A DFT study of diesel exhaust NO x reduction over rare earth CeO 2 catalyst

. Adsorption of NO on the CeO2(110) surface was investigated using RPBE approach of GGA within the framework of density functional theory (DFT) combined with periodic slab model. Two molecular orientations, N-end and O-end, over various adsorption sites, top, hollow, bridge and O site of CeO2(110) sur-face have been considered. Two molecular orientations under different coverage of CeO2(110) surface also have been considered. The optimized results indicate that the N-end adsorption models are more stable than the O-end ones. So N-end adsorption was more favourable than O-end. NO adsorption on a clean CeO2(110) surface was physisorption, while chemical adsorption occurred in the present of surface oxygen vacancy. Adsorption is stable when coverage was set to 0.25 monolayer. Researched on density of states of free NO molecule and adsorbed NO molecule, the results show that there is an interaction between NO molecule and the substrate . The population analysis indicates that the charges transfer from Ce atoms to NO molecule. The charges transfer of O-end is more than N-end.

concentration on CeO2 surface. Ceria based catalysts have sufficient oxygen vacancy to accelerate NO decomposition. However, due to limitation of methods, it is unfeasible to reveal the site, configuration, energy and electronic structure of NO adsorption. Recently, designing new materials from atomic and molecular level has been widely used. Combined with experimental methods, it can greatly reduce dependency on instruments and chemical reagents and theoretically study underlying mechanisms of catalytic reactions. Therefore, it is a suitable ideology to find selective, active and anti-toxic catalyzer. In this paper, the interaction between NO and CeO2 was discussed by theoretical calculation.
The NO adsorption pattern on CeO2(110) surface was systemically studied under density functional theory framework [8][9][10][11][12][13] . Firstly, models of NO adsorption by N terminal and O terminal on various adsorption sites on CeO2(110) surface were calculated. Secondly, stability and energy of adsorption sites of NO on CeO2(110) surface with oxygen vacancy under different coverage were investigated and charge transformation was revealed by state density and layout analysis.

Model and Calculation
The Pure CeO2 is cubic fluorite crystal with face-centered cubic atomic arrangement in unit cell. Each Ce atom is surrounded by eight oxygen atoms, with space group of Fm3m and lattice parameters of a=b=c=5.411Å ， α=β=γ=90° [ 14] . The DFT calculation suggests CeO2(110) surface has the lowest formation energy of oxygen vacancy to generate Ov, compared to CeO2(100) and CeO2(111) [15][16] . Therefore, it can provide more surface reactive oxygen species highly active in catalytic reactions [17] . In this research, CeO2(110)-2×2 and CeO2(110)-3×3 supercells were chosen for NO adsorption by N terminal and O terminal. Figure 1. Shows the models of CeO2(110)-2×2 and CeO2(110)-3×3 supercells. The NO adsorption on CeO2(110) surface was simulated by combined method of periodic slab model and GGA-RPBE of density functional theory. All calculation was carried out by Dmol 3 software kit [18][19][20][21] . For the calculation of geometry structure optimization and transition state, density functional theory has been proved to be a reliable tool [22] . Core electrons of CeO2 atom was substituted by effective core potential (ECP) during calculation. The wave functions were expanded by double number polarization function (DNP). All electron basis set was implemented for N and O atoms. Cutoff energy was set as 380eV. Brillouin zone was sampled at k point with Monkhorst-Pack method [23] . The set of accuracy in energy calculation and structure optimization was as following: (1) Self-consistent field energy convergency was 1.0×10 -4 eV (2) Maximum force was 0.2eV·nm -1 . Converging energy from optimization was less than 1.0×10 -3 eV. Through geometric optimization, bond length of N-O in free NO molecule was 1.169 Å, which was similar to the result from experiments, 1.151Å [24] . 10 Å vacuum was reserved between two layers to erase potential interactions.
Formation energy of oxygen vacancy on CeO2(110) surface was represented by: Where EVCeO2 was the energy of single oxygen vacancy on CeO2(110) surface, EO2 was the energy of gas oxygen molecule, and ECeO2 was the surface energy of clean CeO2.
The adsorption energy on clean CeO2(110) surface was calculated as the change of total energy of all substances during the adsorption: Where Eads was adsorption energy, ENO was energy of NO before adsorption, Esubstrate was energy of substrate before adsorption. E(NO+substrate) was the energy of the whole system after adsorption. Minus value of Eads indicated NO adsorption release heat, vice versa.
The adsorption energy on CeO2(110) surface with oxygen vacancy was defined as: 2 2 ads Where ENO/VCeO2was the energy of NO and CeO2 surface interaction system.

The calculation of NO molecule
Firstly, the bond length and binding energy of NO molecule were calculated by different methods to verify the reliability of the method selected in this study. The results are shown in table 1. GGA-ROBE method generated closest results to experimental results. So this method was implemented in following steps.

The comparison of NO adsorption at various sites on CeO2(110) surface
In order to investigate the adsorption mode of NO on the surface of CeO2(110), the geometric configuration parameters and adsorption energy of NO on the surface of CeO2(110) with oxygen holes and clean were calculated. According to the projection position of center of NO on CeO2(110) surface, four adsorption sites were considered, including Top site, Hollow site, Bridge site and O site. Figure 2 illustrates the four sites.  Table 2 indicates the adsorption energy under coverage of 0.25mL. On clean CeO2(110) surface, the adsorption energy was less than 40kJ/mol and the adsorption was physical. N terminal adsorption was more stable than O terminal at each site. The energy of adsorption by N terminal was O＞top＞hollow＞bridge. The energy was highest with N terminal at O site but only reached to 39.6 kJ/mol. The distance between N and O atoms was 2.55 Å. These results were consistent with the results from Yang et al [26] , which suggests minimum NO adsorption occurred on CeO2(110) surface with complete stoichiometric ratio. The increasing N-O bond length by adsorption suggests the adsorption weakened the NO bond, which is beneficial to further decomposition of NO. In this case, O terminal adsorption was more effective than N terminal adsorption.

NO adsorption on Ov/CeO2(110) surface
Based on the above analysis, NO has the strongest adsorption at the n-terminal at the oxygen level, so we discuss the n-terminal adsorption at the oxygen level on the surface of Ov/CeO2(110). Figure 3(a) is the structure of oxygen vacancy on CeO2(110) surface. By calculation, the formation energy of oxygen vacancy was 180.4kJ/mol which was similar to the result from references [27] . Figure 3(b) was NO adsorption configuration on oxygen vacancy. After adsorption, NO bond length was 1.149Å, shorter than the bond length in free NO molecule. The oxygen significantly increased adsorption energy which were 135.1kJ/mol with N terminal and 80.1kJ/mol with O terminal. Additionally, there was certain interaction between NO and surface of oxygen vacancy. Therefore, NO adsorption will be more effective with N terminal on CeO2(110) surface with oxygen vacancy.

The active of NO adsorption on Ov/CeO2(110) under different coverage
Geometric optimization was implemented to configuration under coverage of 0.25, 0.33, 0.50, 0.67mL and 1.00mL. Table 3 shows the results. The coverage was defined as ratio of number of adsorbed NO molecules and number of Ce atoms on the surface. For instance, when one NO adsorbed by CeO2(110)-2×2 surface, the coverage was 0.25mL. From table 3, adsorption energy decreased with increasing coverage. However, the energy increased when coverage was 1.00mL. The reason was that due to decreasing distance between NO molecules the interaction of NO enhanced with increasing coverage. The decrease of systemic energy after adsorption caused increasing adsorption energy. The calculation of bond length suggested that the NO bond length increased after adsorption and reached highest under coverage of 0.25mL, which was most suitable for further reaction of NO. To deeply understand the mechanisms of NO adsorption on Ov/CeO2(110), state density was calculated before and after adsorption. The results are shown in Table 4. There was a peek of state density of free NO at Femi. Compared to Figure 4(a), there was obvious changes of state density of free NO in Figure 4(b)-(f), which suggested that NO interacted with substrate during adsorption and energy band shifted to low energy level. Based on these results, it was speculated that the formation of adsorption bond was caused by the interaction between d orbit in Ce atom and inverse π orbit in NO molecule. Since d orbit with full electrons while inverse π orbit contains electron vacancy, the electron transferred from d orbit to inverse π orbit, causing elongation of N-O bond.

NO molecular layout analysis
The NO molecular layout under coverage of 0.25mL was further analyzed. Table 4

conclusions
This research calculated the NO adsorption on clean CeO2(110) surface or the surface with oxygen vacancy, with periodic slab model by RPBE approach of the generalized gradient approximation within the framework of density functional theory. The following conclusions are drawn.
(1) NO adsorption was physical with low adsorption energy on clean CeO2(110) surface. When oxygen vacancy existed on the surface, adsorption significantly increased and chemical adsorption occurred.
(2) The lengthening N-O bond after adsorption was beneficial to further decomposition of NO.
(3) The results under various coverage indicated that the smaller coverage induced more stable adsorption. This was caused by mutual repulsion between NO molecule. Therefore, the adsorption was most stable with the coverage of 0.25mL.
(4)Layout analysis suggested that charges transferred from Ce to NO in the whole system. More charges transferred in O-terminal adsorption than in N-terminal adsorption.