Adsorption properties of NO molecules on the hexagonal LaCoO 3 (0 0 1) surface: a density functional theory study †

Six types of adsorption con ﬁ gurations, together with two di ﬀ erent adsorption sites for NO adsorption on LaCoO 3 , were investigated via density functional theory. There were two types of terminal con ﬁ gurations for the LaCoO 3 (0 0 1) surface: CoO 2 - and LaO-terminated. We used the calculated adsorption energy, Mulliken and Hirshfeld charge analysis, the electron density di ﬀ erence and projected density of states analysis methods to determine the electronic and chemical properties of NO adsorbed on LaCoO 3 . We found that the Co-d and N-p orbitals played primary roles during electron transfer for NO adsorption on CoO 2 -terminated LaCoO 3 , and the O-p and N-p orbitals during the electron transfer for NO adsorption on LaO-terminated LaCoO 3 . Therefore, we assert that the optimal adsorption con ﬁ guration is Co – NO (N-end of NO on adsorption CoO 2 – LaCoO 3 ).


Introduction
With the rapid development of the science and technology of materials research, perovskites have received extensive attention 1 for their unique properties, such as stable structure, 2 electromagnetic characteristics, 3 thermal stability, 4 moderate price, widespread sources and gas sensitivity. In addition to the worsening environmental problems, 5-12 the air pollution due to particles is of concern. 13 Perovskites are sensitive to gas and act as gas sensing materials [14][15][16] that can adsorb and detect a very large number of poisonous gases, e.g., CO, NO x , SO 2 and VOCs. 17 These gases have received a wave of attention from research communities studying environmental catalytic materials, 18 and it can be seen that there is a lot of work to be done regarding the research on materials for environmental protection.
Studies have approved perovskites as catalytic materials for gas sensors 19,20 or locomotive tail gas processors to detect and adsorb the various harmful gases. Nunzio Russo et al. have expounded that the Li-substituted chromite catalyst, whose chemical formula is La 0.8 Cr 0.9 Li 0.1 O 3 , an alkali-metal-substituted perovskite compound, exhibits the highest activity in adsorbing poisonous gases, and they found that the catalyst had a great amount of weakly chemisorbed O À species that played key roles in the soot oxidation state. 21 Y. Teraoka et al. also revealed that the La-K-Mn-O perovskites showed activity in getting rid of NO x and soot, and thought that the potassium content was crucial since the activity of the catalyst varied with potassium content. 22 The nano-structured PrCrO 3 on CeO 2 was prefabricated by Debora Fino and Vito Specchia et al., who used the combustion synthesis technique, and then they adopted typical engine vibrations to test the catalytic activity. 23 All of the above cases involved research into the treatment of the exhaust gases by perovskites; however, the research on gas sensitive materials is also quite extensive. Changmin Shi et al. used density functional theory (DFT) to investigate LaMnO 3 , which can be used to detect CO, and calculate the adsorption energy for the CO molecule adsorption on LaMnO 3 . 24 Yongjia Zhang et al. also used DFT to study SrFeO 3 , but they selected the NO molecule to study the probable potential. 25 LaCoO 3 is a classical compound that has been widely studied and applied in various elds. Lihui Sun et al. used LaCoO 3 as the gas sensing material for detecting the CO molecule. 26 Beatriz Rivas-Murias et al. developed ferromagnetic insulating barriers of LaCoO 3 for devising spin-ltering tunnels in spintronic applications, according to the magnetic properties of LaCoO 3 . 27 NO gas has been, in recent years, recognized as a detriment to the atmospheric environment. In this study, we investigate the properties of LaCoO 3 as a catalytic agent for wiping out NO. Studying the electronic structures of the adsorption congurations can provide theoretical guidance for relevant experimental research.

Theoretical methods and computational details
CASTEP 28-33 package of Materials Studio (MS) 8.0. We did some optimization tests for the sake of determining the best optimized structure of the compound . We chose 14 types of orbital  cutoff values (300, 350, 400, 450, 500, 550, 600, 650, 700, 750, 800, 850, 900 and 950 eV) in computer simulation, which are shown in Fig. S1 in the ESI † and tried to gure out the most suitable energy cutoff value. Fig. S1 † shows that the orbital cutoff value of 600 eV is the best value. Based on this, the Kpoints were tested and the data are marked in Fig. S2. † Furthermore, in the process of geometry optimization, the functions were optimized under the LDA and GGA approximations to determine the best one. For these tests, we identied the orbital cutoff value as 600, K-points as 2 Â 2 Â 2, and the function as GGA with the PBEsol method to calculate the exchange and correlation energy. The constringency standards of optimal geometry, with respect to the maximum force, energy and maximum displacement, were 0.05 eVÅ À1 , 2.0 Â 10 À5 eV per atom and 0.002Å, respectively, with ultraso pseudopotentials. 34,35 The dipole correction was used to deal with the electric eld gradients in three-dimensional periodic supercells, which can affect electronic densities and binding energies.
In order to simulate the adsorption behavior of NO, the periodic supercell of 2 Â 2 Â 1 was constructed. This supercell for the CoO 2 -terminated surface of LaCoO 3 (0 0 1) contains 120 atoms, and 180 atoms for the LaO-terminated surface. Based on the literature, the length of the N-O bond was set as l N-O ¼ 1.17 A. 36 In our study, a NO molecule was attracted to the LaCoO 3 surface and the adsorption energy E ad was dened as follows: where E total is the total energy of NO adsorbed by the LaCoO 3 system, and E LaCoO 3 and E NO represent the energy of the LaCoO 3 and the free state of the NO molecule, respectively. There are two types of terminations in LaCoO 3 : LaO and CoO 2 terminations. The periodic boundary qualication was employed in the investigation with the reduplicated slab model. For the LaO-terminated surface, the slab consisted of nine La layers and nine Co layers, and for the CoO 2 -terminated surface, the slab consisted of six Co layers and six La layers, and both are shown in Fig. 1. Numerous early studies have authenticated that the (0 0 1) surface is the best in the ABO 3 , 37,38 and hence the LaOterminated and the CoO 2 -terminated (0 0 1) surfaces of LaCoO 3 are the most stable interfaces. The density functional theory calculations were used to study the adsorbing effect of NO on the LaO and CoO 2 -terminated LaCoO 3 (0 0 1) surface. The data could then guide the NO reaction in subsequent studies.

Results and discussion
3.1 Select functional, test orbital cutoff and K-points LDA and GGA are two types of general exchange-correlation energy approximation methods used during the process of geometry optimization. The structural optimization of LaCoO 3 using the 2 Â 2 Â 1 supercell was conducted by CA-PZ under LDA, and PW91, PBE, WC, RPBE, PBEsol under GGA. The specic computational conditions are shown in Table 1. By comparing the obtained results with experimental values, we found that LDA approximation methods were more applicable for calculating bonds lengths 39 and lattice parameters. 40 The Co-O bond length was 1.925Å and the lattice parameter was 5.446Å as calculated by CA-PZ, which approached the experimental values (1.929Å and 5.444Å); however the electron distributions were strongly restricted by LDA approximation, and the absolute value of the forbidden band width and the system binding energy were not suitable for analysis by LDA. Generally, the metal band gap calculated by GGA was closer to the experimental value than that calculated by LDA.
Relative deviations (%) of the optimized crystal parameters for hexagonal LaCoO 3 were as follows: Taking the experimental values of the lattice constant and energy band gap into consideration, we chose the GGA  approximation PBEsol functional to execute the subsequent study. There were two evident variation trends in Fig. S1: † when the cutoff energy ranged from 300 eV to 350 eV, the curve declined; when the cutoff energy ranged from 350 eV to 450 eV, the curve remained at. However, there was a signicant decline between 450 eV and 600 eV; hence, 350 eV was not the best choice. Aer 600 eV, there was a more stable trend in the image, making it clear that it converged very well in the structure optimization; therefore, we chose 600 eV as the value of orbital cutoff energy. Fig. S2 † clearly shows that it reached convergence for the Kpoints test using the GGA-PBEsol approximation when the value of the cutoff energy was 600 eV. It is clear that when the K-points value was 2 Â 2 Â 2, the image became smooth and did not change much; therefore, we chose 2 Â 2 Â 2 as the K-points value.
3.2 LaO-terminated and CoO 2 -terminated LaCoO 3 (0 0 1) surfaces Fig. 1 shows that the LaO and CoO 2 -terminated LaCoO 3 (0 0 1) surfaces have been adequately relaxed. We used the above functions and parameters to optimize them, and we could nd no drastic change for the LaCoO 3 (0 0 1) surface. The O atoms moved downward while the Co atoms moved upward on the CoO 2 -terminated LaCoO 3 (0 0 1) surface, which is in agreement with Sun's results. 41 During this process, we checked the length of the Co-O bond for the CoO 2 -terminated LaCoO 3 (0 0 1) surface. The length of the Co-O bond was always 1.937Å in every layer, which revealed that relaxation did not occur in this structure. This result is consistent with the slight relaxation phenomenon mentioned by Sun. 41 Nevertheless, we found that the La atoms moved downward and the O atoms shied upward for the LaO-terminated LaCoO 3 (0 0 1) surface. The length of the Co-O bond increased from 1.947Å to 1.953Å. This phenomenon showed that relaxation occurred in this structure.

NO adsorption on LaCoO 3
There were six adsorption congurations to choose from. When NO was adsorbed on different surfaces, including the CoO 2terminated and LaO-terminated LaCoO 3 (0 0 1) surfaces, all possible sites were investigated and only six congurations were suitable, which are listed in Fig. 2-4. We focused on adsorbing NO on the top site and bridge site of CoO 2 -terminated and LaOterminated LaCoO 3 (0 0 1) surfaces.
3.3.1 NO adsorption on the CoO 2 -terminated LaCoO 3 (0 0 1) surface. In this section, we focus on various phenomena and properties of NO adsorbed on the CoO 2 -terminated LaCoO 3 (0 0 1) surface, including adsorption energy, Mulliken charge and Hirshfeld charge analysis, the electron density difference and projected density of states (PDOS).
A. Adsorption energy. First, the clean CoO 2 -terminated LaCoO 3 (0 0 1) surface was fully optimized. Then, we put NO on the support and optimized this adsorption structure. In order to understand the optimal adsorption site of the NO molecules adsorbed on the CoO 2 -terminated LaCoO 3 (0 0 1) surface, we considered several different adsorption congurations. However, we found that only four types of adsorption congurations were not repetitive structures aer optimization, shown in Fig. 2    of these three O atoms is very unusual and they make the surface look like a hole. These O atoms are all connected to the same Co atom and they are also connected to three other Co atoms. In Fig. 4(B), the O atom of the NO molecule is close to the O atoms of the CoO 2 -terminated surface (NO O-end CoO 2 -LaCoO 3 bridge); these two adsorption sites belong to the bridge site.
Adsorption energies of all congurations were calculated on the basis of eqn (1); it can be clearly seen from Table 2 that all the values of adsorption energy were negative, implying that the adsorption structures were stable, and the adsorption processes were exothermic. At the top site (Co-NO and Co-ON), the values of the adsorption energies were À3.59 and À2.165 eV, respectively, and the values of the corresponding bond lengths were 1.649 and 1.732Å, respectively. At the bridge sites (NO N-end and NO O-end of the CoO 2 -LaCoO 3 bridge), the adsorption energies were À1.152 and À1.406 eV, respectively, and the corresponding bond lengths were 2.307 and 2.725Å, respectively.
Based on the above description, we will discuss the four adsorption congurations in this study. Since we will focus on discussing the NO reaction on the LaCoO 3 surface in another report, we will not consider the other factors. The Co atom formed a chemical bond with the NO molecule on the top site. Shi 42 pointed out that when CO was adsorbed on LaMnO 3, forming the covalent bond, the C-O bond length of the adsorbed CO molecule would be greater than that of the free CO molecule, which is in accordance with our calculated results. As mentioned above, the adsorption energy at the top site is relatively large and the values are within the range of chemisorption energy. However, the adsorption energy of the bridge site is much smaller than that of the top site and we found that NO molecules adsorbed on LaCoO 3 formed covalent bond interactions; therefore, we considered that NO molecules adsorbed on the bridge site were not stable chemisorptions. The most outstanding state conguration was the Co-NO conguration. The NO molecule is inclined to be adsorbed on the CoO 2terminated LaCoO 3 (0 0 1) surface, and the results are consistent with the literature, in which Sun 43 obtained the most favorable adsorption structure with the Fe-NO conguration (the N atom of NO molecule connected to the Fe site). Zhang 44 gured out in the adsorption of NO on the TiO 2 -terminated SrTiO 3 (0 0 1) that the N atom of the NO molecule was downward, which was more benecial for adsorption. Yongjia Zhang 45 reported that the optimal conguration was the Fe-NO structure for the FeO-terminated SrTiO 3 (0 0 1) surface adsorbed NO. This indicated that the B element in the ABO 3 perovskite was the key element for adsorbing gases, based on the above conclusions.
B. Mulliken charge and hirshfeld charge analysis. In order to present detailed results, we calculated the Mulliken charge and Hirshfeld charge for NO adsorption on the CoO 2 -terminated LaCoO 3 (0 0 1) surface in Table 2. Aer NO molecules were adsorbed on the CoO 2 -terminated LaCoO 3 (0 0 1) surface, the equilibrium of the initial charge distribution was destroyed. Table 2 shows whether the Mulliken charges of the O atoms of NO were negative for NO adsorption at the top site or bridge site on the CoO 2 -terminated LaCoO 3 (0 0 1) surface. The Mulliken charge of the N atoms of NO was negative on the top site; however, the charge of N atoms on the bridge site was positive. The total charge of O and N atoms (Q O+N Mulliken (e)) was also   (0 0 1). On the other hand, the stable chemical bond did not form at the bridge site, the changes of the values were extremely small, and the electron transfer occurred with NO.
C. The electron density difference analysis. Aer the adsorption of NO on LaCoO 3 , the charge on LaCoO 3 was equably distributed in the chemical bond, instead of collecting on a certain atom, revealing a strong covalent bond. In order to be more straightforward in explaining the impact of the charge density for NO adsorption on LaCoO 3 , we have calculated and drawn the electron density difference for NO adsorption on CoO 2 -terminated LaCoO 3 (0 0 1), as shown in Fig. 5. We dened the electron density difference (Dr) as follows: where r NO-LaCoO 3 is the total electron density of the adsorbed system, r LaCoO 3 is the electron density of the pure LaCoO 3 and r NO was the electron density of the free state of the NO molecule.
As can be seen from Fig. 5(A), the pronounced charge accumulation occurs on the bond between the N atom of NO and Co atom of CoO 2 -terminated LaCoO 3 , indicating that a large electronic accumulation was the key factor for bonding, and the formative chemical bond was very strong. However, Fig. 5(B) shows a similar phenomenon in comparison to Fig. 5(A), between the O atom of NO and the Co atom of CoO 2 -terminated LaCoO 3 , which also forms a stable chemical bond; however, the accumulated charge in Fig. 5(A) is more abundant than that in Fig. 5(B), suggesting that the formative chemical bond for the Co-NO conguration is more stable than that for the Co-ON conguration. This result proves that the adsorption energy of the Co-NO conguration is larger, compared to the Co-ON conguration. Both the O atom and N atom of the NO molecule obtained electrons for NO adsorption on the CoO 2 -terminated LaCoO 3 , and these results agree well with those mentioned above in the Mulliken and Hirshfeld charge analysis.
D. Projected density of states (PDOS) analysis. To obtain a further insight into the contributions of the Co, N and O atoms, we investigated the PDOS for NO adsorption on the CoO 2 -terminated LaCoO 3 (0 0 1) surface, as shown in Fig. 7-10. Fig. 10 shows the PDOS, including the N-p orbital of NO and the O-p orbital of LaCoO 3 , and NO before and aer adsorption. There was an evident change in the O-p PDOS near the Fermi level, and the overlapping peaks aer adsorption were signicantly increased, compared to those before adsorption, indicating that the electrons were transferred from LaCoO 3 to NO and there was a certain interaction between NO and the surface. It is evident from Fig. 9 that the PDOS of the O-p orbital of LaCoO 3 before and aer adsorption had scarcely any change. However, the PDOS of the N-p orbital of NO had some change, suggesting that there was no stronger bonding interaction between NO and LaCoO 3 . Both of the above results were consistent with the Mulliken charge and Hirshfeld charge analysis. We can conclude that less transferred charges meant weaker interactions between NO and the surface.   Compared to the before adsorption, the aer adsorption had a notable change. From the PDOS of N and Co for NO adsorption on the CoO 2 -terminated LaCoO 3 (see Fig. 7 aer), it is clear that the Co-d states offered tremendous contributions to bands in the scope of about À5 eV to 0 eV, with a negligible component of the N-p states. Because the surface lost a lot of electrons, and electrons were transferred to NO, the Co-N bond was formed. A strong overlap of Co-d and N-p states in the range of about À8 eV to 1 eV denoted the appearance of some hybridization between the d orbital of Co and the p orbital of N, indicating that an intense reaction occurred between the adsorbed NO and the Co of the surface. These results were also consistent with Mulliken charge analysis, Hirshfeld charge analysis and the electron density difference analysis. Therefore, we claim that the p orbitals of NO and the d orbitals of Co are the critical factors leading to bonding with adsorbed NO.  Table 2), it was clear that the charges of the O atoms of NO were negative, the charges of the N atoms were 0.160e, 0.120e, 0.120e and 0.05e, respectively, and the charges of N atoms were positive for NO (N downward Fig. 7 The projected density of states (PDOS) of the NO N-p orbital, and Co-d orbital on the CoO 2 -terminated LaCoO 3 (0 0 1) surface at the top site. "Before" indicates that NO was not adsorbed on the LaCoO 3 surface, and NO and CoO 2 -terminated LaCoO 3 were calculated in a single crystal structure (free-NO and free-CoO 2 -terminated LaCoO 3 ); "after" indicates that NO was adsorbed on the LaCoO 3 surface and the N-end (N atom downward) on the CoO 2 -terminated LaCoO 3 . Fig. 8 The projected density of states (PDOS) of the NO O-p orbital, and Co-d orbital on the CoO 2 -terminated LaCoO 3 (0 0 1) surface at the top site. "Before" indicates that NO was not adsorbed on the LaCoO 3 surface, and NO and CoO 2 -terminated LaCoO 3 were calculated in a single crystal structure (free-NO and free-CoO 2 -terminated LaCoO 3 ); "after" indicates that NO was adsorbed on LaCoO 3 surface and O-end (O atom downward) on CoO 2 -terminated LaCoO 3 . Fig. 9 The projected density of states (PDOS) of the NO N-p orbital, and O-p orbital on the CoO 2 -terminated LaCoO 3 (0 0 1) surface at the bridge site. "Before" indicates that NO was not adsorbed on the LaCoO 3 surface, and the NO and CoO 2 -terminated LaCoO 3 were calculated in a single crystal structure (free-NO and free-CoO 2terminated LaCoO 3 ); "after" indicates that NO was adsorbed on the LaCoO 3 surface and N-end (N atom downward) on CoO 2 -terminated LaCoO 3 . or O-NO) adsorption on the LaO-terminated surface. The total charges (Mulliken and Hirshfeld charges) of N and O atoms (Q O+N ) were negative for the N-end of NO adsorption on the LaOterminated surface, while they were positive for the O-end of NO on the LaO-terminated surface. These results revealed that the O atom gained electrons, the N atom lost electrons, and the NO (N-end) acted as an acceptor, due to the NO (N-end) forming stable chemical bonds with the surface for the N-end of NO adsorption on the LaO-terminated surface. Nevertheless, for the O-end of NO adsorption on the LaO-terminated surface, the NO (O-end) acted as a charge donor, forming bonds with the surface. The calculated adsorption energy for the N-end of NO adsorption on the LaO-terminated surface was À3.213 eV, which is much larger than that of the O-end of NO adsorbed on the LaO-terminated surface because the O-NO could form bonds and the O-ON could not form bonds. Fig. 6 shows the electron density difference for NO adsorption on the LaO-terminated surface. It was unmistakable that the charges accumulated between O and NO (Fig. 6A), in which the blue indicated losing electrons and the red indicated obtaining charges. From different electron density maps, we noticed that the result of the population analysis was relative to the electron density, which proved that our calculation was reasonable.
To ascertain the particular atomic orbital in the charge transfer during NO adsorption on the LaO-terminated surface, we investigated the PDOS of N and O, which are shown in Fig. 11 and 12, respectively, in the ESI. † By comparison of the PDOS before and aer adsorption, it was evident that the peaks of the held states shied to lower energy for NO adsorption on the LaO-terminated surface. A strong overlap of N-p and O-p states from À8 eV to 0 eV signied that there was some hybridization between the p states of O and p states of N. This result is in good agreement with Mulliken charge, Hirshfeld charge and the electron density difference. We also considered that the p orbitals of N and O played an important role in explaining the bonding mechanism.

Conclusions
In conclusion, we have conducted an overall inquiry into the adsorption properties of the NO molecule on the LaCoO 3 surface with different adsorption congurations and sites. Analysis of the adsorption energy, Mulliken charge and Hirshfeld charge analysis, electron density difference and projected Fig. 10 The projected density of states (PDOS) of the NO O-p orbital, and O-p orbital on the CoO 2 -terminated LaCoO 3 (0 0 1) surface at the bridge site. "Before" indicates that NO was not adsorbed on the LaCoO 3 surface, and NO and CoO 2 -terminated LaCoO 3 were calculated in a single crystal structure (free-NO and free-CoO 2 -terminated LaCoO 3 ); "after" indicates that NO was adsorbed on the LaCoO 3 surface and the O-end (O atom downward) on CoO 2 -terminated LaCoO 3 . Fig. 11 The projected density of states (PDOS) of the NO N-p orbital and O-p orbital on the LaO-terminated LaCoO 3 (0 0 1) surface at the top site. "Before" indicates that NO was not adsorbed on the LaCoO 3 surface, and NO and LaO-terminated LaCoO 3 were calculated in a single crystal structure (free-NO and free-LaO-terminated LaCoO 3 ); "after" indicates that NO was adsorbed on the LaCoO 3 surface and the N-end (N atom downward) on the LaO-terminated LaCoO 3 . Fig. 12 The projected density of states (PDOS) of the NO O-p orbital, and O-p orbital on the LaO-terminated LaCoO 3 (0 0 1) surface at the top site. "Before" indicates that NO was not adsorbed on the LaCoO 3 surface, and NO and LaO-terminated LaCoO 3 were calculated in a single crystal structure (free-NO and free-LaO-terminated LaCoO 3 ); "after" indicates that NO was adsorbed on the LaCoO 3 surface and the O-end (O atom downward) on LaO-terminated LaCoO 3 . density of states revealed the primary role of the Co-d orbital and N-p orbital during the electron transfer for NO adsorption on the CoO 2 -terminated LaCoO 3 and the pivotal role of the O-p orbital and N-p orbital during the electron transfer for NO adsorption on LaO-terminated LaCoO 3 . All results reected the fact that NO was adsorbed on the LaCoO 3 surface to form bonds such as Co-O, Co-N and O-N. I. Twagirashema et al. 46 and M. Pirez-Engelmann et al. 47 used the experimental method and also observed that LaCoO 3 removal of NO has a good effect.
Our calculations elucidated the predominant role of LaCoO 3 in adsorbing NO exhaust gas. If we allow the CoO 2 -terminated LaCoO 3 to act as the adsorption surface, the absorption efficiency is better. These results provide theoretical support for studying the reaction of NO and exhaust gas on LaCoO 3 , as well as excellent guidance for NO exhaust gas treatment.