Roles of Oxygen Vacancies in NiMoO4: A First-Principles Study

Oxygen vacancy has been suggested to play a role in the electrochemical ability of NiMoO4. The band structure and density of state of NiMoO4 bulks with different concentrations of oxygen vacancy were investigated by the first-principles calculation. Original NiMoO4 shows semiconductive properties with a direct band gap of 0.136 eV. When one to three oxygen vacancies were introduced in the NiMoO4 supercell, the band structure of NiMoO4 transforms to metallic properties, and oxygen vacancies formation energy increases with the increased number of oxygen vacancies. The oxygen vacancies in NiMoO4 lead to the increased electron localization of Ni 3d and Mo 3d state nearby the Fermi level, resulting in higher concentration of carriers in NiMoO4 and thus increase in its electrical conductivity. The results demonstrate that introducing oxygen vacancies can improve the conductive property of NiMoO4.


INTRODUCTION
As a typical transition metal oxides semiconductor, NiMoO 4 has attracted attention for its wide applications in electrochemical energy storage and conversion, such as supercapacitor and electrocatalytic water splitting (Du et al., 2018;An et al., 2019). However, the poor conductivity and electrochemical activity of NiMoO 4 limited its electrochemical energy storage performance. Defects engineering is a common method to change the physical chemistry property of transition oxide materials. As a typical representative of defects, oxygen vacancies can effectively modulate their electronic properties, tune their bandgaps, and optimize their electrical conductivity (Zhang et al., 2020a). It has been proven experimentally that oxygen vacancies also can alter the interlayer spacing of metal oxide to promote faster charge storage kinetics (Kim et al., 2017;Qing et al., 2018). However, theoretical mechanism analysis of oxygen vacancies in NiMoO 4 on its capacitance performance is still scarce.
NiMoO 4 has a typical monoclinic crystal structure. Both the Ni and Mo atoms are in octahedral site, and the distance between Mo and O atom was 2.3-2.4 Å (Rodriguez et al., 1998;Rodriguez et al., 2000). When redox reaction occurs, the Ni 2+ has oxidized to Ni 3+ ; meanwhile, the MoO 4 2− framework remains stable. Due to the band gap of NiMoO 4 of 2.23 eV in natural temperature, the actual pseudo-capacitance performance of NiMoO 4 was unsatisfactory (Yang et al., 2016).
In order to understand the physical property of oxygen vacancies in NiMoO 4 , we performed firstprinciples calculation on the electronic structure, total density of states (TDOS), and partial density of states (PDOS) of NiMoO 4 − x for the case of x 0.0, 0.125, 0.250, and 0.375 (call NMO-0, NMO-1, NMO-2, NMO-3, respectively) by the Vienna Ab-Initio Simulation Package (VSAP) based on density functional theory (DFT). We have constructed a supercell of eight unit cells consisting of 48 atoms. Furthermore, in order to understand the relationship between vacancies structures and electrical properties in NiMoO 4 , the formation energy of neutral oxygen vacancy in different chemical environments has been calculated.

Theoretical Model
The study of oxygen vacancies in NiMoO 4 has been investigated by constructing a perfect supercell approach. Based on the optimized construction of perfect NiMoO 4 , the unit cell is built by 2 × 2 × 2 in the x, y, and z directions, and a supercell consisting of 48 atoms is used for vacancies calculation. To introduce oxygen vacancies, an interior atom is removed from the supercell. The theoretical model is shown in Figure 1.

Computational Method
In order to understand the relationship between vacancies structures and electrical properties in NiMoO 4 , the formation energy of neutral oxygen vacancy in different chemical environments was calculated. The corrected formation energy of an isolated neutral O vacancy in NiMoO 4 (ΔE Vo ) is defined as: where E defective is the total energy of a structure with oxygen vacancies, E perfect is the total energy of the structure without oxygen vacancy, and E O2 is the elemental chemical potential of oxygen in the gas phase. The DFT calculation was implemented in the Vienna Ab-Initio Simulation Package (Kresse and Joubert, 1999). For the exchange and correlation functionals, the Perdew-Burke-Ernzerhof (PBE) version of the generalized gradient approximation (GGA) exchange correlation was used (Blöchl, 1994;Perdew et al., 1996). In the DFT calculation, the NiMoO 4 bulks with different concentrations of oxygen vacancies were used to uncover the electronic properties. Vacuum layer thickness of 20 Å was applied to avoid virtual interaction and obtain more accurate results. The k-grid mesh value was 5 × 5 × 1. In addition, DFT + U method was also introduced to describe the electronic properties and vacancies states in NiMoO 4 bulks. The value of U given to Ni ions was 4 eV (Hinuma et al., 2007). The energy cutoff of 450 eV was used for the wave functions expansion. The energy and force converged to 1.0 × 10 -5 eV atom −1 and 0.03 eV Å −1 to achieve high accuracy.

RESULTS AND DISCUSSION
The calculated formation energy for different amount of oxygen vacancies in NiMoO 4 for a 2 × 2 × 2 bulk cell (48 molecular units) is shown in Table 1. The formation energy for different number of oxygen vacancies in NiMoO 4 was 0.73, 1.95, and 3.56 eV, respectively. The formation energy of two and three oxygen vacancies in NiMoO 4 are 2.67 and 4.88 times than that of the one vacancy, respectively, which suggested that one vacancy is more easily formed in NiMoO 4 crystal. This result shows that it is hard to synthesize two and three oxygen vacancies into NiMoO 4 under normal experimental conditions.    In order to reveal the oxygen vacancy electron doping effect on the electronic structure of NiMoO 4 , the band structure, TDOS, and PDOS, of stoichiometric NiMoO 4 in 2 × 2 × 2 supercell with different amount of oxygen vacancies were calculated. Figure 2 shows the band structure of NiMoO 4 with different numbers of oxygen vacancies from zero to three. The Fermi levels of NMO-0, NMO-1, NMO-2, and NMO-3 were 6.1014, 6.0258, 5.9609, and 5.8729 eV, respectively. All of the Fermi levels were located at zero in all the figures. The valence band maximum of NMO-0 is located at −0.079 eV, and the conduction band minimum is located at 0.056 eV. NMO-0 is a semiconductor with an indirect gap of 0.136 eV. Furthermore, NMO-1, NMO-2, and NMO-3 showed metallic electrical conductivity characteristics. With the introduction oxygen vacancies into NiMoO 4 , the extra-nuclear electrons of Mo have been released, which leading to increasing number of carrier concentration. The results are consistent with the DFT calculation result of SF Matar's work (Matar et al., 2010).
It can be obtained that the valence band of NiMoO 4 can be divided into lower and upper valence bands. The lower band mainly consisted of the O 2d, Ni 3d, and Mo 3d, as shown in Figure 3. The upper valence band consisted of Ni 3d and Mo 3d. While oxygen vacancies were introduced into the NiMoO 4 crystal, the band gap of NiMoO 4 has narrowed. The introduction of oxygen vacancies in NiMoO 4 gives more distribution of state density nearby the Fermi energy level, which indicates that more metallic properties of NiMoO 4 (Zhang et al., 2020b).
The PDOS of O 2p, Ni 3d, and Mo 3d for NMO-0, NMO-1, NMO-2, and NMO-3 are displayed in Figure 4. Nearby the Fermi level, the electronic states of NiMoO 4 mainly consist of Ni 3d and Mo 3d. With the number of oxygen vacancies from zero to three, the half-peak width of Ni 3d and Mo 3d decreased and exhibited higher electron localization effect. This suggests that NiMoO 4 has transformed to metallic properties with oxygen vacancies created into the NiMoO 4 crystal, which is in accordance with the calculation consequence of band structure.

CONCLUSION
In summary, we analyzed the formation energy, band structure, DOS, and PDOS from zero to three oxygen vacancies in 2 × 2 × 2 NiMoO 4 supercell with density functional theory calculation. The result revealed that only one oxygen vacancy can easily form in NiMoO 4 crystal. The original NiMoO 4 shows direct band gap semiconductor characteristic. With the amount of oxygen vacancies increase from one to three, the band gap of NiMoO 4 become narrower and exhibit stronger metallic properties. The electron state nearby the Fermi level of NiMoO 4 are mainly determined by Ni 3d and Mo 3d. Oxygen vacancies into NiMoO 4 accelerate the electron localization effect of Ni 3d and Mo 3d around the Fermi level.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.