term is screened as in the HSE functional but which, unlike HSE, does not include a local expression compensating for the loss of the long-range exchange. We find that defect levels in PBE0 and in HSE almost coincide when aligned with respect to a common ref. potential, due to the close total-energy differences in the two schemes. At variance, the HSE band edges detd. within the same alignment scheme are found to shift significantly with respect to the PBE0 ones: the occupied and the unoccupied states undergo shifts of about +0.4 eV and -0.4 eV, resp. These shifts are found to vary little among the materials considered. Through a rationale based on the behavior of local and nonlocal long-range exchange, this conclusion is generalized beyond the class of materials used in this study. Finally, we explicitly address the practice of tuning the band gap by adapting the fraction of exact exchange incorporated in the functional. When PBE0-like and HSE-like functionals are tuned to yield identical band gaps, their resp. results for the positions of defect levels within the band gap and for the band alignments at interfaces are found to be very close.
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20. 20
  Oba, F.; Kumagai, Y. Design and Exploration of Semiconductors from First Principles: A Review of Recent Advances. Appl. Phys. Express 2018, 11 (6), 060101, DOI: 10.7567/APEX.11.060101
  There is no corresponding record for this reference.
21. 21
  Hinuma, Y.; Kumagai, Y.; Tanaka, I.; Oba, F. Band Alignment of Semiconductors and Insulators Using Dielectric-Dependent Hybrid Functionals: Toward High-Throughput Evaluation. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 95 (7), 075302, DOI: 10.1103/PhysRevB.95.075302
  There is no corresponding record for this reference.
22. 22
  Butler, K. T.; Hendon, C. H.; Walsh, A. Electronic Chemical Potentials of Porous Metal–Organic Frameworks. J. Am. Chem. Soc. 2014, 136 (7), 2703– 2706, DOI: 10.1021/ja4110073
  22
  Electronic Chemical Potentials of Porous Metal-Organic Frameworks
  Butler, Keith T.; Hendon, Christopher H.; Walsh, Aron
  Journal of the American Chemical Society (2014), 136 (7), 2703-2706CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  The binding energy of an electron in a material is a fundamental characteristic, which dets. a wealth of important chem. and phys. properties. For metal-org. frameworks this quantity is hitherto unknown. We present a general approach for detg. the vacuum level of porous metal-org. frameworks and apply it to obtain the first ionization energy for six prototype materials including zeolitic, covalent, and ionic frameworks. This approach for valence band alignment can explain observations relating to the electrochem., optical, and elec. properties of porous frameworks.
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23. 23
  Jacobs, R.; Booske, J.; Morgan, D. Understanding and Controlling the Work Function of Perovskite Oxides Using Density Functional Theory. Adv. Funct. Mater. 2016, 26 (30), 5471– 5482, DOI: 10.1002/adfm.201600243
  23
  Understanding and controlling the work function of perovskite oxides using density functional theory
  Jacobs, Ryan; Booske, John; Morgan, Dane
  Advanced Functional Materials (2016), 26 (30), 5471-5482CODEN: AFMDC6; ISSN:1616-301X. (Wiley-VCH Verlag GmbH & Co. KGaA)
  Perovskite oxides contg. transition metals are promising materials in a wide range of electronic and electrochem. applications. However, neither their work function values nor an understanding of their work function physics have been established. Here, the work function trends of a series of perovskite (ABO3 formula) materials using d. functional theory are predicted, and show that the work functions of (001)-terminated AO- and BO2-oriented surfaces can be described using concepts of electronic band filling, bond hybridization, and surface dipoles. The calcd. range of AO (BO2) work functions are 1.60-3.57 eV (2.99-6.87 eV). An approx. linear correlation (R2 between 0.77 and 0.86 is found, depending on surface termination) between work function and position of the oxygen 2p band center, which correlation enables both understanding and rapid prediction of work function trends. Furthermore, SrVO3 is identified as a stable, low work function, highly conductive material. Undoped (Ba-doped) SrVO3 has an intrinsically low AO-terminated work function of 1.86 eV (1.07 eV). These properties make SrVO3 a promising candidate material for a new electron emission cathode for application in high power microwave devices, and as a potential electron emissive material for thermionic energy conversion technologies.
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24. 24
  Grüneis, A.; Kresse, G.; Hinuma, Y.; Oba, F. Ionization Potentials of Solids: The Importance of Vertex Corrections. Phys. Rev. Lett. 2014, 112 (9), 096401, DOI: 10.1103/PhysRevLett.112.096401
  There is no corresponding record for this reference.
25. 25
  Ping, Y.; Rocca, D.; Galli, G. Electronic Excitations in Light Absorbers for Photoelectrochemical Energy Conversion: First Principles Calculations Based on Many Body Perturbation Theory. Chem. Soc. Rev. 2013, 42 (6), 2437, DOI: 10.1039/c3cs00007a
  There is no corresponding record for this reference.
26. 26
  Deacon-Smith, D. E. E.; Scanlon, D. O.; Catlow, C. R. A.; Sokol, A. A.; Woodley, S. M. Interlayer Cation Exchange Stabilizes Polar Perovskite Surfaces. Adv. Mater. 2014, 26 (42), 7252– 7256, DOI: 10.1002/adma.201401858
  There is no corresponding record for this reference.
27. 27
  Setvin, M.; Reticcioli, M.; Poelzleitner, F.; Hulva, J.; Schmid, M.; Boatner, L. A.; Franchini, C.; Diebold, U. Polarity Compensation Mechanisms on the Perovskite Surface KTaO₃ (001). Science 2018, 359 (6375), 572– 575, DOI: 10.1126/science.aar2287
  27
  Polarity compensation mechanisms on the perovskite surface KTaO3(001)
  Setvin, Martin; Reticcioli, Michele; Poelzleitner, Flora; Hulva, Jan; Schmid, Michael; Boatner, Lynn A.; Franchini, Cesare; Diebold, Ulrike
  Science (Washington, DC, United States) (2018), 359 (6375), 572-575CODEN: SCIEAS; ISSN:0036-8075. (American Association for the Advancement of Science)
  The stacking of alternating charged planes in ionic crystals creates a diverging electrostatic energy-a "polar catastrophe"-that must be compensated at the surface. We used scanning probe microscopies and d. functional theory to study compensation mechanisms at the perovskite potassium tantalate(KTaO3) (001) surface as increasing degrees of freedom were enabled. The as-cleaved surface in vacuum is frozen in place but immediately responds with an insulator-to-metal transition and possibly ferroelec. lattice distortions. Annealing in vacuum allows the formation of isolated oxygen vacancies, followed by a complete rearrangement of the top layers into an ordered pattern of KO and TaO2 stripes. The optimal soln. is found after exposure to water vapor through the formation of a hydroxylated overlayer with ideal geometry and charge.
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28. 28
  Enterkin, J. A.; Subramanian, A. K.; Russell, B. C.; Castell, M. R.; Poeppelmeier, K. R.; Marks, L. D. A Homologous Series of Structures on the Surface of SrTiO₃ (110). Nat. Mater. 2010, 9 (3), 245– 248, DOI: 10.1038/nmat2636
  There is no corresponding record for this reference.
29. 29
  Lazzeri, M.; Selloni, A. Stress-Driven Reconstruction of an Oxide Surface: The Anatase TiO₂ (001)-(1 × 4) Surface. Phys. Rev. Lett. 2001, 87 (26), 266105, DOI: 10.1103/PhysRevLett.87.266105
  There is no corresponding record for this reference.
30. 30
  Zhu, Q.; Li, L.; Oganov, A. R.; Allen, P. B. Evolutionary Method for Predicting Surface Reconstructions with Variable Stoichiometry. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87 (19), 195317, DOI: 10.1103/PhysRevB.87.195317
  30
  Evolutionary method for predicting surface reconstructions with variable stoichiometry
  Zhu, Qiang; Li, Li; Oganov, Artem R.; Allen, Philip B.
  Physical Review B: Condensed Matter and Materials Physics (2013), 87 (19), 195317/1-195317/8CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We present a specially designed evolutionary algorithm for the prediction of surface reconstructions. This technique allows one to automatically explore stable and low-energy metastable configurations with variable surface atoms and variable surface unit cells through the whole chem. potential range. The power of evolutionary search is demonstrated by the efficient identification of diamond 2 × 1 (100) and 2 × 1 (111) surface reconstructions with a fixed no. of surface atoms and a fixed cell size. With further variation of surface unit cells, we study the reconstructions of the polar surface MgO (111). Expt. has detected an oxygen trimer (ozone) motif. We predict another version of this motif which can be thermodynamically stable in extreme oxygen-rich conditions. Finally, we perform a variable stoichiometry search for a complex ternary system: semipolar GaN (10‾11) with and without adsorbed oxygen. The search yields a counterintuitive reconstruction based on N3 trimers. These examples demonstrate that an automated scheme to explore the energy landscape of surfaces will improve our understanding of surface reconstructions. The method presented in this paper can be generally applied to binary and multicomponent systems.
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31. 31
  Wanzenböck, R.; Arrigoni, M.; Bichelmaier, S.; Buchner, F.; Carrete, J.; Madsen, G. K. H. Neural-Network-Backed Evolutionary Search for SrTiO₃ (110) Surface Reconstructions. Digital Discovery 2022, 1 (5), 703– 710, DOI: 10.1039/D2DD00072E
  There is no corresponding record for this reference.
32. 32
  Mochizuki, Y.; Sung, H.-J.; Gake, T.; Oba, F. Chemical Trends of Surface Reconstruction and Band Positions of Nonmetallic Perovskite Oxides from First Principles. Chem. Mater. 2023, 35 (5), 2047– 2057, DOI: 10.1021/acs.chemmater.2c03615
  32
  Chemical Trends of Surface Reconstruction and Band Positions of Nonmetallic Perovskite Oxides from First Principles
  Mochizuki, Yasuhide; Sung, Ha-Jun; Gake, Tomoya; Oba, Fumiyasu
  Chemistry of Materials (2023), 35 (5), 2047-2057CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
  An evolutionary algorithm search in combination with first-principles calcns. is performed to systematically predict the reconstructed surface structures of nonmetallic perovskite oxides. Four types of lowest-energy reconstruction patterns are obtained for the macroscopically stoichiometric (001) surfaces of NaTaO3, KTaO3, CaTiO3, SrTiO3, YAlO3, and LaAlO3 as representatives of A+B5+O3, A2+B4+O3, and A3+B3+O3 systems. We explain chem. trends in the surface energies and band positions of 10 perovskite oxides, addnl. including KNbO3, BaTiO3, BaZrO3, and LaGaO3, in terms of the at. environments at the outermost reconstructed surface layers. Regaining A-O (B-O) coordination nos. and bond lengths at the surfaces is found to stabilize the A2+B4+O3 and A3+B3+O3 (A+B5+O3) surfaces. Decreasing the coordination no. of cation A (B) leads to shallow (deep) valence band maxima and conduction band min. relative to the vacuum level. Our study provides general insights into the surface reconstruction and band alignment of nonmetallic perovskite oxides.
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33. 33
  Kim, S.; Sinai, O.; Lee, C.-W.; Rappe, A. M. Controlling Oxide Surface Dipole and Reactivity with Intrinsic Nonstoichiometric Epitaxial Reconstructions. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 92 (23), 235431, DOI: 10.1103/PhysRevB.92.235431
  There is no corresponding record for this reference.
34. 34
  Stanev, V.; Oses, C.; Kusne, A. G.; Rodriguez, E.; Paglione, J.; Curtarolo, S.; Takeuchi, I. Machine Learning Modeling of Superconducting Critical Temperature. npj Comput. Mater. 2018, 4 (1), 29, DOI: 10.1038/s41524-018-0085-8
  There is no corresponding record for this reference.
35. 35
  Kiyohara, S.; Oda, H.; Miyata, T.; Mizoguchi, T. Prediction of Interface Structures and Energies via Virtual Screening. Sci. Adv. 2016, 2 (11), 1600746, DOI: 10.1126/sciadv.1600746
  There is no corresponding record for this reference.
36. 36
  Schütt, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Müller, K. R. SchNet – A Deep Learning Architecture for Molecules and Materials. J. Chem. Phys. 2018, 148 (24), 241722, DOI: 10.1063/1.5019779
  36
  SchNet - A deep learning architecture for molecules and materials
  Schuett, K. T.; Sauceda, H. E.; Kindermans, P.-J.; Tkatchenko, A.; Mueller, K.-R.
  Journal of Chemical Physics (2018), 148 (24), 241722/1-241722/11CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  Deep learning has led to a paradigm shift in artificial intelligence, including web, text, and image search, speech recognition, as well as bioinformatics, with growing impact in chem. physics. Machine learning, in general, and deep learning, in particular, are ideally suitable for representing quantum-mech. interactions, enabling us to model nonlinear potential-energy surfaces or enhancing the exploration of chem. compd. space. Here, we present the deep learning architecture SchNet that is specifically designed to model atomistic systems by making use of continuous-filter convolutional layers. We demonstrate the capabilities of SchNet by accurately predicting a range of properties across chem. space for mols. and materials, where our model learns chem. plausible embeddings of atom types across the periodic table. Finally, we employ SchNet to predict potential-energy surfaces and energy-conserving force fields for mol. dynamics simulations of small mols. and perform an exemplary study on the quantum-mech. properties of C20-fullerene that would have been infeasible with regular ab initio mol. dynamics. (c) 2018 American Institute of Physics.
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37. 37
  Freeze, J. G.; Kelly, H. R.; Batista, V. S. Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists. Chem. Rev. 2019, 119 (11), 6595– 6612, DOI: 10.1021/acs.chemrev.8b00759
  37
  Search for Catalysts by Inverse Design: Artificial Intelligence, Mountain Climbers, and Alchemists
  Freeze, Jessica G.; Kelly, H. Ray; Batista, Victor S.
  Chemical Reviews (Washington, DC, United States) (2019), 119 (11), 6595-6612CODEN: CHREAY; ISSN:0009-2665. (American Chemical Society)
  In silico catalyst design is a grand challenge of chem. Traditional computational approaches have been limited by the need to compute properties for an intractably large no. of possible catalysts. Recently, inverse design methods have emerged, starting from a desired property and optimizing a corresponding chem. structure. Techniques used for exploring chem. space include gradient-based optimization, alchem. transformations, and machine learning. Though the application of these methods to catalysis is in its early stages, further development will allow for robust computational catalyst design. This review provides an overview of the evolution of inverse design approaches and their relevance to catalysis. The strengths and limitations of existing techniques are highlighted, and suggestions for future research are provided.
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38. 38
  Xie, T.; Grossman, J. C. Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties. Phys. Rev. Lett. 2018, 120 (14), 145301, DOI: 10.1103/PhysRevLett.120.145301
  38
  Crystal Graph Convolutional Neural Networks for an Accurate and Interpretable Prediction of Material Properties
  Xie, Tian; Grossman, Jeffrey C.
  Physical Review Letters (2018), 120 (14), 145301CODEN: PRLTAO; ISSN:1079-7114. (American Physical Society)
  The use of machine learning methods for accelerating the design of cryst. materials usually requires manually constructed feature vectors or complex transformation of atom coordinates to input the crystal structure, which either constrains the model to certain crystal types or makes it difficult to provide chem. insights. Here, we develop a crystal graph convolutional neural networks framework to directly learn material properties from the connection of atoms in the crystal, providing a universal and interpretable representation of cryst. materials. Our method provides a highly accurate prediction of d. functional theory calcd. properties for eight different properties of crystals with various structure types and compns. after being trained with 104 data points. Further, our framework is interpretable because one can ext. the contributions from local chem. environments to global properties. Using an example of perovskites, we show how this information can be utilized to discover empirical rules for materials design.
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39. 39
  Butler, K. T.; Davies, D. W.; Cartwright, H.; Isayev, O.; Walsh, A. Machine Learning for Molecular and Materials Science. Nature 2018, 559 (7715), 547– 555, DOI: 10.1038/s41586-018-0337-2
  39
  Machine learning for molecular and materials science
  Butler, Keith T.; Davies, Daniel W.; Cartwright, Hugh; Isayev, Olexandr; Walsh, Aron
  Nature (London, United Kingdom) (2018), 559 (7715), 547-555CODEN: NATUAS; ISSN:0028-0836. (Nature Research)
  Here we summarize recent progress in machine learning for the chem. sciences. We outline machine-learning techniques that are suitable for addressing research questions in this domain, as well as future directions for the field. We envisage a future in which the design, synthesis, characterization and application of mols. and materials is accelerated by artificial intelligence.
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40. 40
  Kang, S.; Jeong, W.; Hong, C.; Hwang, S.; Yoon, Y.; Han, S. Accelerated Identification of Equilibrium Structures of Multicomponent Inorganic Crystals Using Machine Learning Potentials. npj Comput. Mater. 2022, 8 (1), 108, DOI: 10.1038/s41524-022-00792-w
  There is no corresponding record for this reference.
41. 41
  Shen, C.; Li, T.; Zhang, Y.; Xie, R.; Long, T.; Fortunato, N. M.; Liang, F.; Dai, M.; Shen, J.; Wolverton, C. M.; Zhang, H. Accelerated Screening of Ternary Chalcogenides for Potential Photovoltaic Applications. J. Am. Chem. Soc. 2023, 145 (40), 21925– 21936, DOI: 10.1021/jacs.3c06207
  There is no corresponding record for this reference.
42. 42
  Hwang, S.; Jung, J.; Hong, C.; Jeong, W.; Kang, S.; Han, S. Stability and Equilibrium Structures of Unknown Ternary Metal Oxides Explored by Machine-Learned Potentials. J. Am. Chem. Soc. 2023, 145 (35), 19378– 19386, DOI: 10.1021/jacs.3c06210
  42
  Stability and Equilibrium Structures of Unknown Ternary Metal Oxides Explored by Machine-Learned Potentials
  Hwang, Seungwoo; Jung, Jisu; Hong, Changho; Jeong, Wonseok; Kang, Sungwoo; Han, Seungwu
  Journal of the American Chemical Society (2023), 145 (35), 19378-19386CODEN: JACSAT; ISSN:0002-7863. (American Chemical Society)
  Extensive crystal structure prediction methods, accelerated by machine-learned potentials, were used to study these untapped chem. spaces. The authors examine 181 ternary metal oxide systems, encompassing most cations except for partially filled 3d or f shells, and det. their lowest-energy crystal structures with representative stoichiometry derived from prevalent oxidn. states or recommender systems. Forty-five ternary oxide systems contg. stable compds. against decompn. into binary or elemental phases, the majority of which incorporate noble metals, were discovered. Comparisons with other theor. databases highlight the strengths and limitations of informatics-based material searches.
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43. 43
  Kim, M.; Yeo, B. C.; Park, Y.; Lee, H. M.; Han, S. S.; Kim, D. Artificial Intelligence to Accelerate the Discovery of N₂ Electroreduction Catalysts. Chem. Mater. 2020, 32 (2), 709– 720, DOI: 10.1021/acs.chemmater.9b03686
  43
  Artificial Intelligence to Accelerate the Discovery of N2 Electroreduction Catalysts
  Kim, Myungjoon; Yeo, Byung Chul; Park, Youngtae; Lee, Hyuck Mo; Han, Sang Soo; Kim, Donghun
  Chemistry of Materials (2020), 32 (2), 709-720CODEN: CMATEX; ISSN:0897-4756. (American Chemical Society)
  The development of catalysts for the electrochem. N2 redn. reaction (NRR) with a low limiting potential and high faradaic efficiency is highly desirable but remains challenging. Here, to achieve acceleration, the authors develop and report a slab graph convolutional neural network (SGCNN), an accurate and flexible machine learning (ML) model that is suited for probing surface reactions in catalysis. With a self-accumulated database of 3040 surface calcns. at the d.-functional-theory (DFT) level, SGCNN predicted the binding energies, ranging over 8 eV, of five key adsorbates (H, N2, N2H, NH, NH2) related to NRR performance with a mean abs. error (MAE) of only 0.23 eV. SGCNN only requires the low-level inputs of elemental properties available in the periodic table of elements and connectivity information of constituent atoms; thus, accelerations can be realized. Via a combined process of SGCNN-driven predictions and DFT verifications, four novel catalysts in the L12 crystal space, including V3Ir(111), Tc3Hf(111), V3Ni(111), and Tc3Ta(111), are proposed as stable candidates that likely exhibit both a lower limiting potential and higher faradaic efficiency in the NRR, relative to the ref. Mo(110). The ML work combined with a statistical data anal. reveals that catalytic surfaces with an av. d-orbital occupation between 4 and 6 could lower the limiting potential and potentially overcome the scaling relation in the NRR.
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44. 44
  Chen, C.; Ong, S. P. A Universal Graph Deep Learning Interatomic Potential for the Periodic Table. Nat. Comput. Sci. 2022, 2 (11), 718– 728, DOI: 10.1038/s43588-022-00349-3
  44
  A universal graph deep learning interatomic potential for the periodic table
  Chen Chi; Ong Shyue Ping
  Nature computational science (2022), 2 (11), 718-728 ISSN:.
  Interatomic potentials (IAPs), which describe the potential energy surface of atoms, are a fundamental input for atomistic simulations. However, existing IAPs are either fitted to narrow chemistries or too inaccurate for general applications. Here we report a universal IAP for materials based on graph neural networks with three-body interactions (M3GNet). The M3GNet IAP was trained on the massive database of structural relaxations performed by the Materials Project over the past ten years and has broad applications in structural relaxation, dynamic simulations and property prediction of materials across diverse chemical spaces. About 1.8 million materials from a screening of 31 million hypothetical crystal structures were identified to be potentially stable against existing Materials Project crystals based on M3GNet energies. Of the top 2,000 materials with the lowest energies above the convex hull, 1,578 were verified to be stable using density functional theory calculations. These results demonstrate a machine learning-accelerated pathway to the discovery of synthesizable materials with exceptional properties.
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45. 45
  Bartók, A. P.; Kondor, R.; Csányi, G. On Representing Chemical Environments. Phys. Rev. B: Condens. Matter Mater. Phys. 2013, 87 (18), 184115, DOI: 10.1103/PhysRevB.87.184115
  45
  On representing chemical environments
  Bartok, Albert P.; Kondor, Risi; Csanyi, Gabor
  Physical Review B: Condensed Matter and Materials Physics (2013), 87 (18), 184115/1-184115/16CODEN: PRBMDO; ISSN:1098-0121. (American Physical Society)
  We review some recently published methods to represent at. neighborhood environments, and analyze their relative merits in terms of their faithfulness and suitability for fitting potential energy surfaces. The crucial properties that such representations (sometimes called descriptors) must have are differentiability with respect to moving the atoms and invariance to the basic symmetries of physics: rotation, reflection, translation, and permutation of atoms of the same species. We demonstrate that certain widely used descriptors that initially look quite different are specific cases of a general approach, in which a finite set of basis functions with increasing angular wave nos. are used to expand the at. neighborhood d. function. Using the example system of small clusters, we quant. show that this expansion needs to be carried to higher and higher wave nos. as the no. of neighbors increases in order to obtain a faithful representation, and that variants of the descriptors converge at very different rates. We also propose an altogether different approach, called Smooth Overlap of Atomic Positions, that sidesteps these difficulties by directly defining the similarity between any two neighborhood environments, and show that it is still closely connected to the invariant descriptors. We test the performance of the various representations by fitting models to the potential energy surface of small silicon clusters and the bulk crystal.
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46. 46
  Dulub, O.; Diebold, U.; Kresse, G. Novel Stabilization Mechanism on Polar Surfaces: ZnO (0001)-Zn. Phys. Rev. Lett. 2003, 90 (1), 016102, DOI: 10.1103/PhysRevLett.90.016102
  There is no corresponding record for this reference.
47. 47
  Himanen, L.; Jäger, M. O. J.; Morooka, E. V.; Canova, F. F.; Ranawat, Y. S.; Gao, D. Z.; Rinke, P.; Foster, A. S. DScribe: Library of Descriptors for Machine Learning in Materials Science. Comput. Phys. Commun. 2020, 247, 106949, DOI: 10.1016/j.cpc.2019.106949
  47
  DScribe: Library of descriptors for machine learning in materials science
  Himanen, Lauri; Jager, Marc O. J.; Morooka, Eiaki V.; Federici Canova, Filippo; Ranawat, Yashasvi S.; Gao, David Z.; Rinke, Patrick; Foster, Adam S.
  Computer Physics Communications (2020), 247 (), 106949CODEN: CPHCBZ; ISSN:0010-4655. (Elsevier B.V.)
  DScribe is a software package for machine learning that provides popular feature transformations ("descriptors") for atomistic materials simulations. DScribe accelerates the application of machine learning for atomistic property prediction by providing user-friendly, off-the-shelf descriptor implementations. The package currently contains implementations for Coulomb matrix, Ewald sum matrix, sine matrix, Many-body Tensor Representation (MBTR), Atom-centered Symmetry Function (ACSF) and Smooth Overlap of Atomic Positions (SOAP). Usage of the package is illustrated for two different applications: formation energy prediction for solids and ionic charge prediction for atoms in org. mols. The package is freely available under the open-source Apache License 2.0. Program Title: DScribeProgram Files doi:http://dx.doi.org/10.17632/vzrs8n8pk6.1Licensing provisions: Apache-2.0Programming language: Python/C/C++Supplementary material: Supplementary Information as PDFNature of problem: The application of machine learning for materials science is hindered by the lack of consistent software implementations for feature transformations. These feature transformations, also called descriptors, are a key step in building machine learning models for property prediction in materials science. Soln. method: We have developed a library for creating common descriptors used in machine learning applied to materials science. We provide an implementation the following descriptors: Coulomb matrix, Ewald sum matrix, sine matrix, Many-body Tensor Representation (MBTR), Atom-centered Symmetry Functions (ACSF) and Smooth Overlap of Atomic Positions (SOAP). The library has a python interface with computationally intensive routines written in C or C++. The source code, tutorials and documentation are provided online. A continuous integration mechanism is set up to automatically run a series of regression tests and check code coverage when the codebase is updated.
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48. 48
  Hinuma, Y.; Kamachi, T.; Hamamoto, N. Algorithm for Automatic Detection of Surface Atoms. Trans. Mater. Res. Soc. Jpn. 2020, 45 (4), 115– 120, DOI: 10.14723/tmrsj.45.115
  48
  Algorithm for automatic detection of surface atoms
  Hinuma, Yoyo; Kamachi, Takashi; Hamamoto, Nobutsugu
  Transactions of the Materials Research Society of Japan (2020), 45 (4), 115-120CODEN: TMRJE3; ISSN:1382-3469. (Materials Research Society of Japan)
  Automated identification of surface atoms is very convenient when, for instance, finding atoms that may desorb from a catalyst surface. The proposed algorithm for automated identification is based on the geometry of atom positions and quantifies the solid angle of "open space" around an atom. The solid angle is 2π sr for a prototypical surface atom, while the angle would be larger than 2π sr for a step edge atom, slightly larger than π sr for a surface atom at the foot of a step, and much smaller than π sr for a subsurface atom. The algorithm is expected to accelerate anal. of surface defects of slabs and nanoparticles and contribute to, for example, catalyst design.
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49. 49
  Goodall, R. E. A.; Lee, A. A. Predicting Materials Properties without Crystal Structure: Deep Representation Learning from Stoichiometry. Nat. Commun. 2020, 11 (1), 6280, DOI: 10.1038/s41467-020-19964-7
  49
  Predicting materials properties without crystal structure: deep representation learning from stoichiometry
  Goodall, Rhys E. A.; Lee, Alpha A.
  Nature Communications (2020), 11 (1), 6280CODEN: NCAOBW; ISSN:2041-1723. (Nature Research)
  Machine learning has the potential to accelerate materials discovery by accurately predicting materials properties at a low computational cost. However, the model inputs remain a key stumbling block. Current methods typically use descriptors constructed from knowledge of either the full crystal structure - therefore only applicable to materials with already characterised structures - or structure-agnostic fixed-length representations hand-engineered from the stoichiometry. We develop a machine learning approach that takes only the stoichiometry as input and automatically learns appropriate and systematically improvable descriptors from data. Our key insight is to treat the stoichiometric formula as a dense weighted graph between elements. Compared to the state of the art for structure-agnostic methods, our approach achieves lower errors with less data.
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50. 50
  Wang, A. Y. T.; Kauwe, S. K.; Murdock, R. J.; Sparks, T. D. Compositionally Restricted Attention-Based Network for Materials Property Predictions. npj Comput. Mater. 2021, 7 (1), 77, DOI: 10.1038/s41524-021-00545-1
  There is no corresponding record for this reference.
51. 51
  Hinuma, Y.; Hayashi, H.; Kumagai, Y.; Tanaka, I.; Oba, F. Comparison of Approximations in Density Functional Theory Calculations: Energetics and Structure of Binary Oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2017, 96 (9), 094102, DOI: 10.1103/PhysRevB.96.094102
  There is no corresponding record for this reference.
52. 52
  Hinuma, Y.; Kumagai, Y.; Oba, F.; Tanaka, I. Categorization of Surface Polarity from a Crystallographic Approach. Comput. Mater. Sci. 2016, 113, 221– 230, DOI: 10.1016/j.commatsci.2015.11.042
  52
  Categorization of surface polarity from a crystallographic approach
  Hinuma, Yoyo; Kumagai, Yu; Oba, Fumiyasu; Tanaka, Isao
  Computational Materials Science (2016), 113 (), 221-230CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)
  With ab initio codes that employ three-dimensional periodic boundary conditions, the slab-and-vacuum model has proven invaluable for the derivation of energetic, atomistic, and electronic properties of materials. Within this approach, polar and nonpolar slabs require different levels of treatment, as any polar instability must be compensated on a case-by-case basis in the former. This article proposes an efficient algorithm based on isometries to identify whether a slab with the given surface orientation would be intrinsically polar, and if not, to obtain information on where to cleave the bulk crystal to obtain a stoichiometric nonpolar slab and whether reconstruction is necessary to generate a stoichiometric slab that is not polar.
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53. 53
  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 Genome Approach to Accelerating Materials Innovation. APL Mater. 2013, 1 (1), 011002, DOI: 10.1063/1.4812323
  53
  Commentary: The Materials Project: A materials genome approach to accelerating materials innovation
  Jain, Anubhav; Ong, Shyue Ping; Hautier, Geoffroy; Chen, Wei; Richards, William Davidson; Dacek, Stephen; Cholia, Shreyas; Gunter, Dan; Skinner, David; Ceder, Gerbrand; Persson, Kristin A.
  APL Materials (2013), 1 (1), 011002/1-011002/11CODEN: AMPADS; ISSN:2166-532X. (American Institute of Physics)
  Accelerating the discovery of advanced materials is essential for human welfare and sustainable, clean energy. In this paper, we introduce the Materials Project (www.materialsproject.org), a core program of the Materials Genome Initiative that uses high-throughput computing to uncover the properties of all known inorg. materials. This open dataset can be accessed through multiple channels for both interactive exploration and data mining. The Materials Project also seeks to create open-source platforms for developing robust, sophisticated materials analyses. Future efforts will enable users to perform rapid-prototyping'' of new materials in silico, and provide researchers with new avenues for cost-effective, data-driven materials design. (c) 2013 American Institute of Physics.
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54. 54
  Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50 (24), 17953– 17979, DOI: 10.1103/PhysRevB.50.17953
  54
  Projector augmented-wave method
  Blochl
  Physical review. B, Condensed matter (1994), 50 (24), 17953-17979 ISSN:0163-1829.
  There is no expanded citation for this reference.
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55. 55
  Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54 (16), 11169– 11186, DOI: 10.1103/PhysRevB.54.11169
  55
  Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
  Kresse, G.; Furthmueller, J.
  Physical Review B: Condensed Matter (1996), 54 (16), 11169-11186CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The authors present an efficient scheme for calcg. the Kohn-Sham ground state of metallic systems using pseudopotentials and a plane-wave basis set. In the first part the application of Pulay's DIIS method (direct inversion in the iterative subspace) to the iterative diagonalization of large matrixes will be discussed. This approach is stable, reliable, and minimizes the no. of order Natoms3 operations. In the second part, we will discuss an efficient mixing scheme also based on Pulay's scheme. A special "metric" and a special "preconditioning" optimized for a plane-wave basis set will be introduced. Scaling of the method will be discussed in detail for non-self-consistent and self-consistent calcns. It will be shown that the no. of iterations required to obtain a specific precision is almost independent of the system size. Altogether an order Natoms2 scaling is found for systems contg. up to 1000 electrons. If we take into account that the no. of k points can be decreased linearly with the system size, the overall scaling can approach Natoms. They have implemented these algorithms within a powerful package called VASP (Vienna ab initio simulation package). The program and the techniques have been used successfully for a large no. of different systems (liq. and amorphous semiconductors, liq. simple and transition metals, metallic and semiconducting surfaces, phonons in simple metals, transition metals, and semiconductors) and turned out to be very reliable.
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56. 56
  Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59 (3), 1758– 1775, DOI: 10.1103/PhysRevB.59.1758
  56
  From ultrasoft pseudopotentials to the projector augmented-wave method
  Kresse, G.; Joubert, D.
  Physical Review B: Condensed Matter and Materials Physics (1999), 59 (3), 1758-1775CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  The formal relationship between ultrasoft (US) Vanderbilt-type pseudopotentials and Blochl's projector augmented wave (PAW) method is derived. The total energy functional for US pseudopotentials can be obtained by linearization of two terms in a slightly modified PAW total energy functional. The Hamilton operator, the forces, and the stress tensor are derived for this modified PAW functional. A simple way to implement the PAW method in existing plane-wave codes supporting US pseudopotentials is pointed out. In addn., crit. tests are presented to compare the accuracy and efficiency of the PAW and the US pseudopotential method with relaxed-core all-electron methods. These tests include small mols. (H2, H2O, Li2, N2, F2, BF3, SiF4) and several bulk systems (diamond, Si, V, Li, Ca, CaF2, Fe, Co, Ni). Particular attention is paid to the bulk properties and magnetic energies of Fe, Co, and Ni.
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57. 57
  Perdew, J. P.; Ernzerhof, M.; Burke, K. Rationale for Mixing Exact Exchange with Density Functional Approximations. J. Chem. Phys. 1996, 105 (22), 9982– 9985, DOI: 10.1063/1.472933
  57
  Rationale for mixing exact exchange with density functional approximations
  Perdew, John P.; Ernzerhof, Matthias; Burke, Kieron
  Journal of Chemical Physics (1996), 105 (22), 9982-9985CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  D. functional approxns. for the exchange-correlation energy ExcDFA of an electronic system are often improved by admixing some exact exchange Ex: Exc ≈ ExcDFA + (1/n)(Ex - ExDFA). This procedure is justified when the error in ExcDFA arises from the λ = 0 or exchange end of the coupling-const. integral ∫01dλ Exc,λDFA. We argue that the optimum integer n is approx. the lowest order of Goerling-Levy perturbation theory which provides a realistic description of the coupling-const. dependence Exc,λ in the range 0 ≤ λ ≤ 1, whence n ≈ 4 for atomization energies of typical mols. We also propose a continuous generalization of n as an index of correlation strength, and a possible mixing of second-order perturbation theory with the generalized gradient approxn.
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58. 58
  Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110 (13), 6158– 6170, DOI: 10.1063/1.478522
  58
  Toward reliable density functional methods without adjustable parameters: the PBE0 model
  Adamo, Carlo; Barone, Vincenzo
  Journal of Chemical Physics (1999), 110 (13), 6158-6170CODEN: JCPSA6; ISSN:0021-9606. (American Institute of Physics)
  We present an anal. of the performances of a parameter free d. functional model (PBE0) obtained combining the so called PBE generalized gradient functional with a predefined amt. of exact exchange. The results obtained for structural, thermodn., kinetic and spectroscopic (magnetic, IR and electronic) properties are satisfactory and not far from those delivered by the most reliable functionals including heavy parameterization. The way in which the functional is derived and the lack of empirical parameters fitted to specific properties make the PBE0 model a widely applicable method for both quantum chem. and condensed matter physics.
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59. 59
  Skone, J. H.; Govoni, M.; Galli, G. Self-Consistent Hybrid Functional for Condensed Systems. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 89 (19), 195112, DOI: 10.1103/PhysRevB.89.195112
  There is no corresponding record for this reference.
60. 60
  Gerosa, M.; Bottani, C. E.; Caramella, L.; Onida, G.; Di Valentin, C.; Pacchioni, G. Electronic Structure and Phase Stability of Oxide Semiconductors: Performance of Dielectric-Dependent Hybrid Functional DFT, Benchmarked against GW Band Structure Calculations and Experiments. Phys. Rev. B: Condens. Matter Mater. Phys. 2015, 91 (15), 155201, DOI: 10.1103/PhysRevB.91.155201
  There is no corresponding record for this reference.
61. 61
  Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces. Phys. Rev. Lett. 2008, 100 (13), 136406, DOI: 10.1103/PhysRevLett.100.136406
  61
  Restoring the Density-Gradient Expansion for Exchange in Solids and Surfaces
  Perdew, John P.; Ruzsinszky, Adrienn; Csonka, Gabor I.; Vydrov, Oleg A.; Scuseria, Gustavo E.; Constantin, Lucian A.; Zhou, Xiaolan; Burke, Kieron
  Physical Review Letters (2008), 100 (13), 136406/1-136406/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  Popular modern generalized gradient approxns. are biased toward the description of free-atom energies. Restoration of the first-principles gradient expansion for exchange over a wide range of d. gradients eliminates this bias. We introduce a revised Perdew-Burke-Ernzerhof generalized gradient approxn. that improves equil. properties of densely packed solids and their surfaces.
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62. 62
  Tran, F. On the Accuracy of the Non-Self-Consistent Calculation of the Electronic Structure of Solids with Hybrid Functionals. Phys. Lett. A 2012, 376 (6–7), 879– 882, DOI: 10.1016/j.physleta.2012.01.022
  There is no corresponding record for this reference.
63. 63
  Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P. Electron-Energy-Loss Spectra and the Structural Stability of Nickel Oxide: An LSDA+U Study. Phys. Rev. B: Condens. Matter Mater. Phys. 1998, 57 (3), 1505– 1509, DOI: 10.1103/PhysRevB.57.1505
  63
  Electron-energy-loss spectra and the structural stability of nickel oxide: An LSDA+U study
  Dudarev, S. L.; Botton, G. A.; Savrasov, S. Y.; Humphreys, C. J.; Sutton, A. P.
  Physical Review B: Condensed Matter and Materials Physics (1998), 57 (3), 1505-1509CODEN: PRBMDO; ISSN:0163-1829. (American Physical Society)
  By taking better account of electron correlations in the 3d shell of metal ions in Ni oxide it is possible to improve the description of both electron energy loss spectra and parameters characterizing the structural stability of the material compared with local spin d. functional theory.
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64. 64
  Tasker, P. W. The Stability of Ionic Crystal Surfaces. J. Phys. C Solid State Phys. 1979, 12 (22), 4977– 4984, DOI: 10.1088/0022-3719/12/22/036
  64
  The stability of ionic crystal surfaces
  Tasker, P. W.
  Journal of Physics C: Solid State Physics (1979), 12 (22), 4977-84CODEN: JPSOAW; ISSN:0022-3719.
  For ionic crystals with a dipole moment in the repeat unit perpendicular to the surface, the lattice sums of the electrostatic energy diverge and the calcd. surface energy is infinite. The cause of this divergence is demonstrated and the surfaces of ionic or partly ionic materials are classified into 3 types. Type 1 is neutral with equal nos. of anions and cations on each plane, whereas type 2 is charged, but there is no dipole moment perpendicular to the surface because of the sym. stacking sequence. Both these surfaces have modest surface energies and are stable with only limited relaxations of the surface ions. The type 3 surface is charged and has a dipole moment in the repeat unit perpendicular to the surface and this surface can only be stabilized by substantial reconstruction.
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65. 65
  Hinuma, Y.; Pizzi, G.; Kumagai, Y.; Oba, F.; Tanaka, I. Band Structure Diagram Paths Based on Crystallography. Comput. Mater. Sci. 2017, 128, 140– 184, DOI: 10.1016/j.commatsci.2016.10.015
  65
  Band structure diagram paths based on crystallography
  Hinuma, Yoyo; Pizzi, Giovanni; Kumagai, Yu; Oba, Fumiyasu; Tanaka, Isao
  Computational Materials Science (2017), 128 (), 140-184CODEN: CMMSEM; ISSN:0927-0256. (Elsevier B.V.)
  Systematic and automatic calcns. of the electronic band structure are a crucial component of computationally-driven high-throughput materials screening. An algorithm, for any crystal, to derive a unique description of the crystal structure together with a recommended band path is indispensable for this task. The electronic band structure is typically sampled along a path within the first Brillouin zone including the surface in reciprocal space. Some points in reciprocal space have higher site symmetries and/or have higher constraints than other points regarding the electronic band structure and therefore are likely to be more important than other points. This work categorizes points in reciprocal space according to their symmetry and provides recommended band paths that cover all special wavevector (k-vector) points and lines necessarily and sufficiently. Points in reciprocal space are labeled such that there is no conflict with the crystallog. convention. The k-vector coeffs. of labeled points, which are located at Brillouin zone face and edge centers as well as vertices, are derived based on a primitive cell compatible with the crystallog. convention, including those with axial ratio-dependent coordinates. Furthermore, we provide an open-source implementation of the algorithms within our SeeK-path python code, to allow researchers to obtain k-vector coeffs. and recommended band paths in an automated fashion. Finally, we created a free online service to compute and visualize the first Brillouin zone, labeled k-points and suggested band paths for any crystal structure, that we made available at http://www.materialscloud.org/tools/seekpath/.
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66. 66
  Togo, A.; Tanaka, I. Spglib: A Software Library for Crystal Symmetry Search. arXiv 2018, arXiv:1808.01590, [cond-mat.mtrl-sci] DOI: 10.48550/arXiv.1808.01590
  There is no corresponding record for this reference.
67. 67
  Bartók, A. P.; Kermode, J.; Bernstein, N.; Csányi, G. Machine Learning a General-Purpose Interatomic Potential for Silicon. Phys. Rev. X 2018, 8 (4), 041048, DOI: 10.1103/PhysRevX.8.041048
  67
  Machine Learning a General-Purpose Interatomic Potential for Silicon
  Bartok, Albert P.; Kermode, James; Bernstein, Noam; Csanyi, Gabor
  Physical Review X (2018), 8 (4), 041048CODEN: PRXHAE; ISSN:2160-3308. (American Physical Society)
  The success of first-principles electronic-structure calcn. for predictive modeling in chem., solid-state physics, and materials science is constrained by the limitations on simulated length scales and timescales due to the computational cost and its scaling. Techniques based on machine-learning ideas for interpolating the Born-Oppenheimer potential energy surface without explicitly describing electrons have recently shown great promise, but accurately and efficiently fitting the phys. relevant space of configurations remains a challenging goal. Here, we present a Gaussian approxn. potential for silicon that achieves this milestone, accurately reproducing d.-functional-theory ref. results for a wide range of observable properties, including crystal, liq., and amorphous bulk phases, as well as point, line, and plane defects. We demonstrate that this new potential enables calcns. such as finite-temp. phase-boundary lines, self-diffusivity in the liq., formation of the amorphous by slow quench, and dynamic brittle fracture, all of which are very expensive with a first-principles method. We show that the uncertainty quantification inherent to the Gaussian process regression framework gives a qual. est. of the potential's accuracy for a given at. configuration. The success of this model shows that it is indeed possible to create a useful machine-learning-based interat. potential that comprehensively describes a material on the at. scale and serves as a template for the development of such models in the future.
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68. 68
  De, S.; Bartók, A. P.; Csányi, G.; Ceriotti, M. Comparing Molecules and Solids across Structural and Alchemical Space. Phys. Chem. Chem. Phys. 2016, 18 (20), 13754– 13769, DOI: 10.1039/C6CP00415F
  68
  Comparing molecules and solids across structural and alchemical space
  De, Sandip; Bartok, Albert P.; Csanyi, Gabor; Ceriotti, Michele
  Physical Chemistry Chemical Physics (2016), 18 (20), 13754-13769CODEN: PPCPFQ; ISSN:1463-9076. (Royal Society of Chemistry)
  Evaluating the (dis)similarity of cryst., disordered and mol. compds. is a crit. step in the development of algorithms to navigate automatically the configuration space of complex materials. For instance, a structural similarity metric is crucial for classifying structures, searching chem. space for better compds. and materials, and driving the next generation of machine-learning techniques for predicting the stability and properties of mols. and materials. In the last few years several strategies have been designed to compare at. coordination environments. In particular, the smooth overlap of at. positions (SOAPs) has emerged as an elegant framework to obtain translation, rotation and permutation-invariant descriptors of groups of atoms, underlying the development of various classes of machine-learned inter-at. potentials. Here we discuss how one can combine such local descriptors using a regularized entropy match (REMatch) approach to describe the similarity of both whole mol. and bulk periodic structures, introducing powerful metrics that enable the navigation of alchem. and structural complexities within a unified framework. Furthermore, using this kernel and a ridge regression method we can predict atomization energies for a database of small org. mols. with a mean abs. error below 1 kcal mol-1, reaching an important milestone in the application of machine-learning techniques for the evaluation of mol. properties.
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69. 69
  Kingma, D. P.; Ba, J. Adam: A Method for Stochastic Optimization. arXiv, 2016, arXiv:1412.6980[cs.LG] DOI: 10.48550/arXiv.1412.6980 .
  There is no corresponding record for this reference.
70. 70
  Jaouen, T.; Jézéquel, G.; Delhaye, G.; Lépine, B.; Turban, P.; Schieffer, P. Work Function Shifts, Schottky Barrier Height, and Ionization Potential Determination of Thin MgO Films on Ag (001). Appl. Phys. Lett. 2010, 97 (23), 232104, DOI: 10.1063/1.3525159
  70
  Work function shifts, Schottky barrier height, and ionization potential determination of thin MgO films on Ag(001)
  Jaouen, T.; Jezequel, G.; Delhaye, G.; Lepine, B.; Turban, P.; Schieffer, P.
  Applied Physics Letters (2010), 97 (23), 232104/1-232104/3CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  The electronic band structure and the work function of MgO thin films epitaxially grown on Ag(001) were investigated using x-ray and UPS for various oxide thicknesses. The deposition of thin MgO films on Ag(001) induces a strong diminution in the metal work function. The p-type Schottky barrier height is const. at 3.85 ± 0.10 eV above 2 MgO monolayers and the exptl. value of the ionization potential is 7.15 ± 0.15 eV. Our results are well consistent with the description of the Schottky barrier height in terms of the Schottky-Mott model cor. by an MgO-induced polarization effect. (c) 2010 American Institute of Physics.
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71. 71
  Roessler, D. M.; Walker, W. C. Electronic Spectrum and Ultraviolet Optical Properties of Crystalline MgO. Phys. Rev. 1967, 159 (3), 733– 738, DOI: 10.1103/PhysRev.159.733
  71
  Electronic spectrum and ultraviolet optical properties of crystalline magnesium oxide
  Roessler, David M.; Walker, William Charles
  Physical Review (1967), 159 (3), 733-8CODEN: PHRVAO; ISSN:0031-899X.
  The electronic spectrum of single-crystal MgO, i.e., the real (ε1) and imaginary (ε2) parts of the dielec. response, has been obtained over the region 5-28 ev. from normal-incidence reflectance spectra. Measurements were made on freshly cleaved crystals over the entire region at 295°K. and at 5-11.5 ev. and 77°K. Structure in ε2 was observed near 7.7, 10.8, 13.3, 16.8, 17.3, and 20.5 ev. The first peak, which was a doublet with components at 7.69 ± 0.01 and 7.76 ± 0.01 ev., was attributed to the Γ3/2 and Γ1/2 spin-orbit split exciton. A Lorentzian fit to the exciton components gave oscillator strengths of 0.035 and 0.017 per mol., resp. Subtraction of the exciton structure from the remaining interband structure gave a direct interband edge at 7.77 ± 0.01 ev. A large plasma peak was observed in the energy-loss function near 22 ev., in agreement with recent energy-loss expts. The remaining structure was attributed to interband transitions and will be discussed in terms of recent pseudopotential band-structure calcns. 24 references.
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72. 72
  Käämbre, H. A comment on “The Effective Electron Affinity Estimation from the Simultaneous Detection of Thermally Stimulated Luminescence and Exoelectronic Emission. Application to an α-Alumina Single Crystal”. J. Phys. D Appl. Phys. 1997, 30, 1961– 1962, DOI: 10.1088/0022-3727/30/13/019
  There is no corresponding record for this reference.
73. 73
  Innocenzi, M. E.; Swimm, R. T.; Bass, M.; French, R. H.; Villaverde, A. B.; Kokta, M. R. Room-Temperature Optical Absorption in Undoped α-Al₂O₃. J. Appl. Phys. 1990, 67 (12), 7542– 7546, DOI: 10.1063/1.345817
  There is no corresponding record for this reference.
74. 74
  Kashiwaya, S.; Morasch, J.; Streibel, V.; Toupance, T.; Jaegermann, W.; Klein, A. The Work Function of TiO₂. Surfaces 2018, 1 (1), 73– 89, DOI: 10.3390/surfaces1010007
  There is no corresponding record for this reference.
75. 75
  Meyer, J.; Hamwi, S.; Kröger, M.; Kowalsky, W.; Riedl, T.; Kahn, A. Transition Metal Oxides for Organic Electronics: Energetics, Device Physics and Applications. Adv. Mater. 2012, 24 (40), 5408– 5427, DOI: 10.1002/adma.201201630
  75
  Transition Metal Oxides for Organic Electronics: Energetics, Device Physics and Applications
  Meyer, Jens; Hamwi, Sami; Kroeger, Michael; Kowalsky, Wolfgang; Riedl, Thomas; Kahn, Antoine
  Advanced Materials (Weinheim, Germany) (2012), 24 (40), 5408-5427CODEN: ADVMEW; ISSN:0935-9648. (Wiley-VCH Verlag GmbH & Co. KGaA)
  A review. During the last few years, transition metal oxides (TMO) such as molybdenum tri-oxide (MoO3), vanadium pent-oxide (V2O5) or tungsten tri-oxide (WO3) were extensively studied because of their exceptional electronic properties for charge injection and extn. in org. electronic devices. These unique properties led to the performance enhancement of several types of devices and to a variety of novel applications. TMOs were used to realize efficient and long-term stable p-type doping of wide band gap org. materials, charge-generation junctions for stacked org. light emitting diodes (OLED), sputtering buffer layers for semi-transparent devices, and org. photovoltaic (OPV) cells with improved charge extn., enhanced power conversion efficiency and substantially improved long term stability. Energetics in general play a key role in advancing device structure and performance in org. electronics; however, the literature provides a very inconsistent picture of the electronic structure of TMOs and the resulting interpretation of their role as functional constituents in org. electronics. With this review the authors intend to clarify some of the existing misconceptions. An overview of TMO-based device architectures ranging from transparent OLEDs to tandem OPV cells is also given. Various TMO film deposition methods are reviewed, addressing vacuum evapn. and recent approaches for soln.-based processing. The specific properties of the resulting materials and their role as functional layers in org. devices are discussed.
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76. 76
  Chu, C.-Y.; Huang, M. H. Facet-Dependent Photocatalytic Properties of Cu₂O Crystals Probed by Using Electron, Hole and Radical Scavengers. J. Mater. Chem. A 2017, 5 (29), 15116– 15123, DOI: 10.1039/C7TA03848H
  There is no corresponding record for this reference.
77. 77
  Jacobi, K.; Zwicker, G.; Gutmann, A. Work Function, Electron Affinity and Band Bending of Zinc Oxide Surfaces. Surf. Sci. 1984, 141 (1), 109– 125, DOI: 10.1016/0039-6028(84)90199-7
  77
  Work function, electron affinity and band bending of zinc oxide surfaces
  Jacobi, K.; Zwicker, G.; Gutmann, A.
  Surface Science (1984), 141 (1), 109-25CODEN: SUSCAS; ISSN:0039-6028.
  (000‾1)O, (10‾10) and (0001) Zn faces of ZnO were prepd. by Ar-ion bombardment and annealing at 700 K ((000‾1) and (0001)) and 825 K (10‾10). Work function, electron affinity and band bending were evaluated by using angle-resolved UPS. All quantities show time-dependent changes specific for each face. These changes are interpreted by assuming O diffusion from the surface layer into near-surface bulk vacancies. This process initiates a redistribution of O-derived states at the valence band max.
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78. 78
  Mönch, W. Semiconductor Surfaces and Interfaces, 3rd ed.; Springer Series in Surface Sciences; Springer Berlin Heidelberg: Berlin, Heidelberg, 2001; Vol. 26.
  There is no corresponding record for this reference.
79. 79
  McLeod, J. A.; Wilks, R. G.; Skorikov, N. A.; Finkelstein, L. D.; Abu-Samak, M.; Kurmaev, E. Z.; Moewes, A. Band Gaps and Electronic Structure of Alkaline-Earth and Post-Transition-Metal Oxides. Phys. Rev. B: Condens. Matter Mater. Phys. 2010, 81 (24), 245123, DOI: 10.1103/PhysRevB.81.245123
  There is no corresponding record for this reference.
80. 80
  Swinnich, E.; Hasan, M. N.; Zeng, K.; Dove, Y.; Singisetti, U.; Mazumder, B.; Seo, J. H. Flexible β-Ga₂O₃ Nanomembrane Schottky Barrier Diodes. Adv. Electron. Mater. 2019, 5 (3), 1– 8, DOI: 10.1002/aelm.201800714
  There is no corresponding record for this reference.
81. 81
  Mohamed, M.; Irmscher, K.; Janowitz, C.; Galazka, Z.; Manzke, R.; Fornari, R. Schottky Barrier Height of Au on the Transparent Semiconducting Oxide β-Ga₂O₃. Appl. Phys. Lett. 2012, 101 (13), 132106, DOI: 10.1063/1.4755770
  81
  Schottky barrier height of Au on the transparent semiconducting oxide β-Ga2O3
  Mohamed, M.; Irmscher, K.; Janowitz, C.; Galazka, Z.; Manzke, R.; Fornari, R.
  Applied Physics Letters (2012), 101 (13), 132106/1-132106/5CODEN: APPLAB; ISSN:0003-6951. (American Institute of Physics)
  The Schottky barrier height of Au deposited on (100) surfaces of n-type β-Ga2O3 single crystals was detd. by current-voltage characteristics and high-resoln. photoemission spectroscopy resulting in a common effective value of 1.04 ± 0.08 eV. Furthermore, the electron affinity of β-Ga2O3 and the work function of Au were detd. to be 4.00 ± 0.05 eV and 5.23 ± 0.05 eV, resp., yielding a barrier height of 1.23 eV according to the Schottky-Mott rule. The redn. of the Schottky-Mott barrier to the effective value was ascribed to the image-force effect and the action of metal-induced gap states, whereas extrinsic influences could be avoided. (c) 2012 American Institute of Physics.
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82. 82
  Kröger, M.; Hamwi, S.; Meyer, J.; Riedl, T.; Kowalsky, W.; Kahn, A. P-Type Doping of Organic Wide Band Gap Materials by Transition Metal Oxides: A Case-Study on Molybdenum Trioxide. Org. Electron. 2009, 10 (5), 932– 938, DOI: 10.1016/j.orgel.2009.05.007
  82
  P-type doping of organic wide band gap materials by transition metal oxides: A case-study on Molybdenum trioxide
  Kroger, Michael; Hamwi, Sami; Meyer, Jens; Riedl, Thomas; Kowalsky, Wolfgang; Kahn, Antoine
  Organic Electronics (2009), 10 (5), 932-938CODEN: OERLAU; ISSN:1566-1199. (Elsevier B.V.)
  A study on p-doping of org. wide band gap materials with Molybdenum trioxide using current transport measurements, UPS and inverse photoelectron spectroscopy is presented. When MoO3 is co-evapd. with 4,4'-Bis(N-carbazolyl)-1,1'-biphenyl (CBP), a significant increase in cond. is obsd., compared to intrinsic CBP thin films. This increase in cond. is due to electron transfer from the HOMO of the host mols. to very low lying unfilled states of embedded Mo3O9 clusters. The energy levels of these clusters are estd. by the energy levels of a neat MoO3 thin film with a work function of 6.86 eV, an electron affinity of 6.7 eV and an ionization energy of 9.68 eV. The Fermi level of MoO3-doped CBP and N,N'-bis(1-naphthyl)-N,N'-diphenyl-1,1'-biphenyl-4,4'-diamine (α-NPD) thin films rapidly shifts with increasing doping concn. towards the occupied states. Pinning of the Fermi level several 100 meV above the HOMO edge is obsd. for doping concns. higher than 2 mol% and is explained in terms of a Gaussian d. of HOMO states. We det. a relatively low dopant activation of ∼0.5%, which is due to Coulomb-trapping of hole carriers at the ionized dopant sites.
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83. 83
  Greiner, M. T.; Helander, M. G.; Tang, W.-M.; Wang, Z.-B.; Qiu, J.; Lu, Z.-H. Universal Energy-Level Alignment of Molecules on Metal Oxides. Nat. Mater. 2012, 11 (1), 76– 81, DOI: 10.1038/nmat3159
  83
  Universal energy-level alignment of molecules on metal oxides
  Greiner, Mark T.; Helander, Michael G.; Tang, Wing-Man; Wang, Zhi-Bin; Qiu, Jacky; Lu, Zheng-Hong
  Nature Materials (2012), 11 (1), 76-81CODEN: NMAACR; ISSN:1476-1122. (Nature Publishing Group)
  Transition-metal oxides improve power conversion efficiencies in org. photovoltaics and are used as low-resistance contacts in org. light-emitting diodes and org. thin-film transistors. What makes metal oxides useful in these technologies is the fact that their chem. and electronic properties can be tuned to enable charge exchange with a wide variety of org. mols. Although it is known that charge exchange relies on the alignment of donor and acceptor energy levels, the mechanism for level alignment remains under debate. Here, we conclusively establish the principle of energy alignment between oxides and mols. We observe a universal energy-alignment trend for a set of transition metal oxides-representing a broad diversity in electronic properties-with several org. semiconductors. The trend demonstrates that, despite the variance in their electronic properties, oxide energy alignment is governed by one driving force: electron-chem. potential equilibration. Using a combination of simple thermodn., electrostatics and Fermi statistics we derive a math. relation that describes the alignment.
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84. 84
  Lei, Y.; Lu, X. The Decisive Effect of Interface States on the Photocatalytic Activity of the Silver(I) Oxide/Titanium Dioxide Heterojunction. J. Colloid Interface Sci. 2017, 492, 167– 175, DOI: 10.1016/j.jcis.2017.01.001
  There is no corresponding record for this reference.
85. 85
  Hohmann, M. V.; Ágoston, P.; Wachau, A.; Bayer, T. J. M.; Brötz, J.; Albe, K.; Klein, A. Orientation Dependent Ionization Potential of In₂O₃: A Natural Source for Inhomogeneous Barrier Formation at Electrode Interfaces in Organic Electronics. J. Phys.: Condens. Matter 2011, 23 (33), 334203, DOI: 10.1088/0953-8984/23/33/334203
  85
  Orientation dependent ionization potential of In2O3: a natural source for inhomogeneous barrier formation at electrode interfaces in organic electronics
  Hohmann, Mareike V.; Agoston, Peter; Wachau, Andre; Bayer, Thorsten J. M.; Broetz, Joachim; Albe, Karsten; Klein, Andreas
  Journal of Physics: Condensed Matter (2011), 23 (33), 334203/1-334203/8CODEN: JCOMEL; ISSN:0953-8984. (Institute of Physics Publishing)
  The ionization potentials of In2O3 films grown epitaxially by magnetron sputtering on Y-stabilized ZrO2 substrates with (100) and (111) surface orientation are detd. using photoelectron spectroscopy. Epitaxial growth is verified using x-ray diffraction. The obsd. ionization potentials, which directly affect the work functions, are in good agreement with ab initio calcns. using d. functional theory. While the (111) surface exhibits a stable surface termination with an ionization potential of ∼7.0 eV, the surface termination and the ionization potential of the (100) surface depend strongly on the oxygen chem. potential. With the given deposition conditions an ionization potential of ∼7.7 eV is obtained, which is attributed to a surface termination stabilized by oxygen dimers. This orientation dependence also explains the lower ionization potentials obsd. for In2O3 compared to Sn-doped In2O3 (ITO). Due to the orientation dependent ionization potential, a polycryst. ITO film will exhibit a laterally varying work function, which results in an inhomogeneous charge injection into org. semiconductors when used as electrode material. The variation of work function will become even more pronounced when oxygen plasma or UV-ozone treatments are performed, as an oxidn. of the surface is only possible for the (100) surface. The influence of the deposition technique on the formation of stable surface terminations is also discussed.
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86. 86
  Walsh, A.; Da Silva, J. L. F.; Wei, S.-H.; Körber, C.; Klein, A.; Piper, L. F. J.; DeMasi, A.; Smith, K. E.; Panaccione, G.; Torelli, P.; Payne, D. J.; Bourlange, A.; Egdell, R. G. Nature of the Band Gap of In₂O₃ Revealed by First-Principles Calculations and X-Ray Spectroscopy. Phys. Rev. Lett. 2008, 100 (16), 167402, DOI: 10.1103/PhysRevLett.100.167402
  86
  Nature of the Band Gap of In2O3 Revealed by First-Principles Calculations and X-Ray Spectroscopy
  Walsh, Aron; Da Silva, Juarez L. F.; Wei, Su-Huai; Korber, C.; Klein, A.; Piper, L. F. J.; DeMasi, Alex; Smith, Kevin E.; Panaccione, G.; Torelli, P.; Payne, D. J.; Bourlange, A.; Egdell, R. G.
  Physical Review Letters (2008), 100 (16), 167402/1-167402/4CODEN: PRLTAO; ISSN:0031-9007. (American Physical Society)
  Bulk and surface sensitive x-ray spectroscopic techniques are applied in tandem to show that the valence band edge for In2O3 is found significantly closer to the bottom of the conduction band than expected from the widely quoted bulk band gap of 3.75 eV. First-principles theory shows that the upper valence bands of In2O3 exhibit a small dispersion and the conduction band min. is positioned at Γ. However, direct optical transitions give a minimal dipole intensity until 0.8 eV below the valence band max. The results set an upper limit on the fundamental band gap of 2.9 eV.
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87. 87
  Wardenga, H. F. Surface Potentials of Ceria and Their Influence on the Surface Exchange of Oxygen; Technische Universität Darmstadt: Darmstadt, Germany, 2019.
  There is no corresponding record for this reference.
88. 88
  Meyer, J.; Kröger, M.; Hamwi, S.; Gnam, F.; Riedl, T.; Kowalsky, W.; Kahn, A. Charge Generation Layers Comprising Transition Metal-Oxide/Organic Interfaces: Electronic Structure and Charge Generation Mechanism. Appl. Phys. Lett. 2010, 96 (19), 1– 4, DOI: 10.1063/1.3427430
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Supporting Information
Supporting Information
The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/jacs.3c13574.
- RMSE and MAE of all the considered combinations of the SOAP hyperparameters; profile of the weights from the attention layer; transfer learning versus learning from scratch; theoretical and predicted IPs and EAs for the ternary data sets; convergence of IPs, EAs, and surface energies; learning curve for IPs; prediction accuracies; 134 prototypical binary oxides and surface orientation; PAW datasets and Hubbard U parameters; and hyperparameters of the simple-ANN (PDF)
- Theoretical IPs and EAs of the 2195 binary and 718 ternary oxide surfaces and related properties. Database contains the index, system (binary or ternary), chemical formula, space group number, Miller index, surface energy, IP, EA, and band gap (bulk) (XLSX)
- Supercells before and after structural optimization for the 2195 binary and 718 ternary oxide surfaces (ZIP)
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Band Alignment of Oxides by Learnable Structural-Descriptor-Aided Neural Network and Transfer LearningClick to copy article linkArticle link copied!

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High-Throughput First-Principles Calculations of IPs and EAs of Binary Oxides

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Construction of ANN Models

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Extension of SOAPs and Application to Ternary Oxides

Figure 6

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Methods

Screening of First-Principles Calculation Data: Binary Oxides

Ternary Oxides

First-Principles Calculations of Band Positions

Computational Procedures for Bulk Systems

Computational Procedures for Surfaces

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Machine Learning: SOAP Descriptors

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Band Alignment of Oxides by Learnable Structural-Descriptor-Aided Neural Network and Transfer Learning
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