Role of vacancies, light elements and rare-earth metals doping in CeO2

The magnetic properties and electronic structures of pure, doped and defective cerium oxide (CeO2) have been studied theoretically by means of ab initio calculations based on the density function theory (DFT) with the hybrid HF/DFT technique named PBE0. Carbon (C), nitrogen (N), phosphorus (P), sulphur (S), lanthanum (La) and praseodymium (Pr) doped in CeO2 and CeO2 containing oxygen vacancies (Ov) were considered. Our spin-polarized calculations show that C, N, Pr dopants and Ov defects magnetize the non-magnetic CeO2 in different degree. The optical band gap related to photocatalysis for pure CeO2, corresponding to the ultraviolet region, is reduced obviously by C, N, S, Pr impurities and oxygen vacancies, shifting to the visible region and even further to the infrared range. Especially, N-, S- and Pr-doped CeO2 could be used to photocatalytic water splitting for hydrogen production. As the concentration of Ov increasing up to 5%, the CeO2 exhibits a half-metallic properties.

Scientific RepoRts | 6:31345 | DOI: 10.1038/srep31345 Results Magnetic properties. Cerium oxide (CeO 2 ), or ceria, is a lanthanide oxide with a cubic fluorite structure (Fm3m) and a cell parameter of 5.41 Å at room temperature, in agreement with our PBE0 result of 5.49 Å, as shown in Fig. 1(a).
First, we invested the magnetic properties of pure, doped and defective CeO 2 . Table 1 lists the magnetic moment of doped and defective CeO 2 , and shows that C, N and Pr dopants and O vacancies (O v ) magnetize the pure CeO 2 in different degree. C impurity introduces a global magnetic moment of 2.0 μ B per supercell. The C atom does the most contribution (0.733 μ B ) to the total magnetic moment, and the four nearest Ce and six next-nearest neighboring O atoms provide 0.090 μ B per Ce and 0.035 μ B per O, respectively. Spin-polarized charge density calculation indicates that C 2p electrons diffuse to the second-nearest neighboring O atoms and lead to a polarization of surrounding O and Ce atoms, implying FM coupling between the doped C atom and its neighboring atoms (see Fig. 1(b)). N impurity magnetizes the pure CeO 2 with a magnetic moment of 1.0 μ B per surpercell, being smaller than that of C dopant. The N atom and six second-nearest O atoms contribute 0.563 μ B and 0.048 μ B per atom to the total magnetic moment respectively, whereas the spin-polarized contribution from the nearest Ce could be neglected. In a defective CeO 2 system containing oxygen vacancies, two unpaired electrons localize in one O v , leaving cation dangling bonds. When the O v site is occupied by the C or N dopant, the two unpaired localized electrons fulfill 2p orbitals of the dopant, and according to Hund's rules, the substitutional C or N has four or five 2p electrons with high-spin configuration of 2p 4 (↑ ↓ ↑ ↑ ) for C or 2p 5 (↑ ↓ ↑ ↓ ↑ ) for N, which may create magnetic moment of 2.0 μ B or 1.0 μ B per impurity atom. Additionally, we found that P and S dopants do not produce spin-polarization in pure CeO 2 . For the P-doped case, according to effective charge calculation, 3p elections of the P impurity are much more delocalized than in the N-doped case, which leads to a vanishing of spin polarization.
We have also calculated La-and Pr-doped CeO 2 , to investigate the magnetic properties affected by lanthanide elements. From our calculations, La does not introduce spin polarization, whereas Pr magnetizes the doped CeO 2 with a magnetic moment of 1.0 μ B per supercell. For the Pr-doped CeO 2 , the localized 4f electrons do the most contribution (1.211 μ B ) to the magnetization and the 2p electrons of the eight nearest O atoms occur opposite spin polarization with a non-negligible magnetic moment of − 0.032 μ B per O (see Fig. 1(c)). On the other hand, the La-doped CeO 2 has no magnetizing phenomenon, and it is mainly due to the unpaired electron delocalization, being responsible for spin pairing.
Furthermore, we investigated the defective  Table 2 collects all the band gaps between the top of occupied states and the bottom of the unoccupied states for doped and defective CeO 2 . For the C-doped CeO 2 system, four separated bands are introduced between the VB-CB gap. Because the C impurities magnetize CeO 2 , the band structure of C-doped system is polarized magnetically. Two bands are α-spin states and others β-spin states, as we can see in Fig. 2. Fermi level is located at the top of β1 band and the unoccupied β2 band is below the CB bottom, which leads to a reduced gap of 1.85 eV corresponding to an optical absorption. The two α-spin bands are all above the VB top and below the Fermi level, and the first possible optical absorption corresponds to an electron transition from the α2 band to CB bottom (2.68 eV) in α-spin state. So, the C impurities considerably reduce the forbidden gap of pure CeO 2 by 37% for α-spin and 56% for β-spin states. When the band gap is reduced, electrons from the VB top can migrate easily to the CB bottom by absorbing light, forming electron-hole pairs. The electrons and holes that accumulate on the surface of material are then scavenged by oxygen molecules (O 2 ) and hydroxides (OH − ) dissolved in water to yield highly oxidative species, such as superoxide radical anions ( •− O 2 ) and hydroxyl radicals ( • OH), which are responsible for decomposing and degenerating pollutants. Therefore, photocatalysis is closely related to the optical band gap of materials. C dopant shifts the optical response of CeO 2 from the UV to the visible region and change the photocatalytic properties of CeO 2 .
CeO 2 is not only a potential photocatalyst for water/air purification, but also a candidate used in photocatalytic water-splitting for hydrogen production. Both applications require essential photogeneration of electron-hole pairs, which is closely connected with the band gap. According to our calculations on C-doped CeO 2 , the bottom of unoccupied states of αand β-spin are both higher (negative) than hydrogen production level (E H H O / 2 2 ) by 2.5 eV for α-spin and 2.2 eV for β-spin, meeting the requirement to initiate hydrogen production. On the other hand, the top of the occupied states located much higher than water oxidation level (E O H O / 2 2 ) for both spin states, which does not satisfy the requirement for effective water oxidation. However, the α1 occupied band is close to the E O H O / 2 2 , being slightly higher by 0.3 eV. Though it also does not meet the water oxidation requirement, quite small difference and the ineluctable errors from theoretical calculations make C-doped CeO 2 a probable photocatalyst for hydrogen production.
DOS analysis shows that C and neighbour O 2p orbitals form the α1 band, and the unoccupied β2 band consists of C 2p and the neighbour Ce 4f orbitals. The C 2p states lead to the neighbour O 2p electrons and Ce 4f orbitals separate from the VB top and CB bottom respectively, forming hybridization orbitals, as we can see Fig. 2. Spin-polarized DOS calculations also can reveal the magnetization mechanism. The number of spin-up electrons should be more than that of spin-down states for a system with net magnetic moment. For C-doped CeO 2 , we found that there are obviously more α-spin electrons near the Fermi level, where the C 2p, neighbour O 2p and Ce 4f α-spin states are dominant. The integrated DOS calculations also demonstrated that the magnetism mainly results from the spin-exchange splitting between the αand β-spin states near the Fermi level. Similar scenario is also observed in other C-or N-doped systems 14 . Figure 3 shows that there are three separated β-spin bands introduced between the VB-CB gap and one α-spin band connected with the VB top for N-doped CeO 2 . Fermi level is at the top of β2 band. The gap related to the α-spin electron transition equals to 3.96 eV, being much larger than that of C-doped case and closing to the pure CeO 2 , whereas the corresponding gap for β-spin state is only 0.47 eV (see Table 2). Similar to the C-doped case, N 2p and the neighbour O 2p orbitals do the major contributions to the impurity bands. The N impurities pull the neighbour O 2p electrons from VB top towards Fermi level, however the affection on the neighbour Ce 4f orbitals could be neglected (see Fig. 3). Therefore, a degree of hybridization between the N 2p and neighbour O 2p states can be seen near the Fermi level. The α-spin gap related to photocatalysis meets the requirements for water spitting, whereas the slight reduction of the gap with respect to the pure CeO 2 implies that photocatalytic water splitting occurs near the UV region. We found that occupied-β1 band approximately lies at the same level as E O H O / 2 2 , and unoccupied-β3 bands locates 0.46 eV above the E H H O / 2 2 . Therefore, the optical absorption corresponding to an electron transition from occupied-β1 to unoccupied-β3 bands (1.6 eV), which satisfies the conditions of photocatalytic water splitting, suggests that N-doped CeO 2 could be applied in visible-region photocatalysis for hydrogen production. P-and S-doped CeO 2 do not exhibit the magnetization like C-and N-doped cases, thus the band structures are not spin-polarized. P impurities introduce three separated bands between the VB-CB gap. Two of them are narrow and below the Fermi level, and the third band is expanded and crosses the Fermi level with a tail, which shows a degree of metallic properties, as we can see in Fig. 4. For the S-doped CeO 2 system, there are also three approximately separated bands introduced between the VB-CB gap. The two lower bands are narrow and the third impurity band is expanded but does not cross the Fermi level, unlike the P-doped case, still showing insulating properties (see Fig. 4). The gap between the top of occupied states and the bottom of unoccupied states is 2.85 eV, reducing the VB-CB gap of pure CeO 2 considerably by around 33%. On the other hand, the first impurity band for the P-doped case locates above the VB top 1.55 eV, being much higher than that of the S-doped case (0.49 eV), which implies that P 3p orbitals are more delocalized. Similar to the C-and N-doped cases, for P-and S-doped CeO 2  Lanthanide impurities, such as La and Pr, change the band and electronic structures of pure CeO 2 . We found that unlike the above-mentioned dopants, La impurities do not introduce separated bands between the VB-CB gap. There are a few states crossing the Fermi level, exhibiting a little metallicity for the La-doped CeO 2 system, as   level, meeting the water-spitting requirements. Therefore, Pr-doped CeO 2 also could be used in hydrogen production. DOS calculations demonstrate that these separated vacant bands mainly consist of Pr 4f orbitals and the contributions from other orbitals could be neglect, therefore the f-p hybridization is not remarkable for these bands. We also found that there are a few α-spin states moving out of the VB top towards the Fermi level (see Fig. 5). A slight f-p hybridization between Pr and neighbor O exists near the Fermi level.
Further, we performed calculations on the supercell containing 1, 2, 3 and 4 oxygen vacancies (labeled with 1O v , 2O v , … ) to investigate the electronic structure of defective CeO 2 . For the 1O v case, two connected bands with α-spin state lie 3.08 eV above the VB top, governing the Fermi level, and the gaps between the top of occupied and the bottom of unoccupied bands are 0.79 eV and 4.60 eV for αand β-spin states respectively (see Fig. 6). So, the O v reduces considerably the optical gap (4.24 eV) by around 81% in one spin state, whereas slightly increases it in the other spin state. Therefore, the photocatalysis of CeO 2 containing oxygen vacancies may even shift up to the infrared region. The formation of an O v is known to result in the donation of two electrons which form the defect bands locating between the VB-CB gap. According to our DOS calculations, the defect bands show mostly neighbour Ce 4f character. Then we can conclude that the two electron left behind localize on the f-level traps of the neighbour Ce atoms.
For the 2O v and 3O v cases, there are several α-spin bands lying between the VB-CB gaps, as we can see Fig. 7. The gaps with α-spin state between the top of occupied and the bottom of unoccupied bands are 0.57 eV for the 2O v case and 0.64 eV for the 3O v case, even reducing the optical gap further. Both cases have separated vacant α-spin bands below the CB bottom. Finally, for the 4O v case, corresponding to the defect concentration of around 5%, the defective CeO 2 system shows an obvious half-metallic character (see Fig. 7). Therefore, the charge carriers within the defect bands are sufficiently mobile with an ideal 100% polarization, which meets the need for spin injection where a highly polarized spin current is desired.

Methods
We have studied the magnetic properties and electronic structures of doped and defective CeO 2 by performing first-principles calculations based on the DFT. Ab initio simulations were performed using the projector augmented wave (PAW) method 15 as implemented in the Vienna ab initio simulation package (VASP) code 16,17 . We have chosen the exchange-correlation functional proposed by Perdew et al. using the hybrid HF/DFT calculation denoted hereby PBE0 18 . For Ce atoms, we have used PAW potentials with following orbitals treated as valence states: 5s 2 5p 6 6s 2 4f 1 5d 1 configuration. The calculations were performed using a cutoff energy of 500 eV and sampling the Brillouin zone with fixed Monkhorst-Pack k points (3 × 3 × 3) for conventional cell and (5 × 3 × 1) for a 72-atom (1 × 2 × 3) supercell.