p–d coupling: prerequisite for band-like doping levels in metal oxides

Abstract

Identifying the prerequisite of inducing band-like doping levels in wide bandgap metal oxides is a crucial yet open question. Herein, taking boron (B) and nitrogen (N) codoped anatase TiO₂ as an example and combining density functional theory calculation with machine learning, it has been revealed that the band-like doping levels mainly originate from a strong p–d coupling between O/N-p_π and Ti-t_2g orbitals. Significantly, the existence of strong p–d coupling is an intrinsic characteristic of anatase TiO₂ determined entirely by crystal symmetry, which can be used as a universal criterion to predict whether band-like doping levels can be induced in other metal oxides, and the criterion has been fully verified on rutile and brookite TiO₂, ScTaO₄, WO₃, SnO₂ and MgTa₂O₆. Besides, the strong p–d coupling offers a theoretical basis for the long-held empirical understanding that uniform doping is important in achieving stronger visible light absorption for wide bandgap metal oxide photocatalysts. Overall, the uncovered strong p–d coupling provides a simple yet profound guideline for bandgap engineering of metal oxides.

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Introduction

Narrowing the bandgap of wide bandgap metal oxides is highly desirable for many metal oxide related applications.^1–3 For instance, it is crucial for harvesting light over a broader spectrum and achieving suitable band edge positions for photocatalysis⁴ and optoelectronic applications.⁵ A widely used approach for bandgap narrowing is non-metal doping,^6,7 particularly nitrogen (N) doping,^8–10 since N doping induces doping levels above the valence band maximum (VBM) of metal oxides. Ideally, band-like doping levels with strong dispersion and significant overlap with the VBM are indispensable for band-to-band redshift of the absorption edge⁸ as well as fast charge carrier transport¹¹ of metal oxides. However, the N doping levels are normally localized within the bandgap due to typically low N doping concentrations.^12–17 Increasing the N doping concentrations may only result in multiple localized doping levels with different energy,^18–20 meanwhile aggravating the formation of charge trapping centers such as oxygen vacancy.^13,21–23

Nevertheless, the emergence of red TiO₂ has gone beyond this traditional understanding.^24,25 Specifically, by gradient boron (B) and nitrogen (N) codoping, the first red anatase TiO₂ with a bandgap value of about 2 eV was obtained,²⁴ which exhibits a band-to-band redshift of the light absorption edge compared with pristine anatase TiO₂. Advancing from gradient to uniform doping,²⁵ the photocatalytic oxygen evolution activity of red anatase TiO₂ has been substantially increased, implying a much higher hole mobility contributed by band-like doping levels. Considering the fact that the atomic ratio of N to Ti is only about 5% in red anatase TiO₂,²⁵ it is much lower than the N content in oxynitrides. However, the bandgap value of anatase TiO₂ can still be substantially narrowed from 3.2 to about 2 eV, which is similar to that of oxynitrides.²⁶ This suggests the existence of certain intrinsic character allowing for band-like doping levels at a low N-doping concentration in anatase TiO₂.

Elucidating this intrinsic character necessitates the identification of characteristic B/N-codoping configurations featuring band-like doping levels, which are likely to exhibit the most significant bandgap narrowing among all configurations due to the large energy level broadening of band-like doping levels. Although the bandgap can also be narrowed by localized doping levels related to direct bonding between N dopants,²⁷ this can be easily excluded by scrutinizing the band structures. Therefore, calculating the bandgap values for all possible B/N-codoping configurations in anatase TiO₂ is the precondition to efficiently and accurately identify those configurations featuring band-like doping levels. However, to reproduce the experimental doping level (N : Ti ≈ 5 at%)²⁴ as closely as possible and maintain the charge balance, one needs to substitute three lattice O atoms with three N atoms and introduce one additional interstitial B atom in a 3 × 3 × 1 anatase TiO₂ supercell (N : Ti = 8.33 at%), resulting in a total of 8144 symmetrically inequivalent B/N-codoping configurations. This makes the calculation of bandgap values for all these configurations far beyond the capability of conventional density functional theory (DFT) calculations. Thus, previous studies have only been able to consider a few specific configurations based on researchers' individual intuition and/or expertise.^24,28,29 Consequently, the intrinsic character of anatase TiO₂ allowing band-like doping levels has remained elusive over the past two decades.

Different from conventional DFT calculations, the machine learning (ML)^30–35 methods offer a promising solution to accurately and efficiently predict the bandgap values of all B/N-codoping configurations in anatase TiO₂. Since applying the ML methods requires each B/N-codoping configuration to be represented by a fixed-length array, termed structure descriptor, in this work, we first proposed an accurate structure descriptor, and then trained a highly accurate ML model for predicting the bandgap values of all B/N-codoping configurations in anatase TiO₂. Based on the ML predictions, B/N-codoping configurations with band-like doping levels were identified, and thorough analysis revealed that the existence of strong p–d coupling between O/N-p_π and Ti-t_2g orbitals in anatase TiO₂ is essential for inducing band-like doping levels. Since the existence of strong p–d coupling is entirely determined by crystal symmetry, we further generalized it as a universal criterion to predict whether band-like doping levels can be induced in other metal oxides, and the criterion has been fully verified on rutile and brookite TiO₂, ScTaO₄, WO₃, SnO₂ and MgTa₂O₆.

Results

The application of ML methods requires each B/N-codoping configuration in anatase TiO₂ to be represented by a structure descriptor, and the accuracy of ML prediction is largely determined by whether the structure descriptors can accurately differentiate B/N-codoping configurations. Therefore, we first proposed a novel approach for structure descriptor construction based on a concept of charge transfer path.³⁶ As detailed in the ESI (Fig. S1),† each B/N-codoping configuration in anatase TiO₂ can be represented by a 168-dimensional structure descriptor, and in combination with DFT calculations, a highly accurate XGBoost regression model³⁷ has been successfully trained to predict the bandgap values of all B/N-codoping configurations in anatase TiO₂ (Fig. S2†).

Based on the ML prediction, 20 B/N-codoping configurations with the most significant bandgap narrowing have been identified, which exhibit distinctive periodic features of dopant spatial orderings. Specifically, all three N dopants are located on the same (010) atomic plane and exhibit two characteristic spatial orderings, while the interstitial B dopant can occupy any interstitial site on either the same (highlighted yellow) or the third nearest (010) atomic plane (highlighted purple), as depicted in Fig. 1a and b and S5.† Notably, the band structures of all these 20 B/N-codoping configurations are essentially the same, where band-like doping levels are obtained through level crossing between N-p_σ (p_x/p_z) and N-p_π (p_y) doping levels, as shown in Fig. S6.† Such band-like doping levels can be further confirmed by band structure calculations at the HSE06 level^38–40 for two arbitrarily selected B/N-codoping configurations (configID-809 and configID-862) among the 20 identified ones, as shown in Fig. 1c and d.

Fig. 1 Characteristics of the identified B/N-codoping configurations in anatase TiO₂. (a and b) Atomic structures of two arbitrarily selected B/N-codoping configurations (configID-809 and configID-862) from the 20 identified ones. (c and d) Band structures at the HSE06 level of the two B/N-codoping configurations illustrated in (a) and (b), respectively. The energy values are referenced to the VBM of pristine anatase TiO₂, which is set to be 0.0 eV.

It has also been found that when the B dopant occupies an interstitial site outside the yellow/purple (010) atomic planes found in the 20 identified configurations and the N dopant spatial ordering remains unchanged, which corresponds to another 20 configurations depicted in Fig. S7,† the level crossing between N-p_σ and N-p_π doping levels disappears, resulting in multiple localized doping levels, as shown in Fig. S8.† A closer analysis revealed that when the B dopant is located on the yellow/purple (010) atomic planes, a mirror symmetry σ(xz) exists in the 3 × 3 × 1 anatase TiO₂ supercell, while it is absent when the B dopant is located elsewhere. Consequently, the symmetries of N-p_σ (p_x/p_z) and N-p_π (p_y) orbitals are different in the first case because of the presence of σ(xz), but are identical in the second case due to the absence of σ(xz). According to group theory,⁴¹ when energy levels with different or the same symmetry approach one another, level crossing or level anti-crossing can be expected. This is the reason why level crossing can be observed in the 20 identified configurations (Fig. S6†), while level anti-crossing, giving rise to multiple localized doping levels, has been observed in another 20 configurations (Fig. S8†).

It is important to note that the bandgap narrowing achieved through level crossing between N-p_σ/p_π doping levels in the 20 identified B/N-codoping configurations is more significant (∼1.0 eV at the PBE level) than in previously reported N-doped anatase TiO₂ (typically less than 0.5 eV at the PBE level^18,42). This indicates that the interstitial B dopant can remarkably affect the energies of N doping levels to achieve a more significant bandgap narrowing. To clarify this effect, we took one identified configuration (configID-809) as an example, and compared its band/atomic structures with those of the corresponding N-doping configuration without the interstitial B dopant. As shown in Fig. 2a and d, the interstitial B dopant causes noticeable downshifting/upshifting of two N-p_σ doping levels, labeled as N-p_σ(1) and N-p_σ(2), and the upshifting of N-p_σ(2) results in the more significant bandgap narrowing than the case without the interstitial B dopant. By comparing the atomic structures and charge density isosurface plots shown in Fig. 2b and e, the interstitial B dopant substantially shortens the bond length between the Ti atom labeled as Ti3 and its adjacent N dopant, thereby strengthening the corresponding p_σ bond. This not only results in the downshifting of N-p_σ(1), but also the upshifting of N-p_σ(2) as the repulsion between N-p_σ(1) and N-p_σ(2) is substantially increased.

Fig. 2 Mechanism of the significant bandgap narrowing promoted by the interstitial B dopant. (a and d) Band structures at the PBE level of one identified B/N-codoping configuration (configID-809) without and with the interstitial B dopant. (b and e) Charge density isosurface plots (0.005 e Å⁻³) of two N-p_σ doping levels labeled as N-p_σ(1) and N-p_σ(2) at Γ point. (c and f) Partial density of states (PDOS) of t_2g orbitals (d_yz and d_xy) of three Ti atoms labeled as Ti1, Ti2 and Ti3, and the PDOS of the p_y orbital of the N atom adjacent to the three Ti atoms. A vertical dashed line is added to highlight the energy shift in the antibonding region. The energy values are referenced to the VBM of pristine anatase TiO₂, which is set to be 0.0 eV.

In order to uncover the reason for the Ti3–N bond shortening, we further analyzed the projected density of states (PDOS). As shown in Fig. 2c and f, the Ti3–N bond shortening can be attributed to the markedly enhanced p–d coupling between N-p_y (p_π) and Ti3-d_yz (t_2g) by introducing the interstitial B dopant. This is evident from the more pronounced hybridization peak of these two orbitals and the increased energy of Ti3-d_yz in the antibonding region.⁴³ In contrast, the p–d coupling between N-p_y and Ti-d_xy is much weaker as the hybridization peak of the two orbitals is barely changed by introducing the interstitial B dopant, indicating that the extra electron contributed by the interstitial B dopant for compensating the N³⁻/O²⁻ charge imbalance^24,28 preferentially occupies the molecular orbital formed between N-p_y and Ti-d_yz, rather than the one between N-p_y and Ti-d_xy. This selective occupation leads to the shortening of the Ti3–N bond, thereby achieving the significant bandgap narrowing in the identified B/N-codoping configuration.

In order to understand the origin of the much stronger p–d coupling between p_y and d_yz than that between p_y and d_xy, one needs to move from a molecular picture to the crystal. Due to the translational symmetry of a crystal, an atomic orbital, for instance p_y, at position r should be expressed as a Bloch function ψ = e^ikR p_y, where R denotes a lattice vector and k represents a point in the reciprocal space. In the Bloch function, the k-point determines the phase change of the atomic orbital upon translation between unit cells, and each k-point transforms under a specific point group due to the symmetry of the crystal.⁴¹ To be specific, low-symmetry k-points, i.e., those whose point group has fewer symmetry elements, result in the atomic orbital having amplitudes smaller than the maximum value in some unit cells, while high-symmetry k-points ensure that the atomic orbital has the maximum amplitudes in each unit cell.⁴⁴ Therefore, given a high-symmetry k-point, if two atomic orbitals, for instance p_y and d_yz, transform like the same irreducible representations of its associated point group,⁴⁵ the high-symmetry k-point generates Bloch function ψ = e^ikR (p_y + d_yz), which exhibits strong coupling between the two atomic orbitals within each unit cell.

Based on the above analysis, the much stronger p–d coupling between p_y and d_yz observed in the 20 identified B/N-codoping configurations indicates the existence of high-symmetry k-points that allow a strong p–d coupling in anatase TiO₂. In order to validate this speculation, we summarized the point groups of all high-symmetry k-points in the first Brillouin zone of anatase TiO₂ in Table S1.† From the table, the point group of the high-symmetry k-point X is C_2v, which allows the p–d coupling between p_y and d_yz according to its character table. As illustrated in Fig. 3a and b, under the C_2v point group, both p_y and d_yz transform like the same irreducible representation B₁, thus allowing strong p–d coupling between these two orbitals.⁴¹

Fig. 3 Difference between d_yz and d_xy in coupling with p_y. (a) Symmetry operations of C_2v on both N-p_y and Ti-d_yz. (b) The character table of C_2v. (c) Charge density isosurface plot (0.004 e Å⁻³) of the N doping level in a 2 × 2 × 1 anatase TiO₂ supercell with a single N dopant (some atoms are not shown for visual clarity). (d) Symmetry operations of C_4v on N-p_y and Ti-d_xy. (e) The character table of C_4v. (f) The illustration of the charge density isosurface plot in (c) from another perspective (some atoms are not shown for visual clarity).

In contrast, p_x/p_y and d_xy transform like different irreducible representations under the point groups associated with all high-symmetry k-points of anatase TiO₂. Taking C_4v as an example, in this case, (p_x, p_y) constitutes a two-dimensional irreducible representation E, while d_xy transforms like one-dimensional irreducible representation B₂, as illustrated in Fig. 3d and e. As a result, the p–d coupling between p_y and d_xy is much weaker than that between p_y and d_yz, well consistent with the PDOS results shown in Fig. 2c and f. In order to clearly visualize such a difference, we illustrated the charge density isosurface plot of the N doping level above the VBM of TiO₂, which is induced by a single N dopant in a 2 × 2 × 1 supercell of anatase TiO₂. As shown in Fig. 3c and f, the N doping level mainly originates from the p–d coupling between N-p_y and Ti-d_yz rather than between N-p_y and Ti-d_xy, further confirming the strong coupling between N-p_y and Ti-d_yz.

The existence of strong p–d coupling indicates that the N-p_y (p_π) are not isolated, since they can strongly couple with O-p_π and Ti-d_yz (one of three Ti-t_2g orbitals). In this case, a uniform distribution of the N dopants throughout the crystal supercell can ensure a similar N–N distance between different N dopants and prevent them from clustering, thus inducing delocalized molecular orbitals due to the strong coupling between N/O-p_π and Ti-t_2g orbitals. As these delocalized molecular orbitals correspond to the band-like doping levels above the VBM of pristine anatase TiO₂, the uniform N-doping can be intuitively expected for realizing band-like doping levels in N-doped anatase TiO₂. In order to confirm this, we constructed two B/N-codoping configurations with uniform N dopant spatial orderings (Fig. 4a and b) and calculated their band structures at the HSE06 level.^38–40 As shown in Fig. 4c and d, band-like doping levels with strong dispersion and apparent overlap with the VBM of pristine anatase TiO₂ can be observed for both of the two B/N-codoping configurations, thus achieving a significant bandgap narrowing as much as 0.70 eV.

Fig. 4 B/N-codoping anatase TiO₂ configurations featuring uniform N dopant spatial orderings. (a and b) Atomic structures of two B/N-codoping configurations featuring uniform N dopant spatial orderings. (c and d) Band structures at the HSE06 level of the two B/N-codoping configurations illustrated in (a) and (b), respectively. The energy values are referenced to the VBM of pristine anatase TiO₂, which is set to be 0.0 eV.

Based on the above discussions, the existence of strong p–d coupling in anatase TiO₂ is essential for achieving band-like doping levels. Due to the strong p–d coupling, the band-like doping levels can be achieved by dopant spatial orderings that are either uniform, or exhibit distinctive periodic features to enable apparent level crossing between N-p_σ and N-p_π doping levels. Both of these characteristic dopant spatial orderings match the experimental results, where both the substitutional N and interstitial B contents exhibit very small fluctuations throughout the TiO₂ microsphere.²⁵ Notably, as the existence of strong p–d coupling is determined by the crystal symmetry of anatase TiO₂, it enables us to effectively break out of the paradigm of correlating the origin of band-like doping levels with the electronic structures of a few specific B/N-codoping configurations. More significantly, it also enables the generalization of this p–d coupling criterion for the prediction of the feasibility of inducing band-like doping levels in other metal oxides. In order to validate this generalization, we further considered the other two polymorphs of TiO₂, namely rutile and brookite TiO₂.

As for rutile TiO₂, the point groups of the high-symmetry k-points in the first Brillouin zone are either D_4h or D_2h as summarized in Table S1.† Since p_π and t_2g orbitals transform like different irreducible representations in both of the point groups, the p–d coupling is much weaker in rutile TiO₂ compared to that in anatase TiO₂. Aiming to illustrate such a difference between rutile and anatase TiO₂, we have calculated the PDOS onto N-p_π and Ti-t_2g orbitals for both N-doped anatase and rutile TiO₂. As shown in Fig. S9,† the hybridization peak between N-p_π and Ti-t_2g orbitals is sharper and has a much higher value in N-doped anatase TiO₂ than in N-doped rutile TiO₂, demonstrating a much stronger p–d coupling between N-p_π and Ti-t_2g orbitals in anatase than in rutile TiO₂.

Therefore, it can be predicted that band-like doping levels are hard to be achieved in rutile TiO₂. In order to verify this, we also predicted the bandgap values of all possible B/N-codoping configurations in a 2 × 2 × 3 rutile TiO₂ supercell by using the established ML method. Specifically, by substituting three lattice O atoms with three N atoms and introducing one interstitial B atom, a total of 2576 symmetrically inequivalent B/N-codoping configurations can be obtained. Among these, 678 representative ones were uniformly sampled for DFT calculations, thus enabling the training of a highly accurate XGBoost model for the prediction of bandgap values, as summarized in Fig. S10.† Based on the ML prediction, we identified the 40 B/N-codoping configurations that exhibit the most significant bandgap narrowing, as shown in Fig. S11.† Besides, we also calculated the band structures of the two B/N-codoping configurations with the most significant bandgap narrowing at the HSE06 level.^38–40 As shown in Fig. S12,† the doping levels are largely localized in B/N-codoped rutile TiO₂, which is in accordance with the prediction made based on the p–d coupling criterion. Actually, this is in accordance with the previous DFT study on the effect of N doping on rutile TiO₂, where N doping typically induces localized doping levels above the VBM of rutile TiO₂ according to the PDOS plots.⁴⁶ Moreover, we also validated the prediction by synthesizing the B/N-codoped rutile TiO₂ using an approach similar to that for synthesizing the B/N-codoped anatase TiO₂.^24,47 As shown in Fig. S13,† only a shoulder-like absorption edge around 450 nm can be observed in the obtained B/N-codoped rutile TiO₂. This is typically induced by localized doping levels, since the localized doping levels are discrete within the bandgap, thereby only promoting light absorption at specific wavelengths rather than inducing a band-to-band redshift of the absorption edge. It should also be noted that the obtained B/N-codoped rutile TiO₂ has a greenish color rather than red, and a tail-like visible light absorption band can be observed in the UV-visible absorption spectra, which can be ascribed to the existence of a high concentration of oxygen vacancies.⁴⁸ However, in the N doped rutile TiO₂ where substitutional fluorine (F) was adopted as the charge compensator rather than the interstitial B, the obtained N/F-codoped rutile TiO₂ has an orange color,⁴⁹ indicating that the substitutional F can more effectively compensate for the charge imbalance between N³⁻ and O²⁻, thereby substantially lowering the concentration of oxygen vacancies. Noting that, the N/F-codoping still induces localized doping levels above the VBM of rutile TiO₂, which is also in agreement with the prediction made based on the p–d coupling criterion.

For brookite TiO₂, its high-symmetry k-point S in the first Brillouin zone allows p–d coupling, as summarized in Table S1.† Thus, it can be predicted that band-like doping levels can be achieved by uniform N doping in brookite TiO₂. In order to validate this, by introducing one interstitial B dopant and three substitutional N dopants in a 2 × 2 × 1 brookite TiO₂ supercell, we constructed a B/N-codoping configuration with uniform N dopant spatial ordering (Fig. S12c†). As shown in Fig. S12f,† band-like doping levels with strong dispersion and apparent overlap with the VBM of pristine brookite TiO₂ can be observed for this B/N-codoping configuration, thus achieving a significant bandgap narrowing as much as 0.63 eV.

Since the p_π orbitals originate from sp² hybridization of the three-coordinated N/O atoms, and the t_2g orbitals arise from the splitting of metal d orbitals by the O_h point group symmetry of the MO₆ cluster, rather than being unique to Ti atom. Therefore, the physical picture of the p–d coupling criterion is in principle also applicable for other MO₆-cluster-based metal oxide semiconductors. To confirm this, we further studied the effect of N-doping on the electronic structures of four more wide bandgap metal oxides including ScTaO₄, WO₃, SnO₂ and MgTa₂O₆. By analyzing the point groups as summarized in Table S2,† strong p–d coupling is allowed in ScTaO₄ and WO₃, while it is absent in both SnO₂ and MgTa₂O₆. Therefore, it can be predicted that band-like doping levels can also be obtained in ScTaO₄ and WO₃ by uniform N-doping, while this is hard to be fulfilled in SnO₂ and MgTa₂O₆.

In order to validate the prediction for ScTaO₄, we constructed a uniform N-doping configuration based on a 2 × 2 × 2 ScTaO₄ supercell, and a B/N-codoping configuration by further introducing an interstitial B dopant into the N-doping configuration. The electronic structures of these two doping configurations are shown in Fig. S14.† Clearly, uniform N-doping results in band-like doping levels that merge apparently with the VBM of ScTaO₄. Moreover, the charge compensation effect of the interstitial B dopant can further broaden the band-like doping levels to achieve a larger bandgap narrowing of about 1.1 eV. These results well explain the significant overall bandgap narrowing (up to 1.32 eV) achieved experimentally in ScTaO₄ by codoping with N and charge compensators.⁵⁰ As for WO₃, we also constructed a uniform N-doping configuration based on a 2 × 2 × 1 WO₃ supercell. From the calculated electronic structures shown in Fig. S15,† band-like doping levels above the VBM of WO₃ can also be obtained, and this should be the real cause for the smooth shift of the absorption edge towards the visible light region in N-doped WO₃ observed in experiment.⁵¹

Notably, the demonstrated uniform doping mechanism has significant implications, since it explains, for the first time, why uniform N doping is essential for better performance in metal oxides. This can be highlighted by comparing the first red anatase TiO₂ (ref. 24) with the later improved one,²⁵ which features a more uniform N doping instead of gradient N doping. Due to the uniform N doping, not only the band-to-band light absorption but also the photocatalytic oxygen evolution activity was significantly improved. In fact, besides the above metal oxides, uniform N doping is also the key for achieving state-of-the-art photoelectrochemical and photocatalytic performances in other metal oxides, for instance Cs_0.68Ti_1.83O₄,⁵² where strong p–d coupling exists in both metal oxides according to symmetry analysis, as summarized in Table S3.†

As for the other two metal oxides (SnO₂ and MgTa₂O₆) without strong p–d coupling, the absence of band-like doping levels has been firmly confirmed by considering a sufficient number of N-doping configurations with the most uniform N dopant spatial orderings. In specific, within a 2 × 2 × 3 SnO₂ supercell, we first identified the 24 doping configurations with the most uniform distributions of three N dopants, and calculated the corresponding band structures, as shown in Fig. S16.† Clearly, the doping levels are largely localized within the bandgap and exhibit no overlap with the VBM of SnO₂. Besides, as for the 24 N-doping configurations with the most uniform distributions of three N dopants within a 2 × 2 × 1 MgTa₂O₆ supercell, similar localized doping levels can also be observed, as shown in Fig. S17.† These results are in full accordance with the predictions based on the p–d coupling criterion.

Conclusion

In conclusion, based on the ML methods and DFT calculations, it was revealed that the existence of strong p–d coupling between O/N-p_π and Ti-t_2g orbitals in anatase TiO₂ is the prerequisite of inducing band-like doping levels. As the existence of the strong p–d coupling between p_π and t_2g orbitals in anatase TiO₂, as well as in other metal oxides, is entirely determined by crystal symmetry regardless of specific metal elements, we proposed a universal criterion based on p–d coupling to predict whether band-like doping levels can be induced in metal oxides through N doping. Notably, the accuracy of the criterion has been comprehensively verified on rutile/brookite TiO₂, ScTaO₄, WO₃, SnO₂ and MgTa₂O₆. Overall, our work provides a fundamental understanding and design guidelines for bandgap engineering of wide bandgap metal oxides.

Data availability

The data supporting this article have been included as part of the ESI.†

Author contributions

Conceptualization, G. L., L. C. Y. and K. Y. Z.; investigation, K. Y. Z.; writing – original draft, K. Y. Z.; writing – review & editing, K. Y. Z., L. C. Y., G. L. and X. Q. C.; funding acquisition, L. C. Y. and G. L.; resources, L. C. Y., G. L. and H. M. C.; supervision, L. C. Y., G. L. and H. M. C.; experiments, G. Q. D. All authors discussed the results and commented on the manuscript.

Conflicts of interest

There are no conflicts to declare.

Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 52425201, 51972312), the National Key R & D Program of China (No. 2021YFA1500800), and the International Partnership Program of Chinese Academy of Sciences, Grant No. 172GJHZ2022010MI. The theoretical calculations in this work are performed on TianHe-1(A) at the National Supercomputer Center in Tianjin. Authors are thankful to Prof. Xinzheng Li, Prof. Junwei Luo and Prof. Yan Sun for valuable discussions. Gang Liu is thankful for the financial support from the New Cornerstone Science Foundation through the XPLORER PRIZE.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: https://doi.org/10.1039/d4ta05577b

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