The influence of the oxygen vacancies on the Pt/TiO2 single-atom catalyst—a DFT study

The titanium dioxide (TiO2) surface is suitable as a substrate for single-atom catalysts (SACs) for oxygen reduction reaction (ORR). As a common defect on TiO2, oxygen vacancies may have a significant impact on the adsorption and activity of the adatoms. This work aims to investigate whether titanium dioxide containing surface oxygen vacancies is more suitable as a base material for SACs. This paper calculates the changes in the adsorption energy of the Pt atom and the energy of the d-band center on the perfect surface and the surface containing oxygen vacancies. Concerning the perfect surface, the surface containing oxygen vacancies fixes the Pt atom more firmly and increases the center energy of the d-band of Pt, thereby improving the performance of the Pt atom as SACs. Consequently, the (110) surface of rutile TiO2 with oxygen vacancies may be the best substrate for SACs.


Introduction
Oxygen reduction reaction (ORR) plays a vital role in various energy conversion and storage systems (such as fuel cells and metal-air batteries) and understanding which electronic factors are involved in the oxygen reduction reaction is a top priority. With the advent of single-atom catalysts (SACs), using a single-metal atom to promote chemical reactions has become a more efficient method. The interaction between the substrate (holding materials) and the active metal atoms may have a significant impact on the catalytic activity of the metal. On the one hand, to obtain a stable contact, the adsorption energy of the metal atom on the substrate needs to be high. On the other hand, the influence of the substrate on the electronic structure of the metal needs to be taken into account. Hammer and Nørskov [1][2][3][4] proposed the d-band center theory, which claims that the adsorption energy of the molecule is mainly determined by the occupancy rate of the bonding and anti-bonding states formed by the hybridization of the d-state electrons wave function of the adsorbate and the substrate. If the anti-bonding state lies below the Fermi level (E F ), the interaction between the adsorbate and the metal surface will become repulsive, resulting in weak chemical adsorption. This situation can be well characterized by the position of the d-band center of the metal. The downshift of the d-band center will lead to stronger chemisorption. In addition, Stamenkovic et al. [5] found that ORR activity is correlated with the d-band center of the platinum crystal. As the center of the d-band moves away from the E F , the observed ORR activity of Pt is higher. Lu et al. [6] also observed a strong correlation between the d-band center and oxygen adsorption energy on the surface of various single-crystal metals, which is consistent with the d-band center model. TiO 2 is considered to be an excellent substrate for loading noble metal atoms as catalysts. FB Li et al. [7] used Pt/ TiO 2 catalyst to improve photodegradation efficiency. The TiO 2 /Pt catalysts in the ORR reaction of proton exchange membrane fuel cells (PEMFCs) have been studied by Mirshekari G. R. and Rice C. A. [8]. In order to improve the utilization of noble metal atoms, scattered Pt/TiO 2 catalysts and single-atom Pt/TiO 2 catalysts are growing. For scattered Pt loaded on TiO 2 , Humphrey N presents a multi-scale modeling study of atomically dispersed Pt on the (110) surface of rutile TiO 2 , probing the dynamic evolution of the catalytic surface at elevated temperatures. [9] Tianyi Wang et al.  [10], including Pt single atom, and obtained the relationship between the different adsorption energies and the center of the d-band center; it is believed that the (001) and (101) faces of anatase TiO 2 are suitable for single-atom catalyst substrates. Therefore, the study of anatase and rutile TiO 2 as a single-atom catalyst substrate is important.
Besides, the surface defects of the substrate usually have a great influence on the adsorption energy and the center of the d-band. Oxygen vacancies in metal are of great importance in the structural evolution of active centers in singleatom catalysts (SACs) [11]. Among the various defects in TiO2, oxygen vacancies are the most common one due to their low formation energy. However, the oxygen vacancyrich surface is more likely to affect the d-band center and further affect the ORR performance [12][13][14]. Therefore, it is necessary to explore the influence of oxygen vacancies of the TiO 2 substrates on the d-band center.
In this study, we systematically calculated the adsorption energy of the single Pt adatom on the (001) and (101) surface of anatase TiO 2 and (100), (011), (110) surface of rutile TiO 2 in the presence of oxygen vacancy, and the d-band center of the Pt adatoms by density functional theory(DFT) method. The calculation results show that the (110) surface of rutile TiO 2 with oxygen vacancies has a better balance between the adsorption energy and the center of the d-band among the five common surfaces calculated and is more suitable for SACs.

Computational method
We used the DFT method by Vienna Initio Simulation Package (VASP) to calculate the single-point energy and spin polarization geometry calculations and used HSE06 to process the corrected electronic correlation function. Grimme's zero-damping DFT-D3 method is used to consider van der Waals interaction. The cutoff energy for geometric optimization and self-consistent calculation is set to 520 eV, and the K point is selected as 3 × 3 × 1.
For the adatom-TiO 2 system, a single Pt atom is adsorbed on the (2 × 2) supercell of anatase TiO 2 (001) (101) surface and (2 × 2) supercell of rutile TiO 2 (100), (011), and (101) surface. A vacuum space of 15 Å is applied in the vertical direction to eliminate non-physical interactions between adjacent images. All geometric structures were optimized until the residual force is less than − 0.001 eV /Å. The interaction between Pt atom and TiO 2 surface is described as average adsorption energy (E(ads)). The calculation formula is defined as E(ads) = E(Pt + TiO 2 ) − E(TiO 2 ) − E(Pt), where E(Pt + TiO 2 ) is the total energy after adsorption of the Pt atom, E(TiO 2 ) is the energy of the TiO 2 surface without Pt atom, E(Pt) is the energy of a single platinum atom. E(ads) is usually calculated to check the adsorption stability, and a negative value indicates exothermic adsorption [15,16]. The greater the negative value of E(ads), the more stable the system should be. Therefore, negative E(ads) means that the single metal can be stably fixed on TiO 2 . In addition, the calculation formula of cohesive energy E(coh) is defined as E(coh) = E(metal) − E(single), where E(metal) and E(single) represent the total energy derived from bulk Pt metals and single Pt metal. In our work, the total energy is the energy of a unit cell, which includes 4 Pt atoms.

Computational models
The adsorption positions of single atoms or clusters on the perfect surface have existing research. Tianyi Wang et al. [10] constructed the models for the adsorption of transition metal atoms on anatase's (001) (101) perfect surface. The computational models of Pt atom on anatase TiO 2 with different designed sites are presented in Fig. 1 (001) and (101). Ti, O, and Pt are indicated as blue, red, and grey ◂ sites for fixing metal atoms but also affect the catalytic performance. The anatase (001) and (101) topmost oxygen vacancies computational models have been given by Aiura Y. [20], Gong et al. [21], and Xue-Qing et al. [22]. Cheng H. et al. [23] and Petrik N. G. et al. [24] presented the computational models for rutile (100), (011), and (110) surface with topmost oxygen vacancies. Taking into account that the introduction of oxygen vacancies will change the coordination numbers of Ti atoms, the metal atom will be introduced on top sites, bridge sites, and hollow sites near the Ti atom with decreasing coordination numbers or the nearest oxygen atom [9,[21][22][23], shown in Fig. 3 and

Results and discussion
We calculated the adsorption energy of all the models above to find the most stable energy in supporting information Table S1, and the models after structural relaxation are given in supporting information in picture 1 and picture 2. The structure with the lowest adsorption energy after structural relaxation is considered the most stable structure. We calculated the adsorption energy (E(ads)) of oxygen vacancies and perfect surfaces for comparison in Fig. 5 and Fig. 6. These models are considered to be the most stable structures. We found that the adsorption energy we calculated always shows the same trends on these surfaces: the adsorption energy of the surface containing oxygen vacancies is significantly higher than that of the perfect surface. It is speculated that the oxygen vacancies change the electronic distribution state of the surrounding Ti atoms, which makes the binding force of Pt and Ti atoms stronger.
The d-band center energy of (001) and (101) surface of anatase TiO 2 and (100), (011), and (110) surface of rutile TiO 2 have been calculated in supporting information Table S2. We plot the d-band center energy with the most stable adsorption energy on the surface in Fig. 7. We found from Fig. 7 that for the five types of TiO 2 surfaces, the movement of the center energy of the d-band also shows the same trend: for a surface containing oxygen vacancies, the d-band center energy of the Pt atom will be closer to the Fermi level. This shows that the surface containing oxygen vacancies may be more suitable The partial density of states of perfect surface and oxygen vacancies surface of anatase (001), (101) and rutile (100), (011), (101) are given in Fig. 8 and Fig. 9. We can see the change of the d-band energy of the Pt on a different surface. For the five types of surfaces, the d-band energy of Pt after introducing oxygen vacancies has increased significantly. At the same time, the energy hybridization between O atoms and Pt atom becomes weak, and the hybridization between Pt atom and Ti atoms increases. The interaction between the Pt atom and Ti atoms may be the reason for increasing the d-band energy of the Pt atom.
Otherwise, We calculated the d-band center energy of the Pt atom on the Pt metal bulk, which is − 2.22 eV, consistent with − 2.23 eV which was calculated by Tianyi  Wang et al. [10]. We found that the d-band centers of Pt atom on selected TiO 2 surfaces are closer to the Fermi level than the d-band centers of Pt atom on the metal bulk. According to the d-band center theory of transition metals, the Pt atom on the surface containing oxygen vacancies is more conducive to adsorbing other atoms than the Pt atom on the metal bulk. Figure 10 shows the relationship between the adsorption energy and the center of the d-band of Pt atom on different surfaces under the line is the perfect surface, above the line is the oxygen vacancies surface. Compared with the perfect surface, it is much easy to obtain larger adsorption energy or a higher d-band center for the containing oxygen vacancy surface.
Generally, the adsorption energy and cohesive energy were compared to evaluate the thermodynamic stability of SACs. The cohesive energy of Pt is − 5.48 eV calculated in our work in supporting information Table S3, consistent with 5.53 eV which was calculated by Philipsen P H T [25]. Figure 11 shows the relationship between adsorption energy and cohesive energy of different TiO 2 surfaces. We found that on the surface of rutile (110) and rutile (011) with oxygen vacancies, the adsorption energy of the Pt atom is higher than the cohesive energy of Pt metal. This means that its thermodynamic stability is much better than that of those perfect surfaces whose adsorption energy is much smaller than their cohesive energy which may not be stable enough as SACs except rutile (110).
In order to more accurately simulate the working temperature of SACs, we calculated the cohesive and adsorption energies at 298.15 K, corrected by free energy. The adsorption energy and cohesive energy at 298.15 K are 0.08 eV and 0.07 eV smaller than those at 0 K. Therefore, we believe that the thermodynamic stability at room temperature is almost the same as that at 0 K. This is also one of the reasons why Pt/TiO 2 single-atom catalysts can be widely used in ORR.

Conclusion
The calculation shows the effect of oxygen vacancy on the adsorption energy and d-band center energy of Pt atom on the surface of anatase and rutile TiO 2 . On the one hand, the introduction of oxygen vacancies will make the adsorption energy of TiO 2 for a single Pt atom increase, so that the Pt atom can be more stably adsorbed on TiO 2 . On the other hand, it will also cause the d-band center of the Pt atom toward the Fermi level, which will make it possible to have better catalytic performance. After introducing oxygen vacancies, the increase of adsorption energy makes the adsorption energy on some surfaces higher than the cohesive energy of Pt, which improves the thermodynamic stability of loading Pt atom on TiO 2 as SACs. The calculation results show that the (110) surface of rutile TiO 2 with oxygen vacancies has a better balance between the adsorption energy and the center of the d-band among the five common surfaces calculated, and is more suitable for SACs.