Modulation of electronic structures in N‐doped TiO2(B) for hydrogen evolution: A density functional theory study

N‐doping is an effective technique for enhancing the exploitation of TiO2 under visible light, thanks to the level of doping introduced. It is also important to explore N‐doping in the metastable polymorph TiO2(B), which is renowned for its applications in energy materials. In order to investigate the impact of N‐doping on the optical properties of TiO2(B), a systematic comparison of the electronic structural and optical properties of pure and N‐doped TiO2(B) was conducted using density function theory (DFT) calculations. The results indicate that N‐doping is more thermodynamically favorable at the O site with four coordinated atoms. Upon N‐doping, impurity states emerged within the bandgap of TiO2(B), leading to a significant reduction in the energy gap. Consequently, N‐doping primarily enhances the absorbance of visible light, which is crucial for photocatalysis. Furthermore, the adsorption energy of H at the (0 0 1) surface of N‐doped TiO2(B) decreased by 2.75 eV, providing valuable insight for the design of TiO2(B) with exceptional photo‐ and electro‐catalytic performance.

(B).[10][11][12][13] Notably, the application of TiO 2 (B) in the photocatalytic field is limited due to its relatively large bandgap energy (E g ) value of approximately 3.2 eV.5][16] Several studies have focused on enhancing the photocatalytic performance of TiO 2 (B), such as the work by Huang et al., who found that g-C 3 N 4 -coated TiO 2 (B) facilitates efficient charge extraction. 17However, most of these studies have primarily focused on photocatalytic applications, neglecting the exploration of the intrinsic theory behind TiO 2 (B).TiO 2 (B) possesses a monoclinic C2/m space group crystal structure, consisting of TiO 6 octahedra that are connected through edge and corner-sharing.In order to comprehend the impact of crystal structure variation on the physiochemical properties of TiO 2 (B), López-Corral et al. 18 have revealed the enhancement mechanism of the light absorption characteristics of TiO 2 (B) by introducing carbon (C) doping.One step further, thoroughly investigating the effect of heteroatom-doping on hydrogen adsorption may provide additional information for the optimization of TiO 2 (B) catalysts.
0][21][22][23] It should be noted that N doping has achieved remarkable results in improving the photocatalytic performance of other phases of TiO 2 .Javier Fdez et al. 24 examined all the positions for the adsorption of atomic N on the rutile TiO 2 surface.The consensus is that nitrogen doping in anatase or rutile leads to the injection of defect electronic states within the bandgap, thus achieving the increase of light absorption.Pacchioni et al. 25 calculated the detailed N-doping concentration tendency in (0 0 1)-(1 0 1) anatase TiO 2 heterojunction and proposed the dopant segregation at low N concentrations and doping in the bulk regions at larger concentrations.N-doping strongly stabilizes oxygen vacancies, which in turn enhances the light absorption properties.Nevertheless, because of the more complex crystal structure and lower symmetry of TiO 2 (B), the previous research results regarding rutile and anatase are not applicable to TiO 2 (B).Besides, the detailed understanding of the initial N-doping sites and H atom adsorption mechanism is still scarce.
In this work, the effect of N doping on TiO 2 (B) was systematically studied by density function theory (DFT) calculations.For that, we first modeled non-doped and N@O doped TiO 2 (B) bulk phases, and then evaluated the density of states.Based on the results, the more active surface and the more stable H adsorption energy were explored to reveal the reaction of TiO 2 (B) (0 0 1) and (1 0 0) surfaces on the optimized systems.This study can provide a theoretical basis for the improvement of photocatalytic and energy systems based on N-doped TiO 2 (B).

COMPUTATIONAL METHOD
All density functional theory (DFT) calculations were carried out within the Projector Augmented Wave (PAW) scheme as implemented in the Vienna Ab initio Simulation Package (VASP). 26The exchange-correlation energy was described by generalized gradient approximation Perdew-Burke-Ernzerhof (GGA-PBE) functional considering van der Waals (VDW) interactions treated by the zero damping DFT-D3 corrected method. 27,28Based on the convergence test, the plane-wave cutoff energy was chosen as 500 eV.The Brillouin zone integration was conducted using a 0.03 1/Å k-point separation.
According to this setting, the Monkhorst-Pack k-point grid is 9 × 9 × 5 and 5 × 3 × 1 for the primitive cell of TiO 2 (B) and the surface of TiO 2 (B), respectively.The slab models were separated by 20 Å of vacuum space perpendicular to the slab surface.The structures were allowed to relax until the interatomic force decreased to 0.01 eV/Å, and self-consistent field iteration could converge with total energy variation less than 10 −5 eV eV/atom.Appropriate structural and electronic parameters were obtained with U eff = 3.5 eV.All the proposed models were visualized using VESTA.

The optimum site and appropriate concentration of N doping
The optimized lattice constants of TiO 2 (B) unit cell are determined to be 6.430Å in a, and 6.611 Å in c.First, the substitutional doping sites of a single N atom in TiO 2 (B) have been considered systemically.There are four types of O atoms ), and four-coordinated (O 4C ), while Ti atoms for six-coordinated but two nonequivalent environments (octahedral coordination Ti 6C1 , square-pyramidal Ti 6C2 ).All doping sites (N@O 2C , N@O 3C1 , N@O 3C2 , N@O 4C , N@Ti 6C1 , and N@Ti 6C2 ) have been considered in our work, as shown in Figure S2.
In order to ensure the stability of our doping systems, the defect formation energy (E f ) was calculated according to the following equation: where, E N@X and E pure are the total energies with and without N doping, respectively. N is the chemical potential of a free N atom, which is half the total energy of a nitrogen molecule.While  X is the chemical potential of Ti or O atom.The structures with lower E f (N@X) indicate the more stable system.After the optimization, Figure 1B illustrates the E f (N@X) of TiO 2 (B) with N doping at different sites.Among them, the N@O 4C exhibits the lowest E f (N@X) (3.11 eV), suggesting that N tends to substitute the O atom at this site.The optimized structure of TiO 2 (B) with N doping at different sites is shown in Figure 2, and corresponding lattice parameters and average Bader partial charge are summarized in Table 1 and Table S1-S2.For the N@O model, Ti-N bonds are longer than the corresponding Ti-O bonds of pure TiO 2 (B) except N@O 4C (2.34 vs. 2.30 Å).Therefore, the parameter of optimized N@O x (x = 2C, 3C1, 3C2, and 4C) doped TiO 2 (B) structure is greater compared to pure TiO 2 (B) resulting in inflated cells.Among all models, the N@O 4C model lead to the minimum distortion (147.53 vs. 146.32Å 3 ).In stark contrast, the N@O x (x = Ti6C1, Ti6C2) doped structure possesses detrimental E f (N@X) triggered from shrunken cells.These changes are owing to the variations in bond lengths.The distortion of the lattice is largely restricted around the impurity and depends on the anionic radius of the dopant element with respect to that of O. Fortunately, it has been confirmed that N doping has a lower impact due to the similar radius for N and O elements. 29owever, the distortion in N@Ti models is greater because the N atoms have different coordination numbers compared with Ti atoms, not keeping the previous configuration totally.It can be seen from Table S1 that two of the N-O bonds shrink dramatically, which could speculate the existence of a covalence response.While the other two N-O bonds enlarge correspondingly, where the N atom acts as an electron donate to the O atoms and thus has a positive oxidation state. 18ccording to experimental and performance aspects, it is easy to aggregate or distribute unequally if doping too much or little results in negative influence.Therefore, to determine the appropriate N doping concentration, the formation energy of TiO 2 (B) with different concentrations of N doping at O 4C site was further calculated.In bulk system, pure and N-doped TiO 2 (B) are 1 × 1 × 1 cell with 4 Ti and 8 O atoms.The N doping concentration of TiO 2 (B) is 8% by replacing  TA B L E 2 N-doping formation energy for N@O 4C -doped TiO 2 (B) bulk models along different axis.
N@O 2C -4% (eV) N@O 3C1 -4% (eV) N@O 3C2 -4% (eV) N@O 4C -4% (eV) N@O 4C -3% (eV) N@O 4C -2% (eV) x-axis either one Ti or O atom with one N atom.Extensively, in order to simulate the different N doping concentrations, TiO 2 (B) was adopted to 2, 3, and 4 fold supercells.In this case, the doping concentrations obtained by replacing the O 4C atom with an N atom are 4%, 3%, and 2%, respectively.Meanwhile, system energy can also be affected by the cell expansion along the different axis.Our study considered the influence of the x, y, and z-axis, as shown in Figures S3-S5.Taking all factors into consideration, TiO 2 (B) with 4% N doping at the O 4C site (N@O 4C -4) exhibits the lowest formation energy (3.105 eV) (Table 2 and Figure S6).

DOS for doping bulk TiO 2 (B)
Generally, the geometric change of materials is accompanied by the change in electronic structures.To better explain the variation of N doping on bulk 4% TiO 2 (B), the density of states (DOS) of the original and four N@Ox doping TiO 2 (B) are calculated and depicted in Figure 3.For all systems, the valence band is mainly contributed by O-2p states, while the conduction band is dominated by Ti-3d orbitals.When doping N in the TiO 2 (B), there are impurity states of N-2p orbitals in the valence band, and the new states are expected to be less bound due to the smaller nuclear effective charge. 30That is, the smaller the atomic number, the higher the energy of the p states.In addition, because one hole is present in the case of N doping, the Fermi energy exceeds the top of the valence band to form p-type doping.On this occasion, the holes in the system could be favorable for conducting the application process.In the meantime, the reduction of the bandgap spontaneously results in the increase of the photo-absorption region, which is also beneficial to the capture of photons and crucial to the photoexcitation reaction.These trends are further confirmed by the calculation results using the HSE06 method (Figure S7), which employs a hybrid functional that more accurately reflects the inherent electronic properties.Furthermore, the optical absorption curves of original and doped TiO 2 (B) have been calculated and plotted in Figure S8.Due to its broad band gap, the photo response range of original TiO 2 (B) is restricted to UV light.In comparison to pure TiO 2 (B), N-doped TiO 2 (B), particularly the N@O 4C TiO 2 (B), exhibit a considerable absorption tail in the visible region between 400 and 600 nm, which is caused by the introducing nitrogen to TiO 2 (B) and consistent with the DOS results.The light absorption of N@Ox doping TiO 2 (B) in the visible light region is critical for its photocatalysis application because it can be triggered even by visible light.

Study of H atom adsorption
The choice of H adsorption surface Among the above results, the N@O 4C -4 TiO 2 (B) is decided to study the surface properties and H adsorption aiming to explain the performance mechanism for the energy system.2][33][34] Therefore, an active surface must be selected and then the surface energies () for two types of N@O 4C -4 TiO 2 (B) surfaces are compared.Figure 4 displays the models of N@O 4C -4 TiO 2 (B) slabs with different surface structures.The (0 0 1) and (1 0 0) surfaces are considered to be the most active.The  is calculated according to the following equation:  where, E relax and E unrelax are the total energies with and without a relaxed surface, respectively.E b denotes the energy of the chemical formula units, and N represents the number of chemical formula units.A denotes the surface area of the slab.The structures with higher  indicate a more active surface.Figure 4 illustrates the  of N@O 4C -4 TiO 2 (B) slab with different surface structures.Among these two N@O 4C -4 TiO 2 (B) surfaces, the (0 0 1) surface exhibits the higher .Therefore, the N@O 4C -4 TiO 2 (B) (0 0 1) surface is selected to study the H adsorption process in the following section.

Adsorption of H atoms
The adsorption sites of a single H atom at N@O 4C -4 TiO 2 (B) (0 0 1) surface (Figure 5A) are investigated.The possible adsorption sites at N@O 4C -4 TiO 2 (B) (0 0 1) surface are shown in Figure 5B.According to the structural symmetry of N@O 4C -4 TiO 2 (B), in the first atomic layer of the (0 0 1) surface, the adsorption sites on the top of Ti1, Ti2, N, O1, and O2 are labeled as Ti1 site, Ti2 site, N site, O1 site, and O2 site, respectively.In addition, the adsorption site between two atoms is marked as a bridge-1-5 site, and the adsorption site between N, O2, and Ti1 is marked as a hollow site, as shown in Figure 5B.In contrast, the possible adsorption sites for undoped TiO 2 (B) (0 0 1) surfaces are displayed in Figure S9.The adsorption energies of the H atom (E H ) are calculated as follows: Herein E H and E 0H represent the total energies of the structures with and without H atoms on the surface, respectively. H is the chemical potential of a free H atom, which is half the total energy of a hydrogen molecule. 35he optimal configurations with an H atom adsorbed at 11 different sites and the corresponding adsorption energies are shown in Figure S10 and Figures 6 and 7, respectively.As for N@O 4C -4 TiO 2 (B) (0 0 1) surface, Figure 6 indicates that the H atoms adsorbed at Ti1, bridge1, bridge3, and hollow sites are unstable and spontaneously migrate to the N site after the structural optimization.Moreover, the H atoms adsorbed at Ti2, O3, bridge2, bridge4, and bridge5 sites cause lattice distortion of different degrees.Owing to the highly similar optimized structures, the E H at Ti1, bridge1, bridge3, and hollow sites are nearly equal (Figure 7), and the same conclusion occurs for O3, bridge2, bridge4, and bridge5 sites.On the contrary, the most stable sites are N and O2 sites, which have adsorption energy of −5.97 and −5.37 eV, respectively.Among those adsorption sites, the N site shows the most negative E H , indicating that the H adsorption of N@O 4C -4

CONCLUSION
In summary, DFT calculations indicate that the most stable site for N-doping in TiO 2 (B) is the replacement of the four-coordinated O atom, which requires an inflated supercell.This substitution leads to a reduction in the bandgap, expanding the photo-absorption range and enhancing light absorption, thereby promoting photocatalysis.However, excessive or insufficient doping levels result in reduced stability.Consequently, simulating a 4% N-doping in N@O 4C -4 TiO 2 (B) demonstrates the lowest formation energy.Furthermore, we investigated the hydrogen adsorption behavior on the (0 0 1) surfaces of TiO 2 (B) and N@O 4C -4 TiO 2 (B).Notably, adsorbing H atoms on the more stable N@O 4C -4 TiO 2 (B) (0 0 1) surface revealed lower hydrogen reaction energy in the N-doped system.Conversely, the deposition of H atoms exhibited higher reaction barriers, which could be improved through combination with other components.Consequently, TiO 2 (B) exhibits advantages in the field of electrocatalytic hydrogen evolution reaction.Hopefully, our findings would provide valuable insights for developing N-doped TiO 2 (B) photo-active materials in catalysis-related application.

F
I G U R E 1 (A) Crystal structure for the original unit cell of TiO 2 (B); (B) N-doping formation energy for pure and N-doped TiO 2 (B) bulk models.and two types of Ti atoms in TiO 2 (B) (Figure 1A and Figure S1): O atoms for two-coordinated (O 2C ), three-coordinated (O 3C1 & O 3C2

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I G U R E 2 Optimized N-doped TiO 2 (B) models shown in polyhedral view.Atoms in red are oxygen, in blue are nitrogen and in light blue are titanium.TA B L E 1 Structural parameters for pure and N-doped TiO 2 (B) bulk models.
of the bulk TiO 2 (B) and N@Ox doping TiO 2 (B) (Fermi energy is marked as the deep pink line).