Density functional theory analysis for H2S adsorption on pyridinic N- and oxidized N-doped graphenes

Biomass discharged from primary industries can be converted into methane by fermentation. This methane is used for generating electricity with solid oxide fuel cells (SOFCs). This methane fermentation provides H2S, which reduces the efficiency of SOFCs even at a level as low as a few parts per million. It has been experimentally reported that a nitrogen (N)-doped graphene-based material known as pyridinic N removes H2S via an oxidation reaction compared with another graphene-based material known as oxidized N. To understand this experimental result, we investigated H2S adsorption on pyridinic N and oxidized N by a density functional theory analysis and further examined the activation barrier of dissociation reactions. We found that the adsorption of H2S on pyridinic N is more stable than that on oxidized N. In addition, the H2S dissociation reaction occurs only on pyridinic N.


Introduction
Approximately 80% of the world's ever-increasing energy demand is met by fossil fuels. 1,2 They supply a signicant amount of electrical energy to our society. These reserves are nite and many countries are actively promoting the use of renewable energy sources in anticipation of their depletion in the future. 3,4 As constant generation of electricity from renewable energy sources is difficult, storage of the electrical energy using hydrogen as an energy carrier has received attention. Compared to conventional batteries, hydrogen is superior in storing energy on a large scale and for long time. 5 To extract electricity from hydrogen, we can use fuel cells that emit only water and then have a low impact on the environment. 6 The economic activity of producing, storing, and nally using hydrogen is called the hydrogen-based economy, and it is increasingly expected to be the economy that supplies electric energy to society in a sustainable way. [7][8][9] One of the most environmentally friendly ways to produce hydrogen is water electrolysis using renewable energy. Some Organisation for Economic Cooperation and Development (OECD) countries such as Japan and Germany started demonstration. 10,11 However, due to protability issues, only the countries mentioned above attempt to make it a self-sustaining economic activity, while non-OECD countries do not. 12,13 The non-OECD countries account for more than 80% of the total number of world countries, 14 and the growth of energy demand in the future is expected to be much larger than that of OECD countries. Then, introducing the hydrogen-based economy with environmentally friendly ways to non-OECD countries is a major challenge to build a sustainable society on a global scale. 14 As one of the ways to lead the challenge to success, combining biogas and fuel cells has attract ed attention. 15 The ow diagram shown in Fig. 1 illustrates the use of biomass from primary industries such as agriculture and aquafarming. This biomass is converted into biogas by anaerobic digestion also known as methane (CH 4 ) fermentation. This CH 4 in biogas is used as an energy carrier of hydrogen and it is converted into electrical energy with solid oxide fuel cells (SOFCs). Following a reforming reaction shown in eqn (1) and (2), the H 2 gas is extracted from CH 4 , with H 2 O, CO 2 , and CO. 16 Then, hydrogen reacts with oxide ions (O 2À ) coming from the cathode side in fuel cells, as shown in eqn (3). 17 This O 2À is supplied from O 2 gas in the cathode side. Regarding CO shown in eqn (1) and (2), it reacts with oxygen in the air and it is released into the atmosphere as CO 2 . One of the attractions of biomass is that it absorbs a certain amount of CO 2 already at the plant growth stage. Therefore, the environmental impact of biomass is considerably smaller than that of CO 2 generated when simply burning geo-derived resources such as coal and oil. This can be said to be the same advantage of bioethanol. 18,19 In fact, the demonstration experiment has been started by Shiratori et al., and they fermented biomass derived from aquafarming of shrimp in Vietnam. 20 This initiative is a remarkable attempt to use CH 4 as an energy carrier of hydrogen and introduce the hydrogen-based economy because non-OECD countries are mainly dominated by primary industries and they do not have a well-equipped hydrogen infrastructure. 21 For the realization of the hydrogen-based economy using biogas, it is essential to increase the power generation efficiency of SOFCs. Ideally, it is the best way using pure CH 4 . However, actual biogas provided from biomass contains some amount of hydrogen sulde (H 2 S), [22][23][24] and it contaminates biogas in the process of anaerobic digestion process to form CH 4 . 25 The amount of H 2 S is approximately 1 ppm and such amount reduces the efficiency of SOFCs 26 and degrades even metallic materials such as pipes. 27,28 Even if the amount of H 2 S is reduced to 0.001 ppm, the efficiency still decreases, and then H 2 S in biogas is recognized as a substance that should be removed as much as possible. 29 For this purpose, some zeolites were reported to absorb it, but they have problems on protability and durability. [30][31][32][33][34] However, a more attractive method has been reported and it is called the Claus process. 35 In this process, H 2 S is recovered externally as a single sulfur (S) via an oxidation reaction, as shown in eqn (4): [36][37][38] To accelerate this process, metal oxides such as Fe 2 O 3 , V 2 O 5 , Al 2 O 3 , and TiO 2 have been developed as catalysts. [39][40][41][42] However, these metal oxides are corrosive to H 2 S and this causes lower efficacy of the oxidation process. 43 Instead of these metal oxides, nanocarbons that are nano-scale carbon materials have recently attracted attention. Surprisingly, it can be useful in a wide temperature range from room temperature to even around 900 C. Moreover, it has a high surface area with pore structures and unique surface function. [44][45][46][47][48][49] Because nanocarbons can be utilized without metal-based active sites, it is expected that the reduction of catalytic performance due to H 2 S poisoning is avoided. The rst reaction to remove H 2 S on nanocarbons is shown in eqn (5) as a dissociation reaction. Then, HS À reacts with oxygen radicals (O*) and sulfur (S) is recovered following eqn (6): 50 H 2 S $ H + + HS À (5) Because the carbon site itself in nanocarbons is inactive to remove H 2 S, substitution of heteroatoms with some carbon sites is a reasonable approach to make the inactive site active one. It was rst shown by Chizari et al. that a nitrogen (N)-doped carbon nanotube had excellent activity for the oxidation reaction of H 2 S. 51 Since then, several researchers have started studies on N-doped nanocarbons focusing on detailed microstructures, 52 controlling the nitrogen content, 53 investigating the effect of caustic alkali impregnating agents, 54 and developing the preparation process for mesoporous materials. 55 Furthermore, it is interesting to report that the edge site of Ndoped graphene sheets promotes the oxidation reaction of H 2 S than the ordered plane (cf. pure graphene structures). 56,57 Such sites might act as the origin of the high catalytic performance for H 2 S selective oxidation. Then, focusing on hetero atoms such as N-doped nanocarbons becomes one of the most important approaches. In other words, nding the best active site promoting the oxidation is the common target. However, because the guideline is still not clear, the industrial-scale application has been hampered.
Recently, Shiyan et al. have conducted comparative experiments on the effects of N-and O-doped nanocarbons on the oxidation reaction of H 2 S. They conducted experiments demonstrating that pyridinic N ( Fig. 2(a)), in which N is doped into nanocarbon and hydrogen is bonded to the nitrogen as a terminal atom, promotes the oxidation reaction the most. However, another graphene-based structure known as oxidized N ( Fig. 2(b)), in which an oxygen atom is substituted for the hydrogen bonded next to the nitrogen atom in pyridinic N, showed the least enhancement of the oxidation reaction of H 2 S. To understand the difference in enhancement between pyridinic N and oxidized N at an atomic level, they attempted a density functional theory (DFT) approach. They reported that the adsorption of HS À on pyridinic N was the highest compared with that on oxidized N that showed least adsorption. 58 However, this previous study has the following demerit: HS À is a dissociate of H 2 S, and the stability of HS À cannot be discussed unless it is shown that H 2 S gets adsorbed onto pyridinic N and oxidized N. Therefore, the aim of this study is to clarify the adsorption properties of H 2 S on pyridinic N and oxidized N by DFT.

Computational details
All DFT calculations were performed using the Vienna Ab initio Simulation Package (VASP). 59-61 The Perdew-Burke-Ernzerhof (PBE) 62 exchange-correlation functional was employed based on the projector augmented wave (PAW) method. 61 The cutoff energy for the plane wave basis was set to 400 eV, referring to a previous study. 63 First, a 4 Â 4 graphene sheet was constructed and optimized using 5 Â 5 Â 1 Monkhorst-Pack kpoint meshes. Moreover, the spin polarization was applied. For the projector augmented wave (PAW) method, pseudopotentials with valence states of C (2s 2 , 2p 2 ), N (2s 2 , 2p 3 ), S (3s 2 , 3p 4 ), O (2s 2 , 2p 4 ), and H (1s) were used. All ionic positions were optimized by a conjugate gradient method until the forces on each ion were below 10 À3 eVÅ À1 . The electronic energy was converged to less than 10 À5 eV. Then, aer the geometrical optimization of the 4 Â 4 graphene sheet under the abovementioned conditions, the length of the C-C bond was found to be 1.426Å, which is in good agreement with previous results. [64][65][66] In addition, the internal angles of the six-membered ring of graphene structures were within the range of 120 to AE 0.025%, which is also in good agreement with the results of previous studies. 67,68 Next, with the optimized graphene sheet spreading to a-and b-axis directions, we added a vacuum slab on it by making 15Å height in the c-axis direction. Then, geometry optimization was performed while keeping the vacuum slab. From the optimized graphene sheet with a vacuum slab, a six-membered ring structure consisting of six carbons was removed. Then, hydrogen atoms were introduced to terminate the remaining carbon atoms. The edge of the graphene sheet is reported to be bonded with hydrogen atoms, 69 which prevents the carbons from becoming radicalized and destabilized. Finally, the carbon site was replaced with  Fig. 2(a), and with nitrogen and oxygen, as shown in Fig. 2(b). The respective structure is called pyridinic N and oxidized N, respectively. 58 They were visualized using VESTA. 70 Fig. 2(a) and (b) show that hydrogen sulde (H 2 S) was adsorbed onto pyridinic N and oxidized N, and H 2 S itself was optimized. For this, H 2 S was rst structurally optimized in vacuum. H 2 S has a bent structure with lone-pair electrons in the S atom, and the calculated S-H bond length is 1.35Å (1.35Å and 1.33Å). Moreover, the H-S-H angle was found to be 91.2 (91.6 and 92.2 ), which is in good agreement with the previous experiment and calculated values in parentheses. 71 This single molecule of H 2 S in vacuum was structurally optimized with 1 Â 1 Â 1 Monkhorst-Pack k-point meshes. For each of the above-mentioned pyridinic N and oxidized N, H 2 S was placed on a nitrogen atom and the structure was optimized. The position of H 2 S was referred from the previous study by Shiyan et al. 72 To accurately determine the stability of H 2 S on pyridinic N and oxidized N, we considered adsorption energy (E ads ). 73,74 It is dened in eqn (7), which is the sum of the interaction energy (E int ) in eqn (8), and deformation energy (E def ) shown in eqn (9). The deformation energy is obtained as follows: H 2 S and pyridinic N form the most stable structure when they are placed in vacuum with no other atoms around them. However, H 2 S and pyridinic N deforms when they are close to each other due to their interaction. The change in the electrostatic potential at this time is dened as the deformation energy. The interaction energy (E int ) and deformation energy (E def ) shown in eqn (8) and (9) are the case for pyridinic N with H 2 S. When the adsorption energy was calculated as negative, H 2 S gets adsorbed onto pyridinic N stably.
E H 2 S+pyrindinic N , E pyridinic N , and E H 2 S are the electrostatic potential for pyridinic N and adsorbed H 2 S, pyridinic N, and single H 2 S, respectively.
Moreover, the minimum energy paths and the energy barriers for H 2 S dissociation on graphene-based structures were obtained by the climb image nudged elastic band (NEB) method. Five intermediate images were used to sample the reaction path between the initial adsorption state and the nal dissociated state. The spring constant of the NEB calculations was 5.0 eVÅ À2 and the NEB force convergence criteria was 0.01 eVÅ À1 using 3 Â 3 Â 1 Monkhorst-Pack k-point meshes.

Results and discussion
The calculated adsorption energies for H 2 S on pyridinic N and oxidized N are given in Table 1. The electrostatic potentials are summarized in Table 2. As shown in Table 1, H 2 S on pyridinic N shows À0.117 eV as the adsorption energy, and this number is 21% lower than that of oxidized N as À0.097 eV. This indicates that H 2 S is more stably adsorbed onto pyridinic N than onto oxidized N, indicating that pyridinic N is a more favorable material than oxidized N to proceed the oxidation reaction (2H 2 S + O 2 $ (2/n) S n + 2H 2 O), as shown in eqn (4). Shiyan et al. experimentally reported the same trend, 72 and the result of our study supports their result successfully by DFT. Notably, oxidized N does not adsorb H 2 S as readily as pyridinic N, but this indicates that H 2 S on oxidized N can be desorbed relatively easily by external energies such as heat. This suggests that the structure of oxidized N could be applied to the reusable desorption sheet to remove H 2 S.
The reason why H 2 S adsorption occurs more favorably on pyridinic N than on oxidized N is explained as follows. As mentioned before, the adsorption energy is expressed as the sum of the interaction energy, shown in eqn (8), and the deformation energy, also shown in eqn (9). Their values are presented in Table 1 and their amount is graphically visualized in Fig. 3.
As shown in Fig. 3, it is clear that the effect of the interaction energy is much larger than that of the deformation energy in determining the adsorption energy. The rst factor that determines the amount of the interaction energy is reported with the idea of attractive force (intermolecular force) that acts between materials caused by the transfer of charge. 75,76 Fig. 4 shows electric charges of adsorbed H 2 S and its surrounding atoms: N and O. Every charge was obtained by Bader charge analysis. 77 This gure shows pyridinic N ( Fig. 4(a)) and oxidized N ( Fig. 4(b)) with adsorbed H 2 S, respectively, and each structure has already been geometry optimized. Fig. 4(c) shows H 2 S placed in vacuum. From pyridinic N and oxidized N, H 2 S is adsorbed approximately 2Å away, and this value has good agreement compared to previous studies reporting the adsorption distances between molecules and graphene-based structures. 78,79 As shown in Fig. 4(a), the charge of the entire H 2 S was calculated as +0.19 e (electron), and the charge of the N atom of pyridinic N adjacent to H 2 S was polarized to À1.18 e. However, as shown in Fig. 4(b), H 2 S is polarized to À0.02 e, and the repulsive forces are at work between them. Despite the presence of repulsive force between H 2 S and oxidized N, the reason why the adsorption energy is negative as shown in Table 1 can be the formation of ionic or covalent bonds that have a stronger binding force than the repulsive force generated by intermolecular force. Therefore, in addition to pyridinic N and H 2 S, the covalent nature between oxidized N and H 2 S was investigated as follows.
In fact, the relationship between the covalent nature and the interaction energy has been discussed in several papers. Wang et al. reported the bonding nature of PbO molecules on the aluminium surface, and they showed that the magnitude of covalent bonding contributes to the value of interaction energy. 81 Moreover, Zhou et al. mentioned that ammonia molecules adsorbed onto SiSe layers showed more stability with greater covalency. 82 In addition, covalent bonding can be explained by the amount of electrons between atoms, and the bonding between zirconium and oxygen atoms seems to be greater than that between cerium and oxygen atoms in perovskite structures. 83 Considering these previous studies, the magnitude of the covalency in terms of the number of electrons between atoms has a signicant effect on the interaction energies. Fig. 5(a) shows the electron mapping obtained by slicing the coordinates of the following three atoms: the N atom of pyridinic N, the S atom of H 2 S, and the H atom of H 2 S. Fig. 5(b) describes the density of states of the H atom in H 2 S and the N atom in pyridinic N, which are neighbouring atoms, and Fig. 5(c) shows the density of states of S in H 2 S and N in pyridinic N. In Fig. 5(a), it seems that there is little sharing to create a covalent bonding between the H atom and the N atom. However, as shown in Fig. 5(c), the s-and p-orbitals of the N atom in pyridinic N clearly overlap on the p-orbital band structure of the S atom. From the above, it is shown that the electrons between H 2 S and pyridinic N shown in Fig. 5(a) make a covalent bond between S of H 2 S and the N of pyridinic N. This electron sharing stabilizes H 2 S on pyridinic N and it helps determining the number of interaction energy to be À0.129 eV, as shown in Table 1. However, Fig. 5(d) shows the electron mapping of H 2 S adsorbed onto oxidized N using the coordinates of the O and N atoms of oxidized N, and the H atom of H 2 S. From this gure, it is observed that there are electrons between the O atom of oxidized N and the H atom of H 2 S. This number of electrons in Fig. 5(d) seems to be larger than that of electrons between pyridinic N and H 2 S, as shown in Fig. 5(a). However, Fig. 5(e) shows that s-and p-orbitals of the H atom in H 2 S hardly overlap with the s-and p-orbitals of the O atoms in oxidized N. The is the proof that the type of bond between H 2 S and oxidized N is ionic bond. Focusing on the p-orbital of the O atom, the bond between O and H appears to be formed as a covalent bond, as shown in Fig. 5(d), as the density of state in the p-orbital of O is distributed over a wide range of energy, as shown in Fig. 5(e) and then electrons of the p-orbital are widely delocalized around the O atom. In other words, there is no covalent but mainly ionic bond between H 2 S and oxidized N. Although there was repulsive intermolecular force between H 2 S and oxidized N, this ionic bonding between them makes H 2 S stable on oxidized N, which results in the negative adsorption a The values of "pyridinic N non-relaxed" and "oxidized N non-relaxed" mean the electrical potential of pyridinic N and oxidized N without performing geometry optimization by removing H 2 S from "H 2 S with pyridinic N" and "H 2 S with oxidized N", respectively. In addition, the energy for each angle of H 2 S is listed in the last three lines.   energy, as shown in Table 1. As described above, the difference in the interaction energies presented in Table 1 can be attributed to the difference in the degree of covalent bonding property between H 2 S and pyridinic N or oxidized N.
Finally, regarding the deformation energy, it is signicantly smaller relative to the interaction energy, as shown in Table 1 and Fig. 3. However, to exactly determine the adsorption energy in this study, it is important to explain the effect of such minor energy contribution. First, the deformation energies of pyridinic N and oxidized N aer adsorption of H 2 S were calculated as +0.009 eV and +0.015 eV, respectively. The reason for the higher deformation energy of oxidized N is that the O atom is attracted to the H atom of H 2 S by intermolecular force, as shown in Fig. 1 and 4. As for the deformation energy of H 2 S, the value for H 2 S on pyridinic N is +0.003 eV, and that for oxidized N is +0.002 eV. The reason for the difference is that the bond angle of H 2 S on pyridinic N is 92.0 and this value is larger than the bond angle (91.9 ) on oxidized N, as shown in Fig. 4(a) and (b). In fact, both angles are larger than the angle of H 2 S in vacuum (91.2 ), as shown in Fig. 4(c). The origin of such angle change has already been well discussed in previous studies and the cause comes from the result of charge transfer in molecules. Bajdich et al. reported that charge transfer occurs to CO 2 adsorbed on the Au surface, leading to a change in bond angle. 84 Indeed, as shown in Fig. 4(a) and (b) in our study, the charge transfer between H 2 S and pyridinic N is larger than that between H 2 S and oxidized N. Therefore, the bond angle of pyridinic N is considered to be larger than that of oxidized N. The bond angle change is also explicable from the viewpoint of the electronic structure of Walsh diagram, as shown in Fig. 6. 85 The diagram shows that the energy of orbitals b 1 and 2a 1 increases as the angle of H 2 S increases in the narrow range of 91.2 to 92.0 . The above-mentioned difference can be claried if we can describe the density of state with sufficiently high accuracy. However, the VASP used in this study was unable to follow the change in the Walish diagram within 1.0 of the H 2 S bond angle. Therefore, it is signicantly desirable to have a method that can discuss the change in the density of states for a very narrow range of bond angle, which is less than 1 .
Moreover, we determined the activation barrier for H 2 S molecules to dissociate on the graphene structure. Fig. 7 shows  H 2 S dissociated as HS À and H + on Pyridinic N. Fig. 7(a) shows the case where H 2 S is dissociated while maintaining the electrically neutral condition, and Fig. 7(b) shows the case where one electron is added to the entire system. Both cases show cases where the most dissociated H 2 S is stabilized at several locations around the nitrogen atom. The electron-added system shown in Fig. 7(b) was chosen for investigation because of the reduction reaction. A previous study has also considered the possibility that pyridinic N was reduced by experimental residual reducing gases such as carbon monoxide and hydrogen gas. 72 In fact, a previous study also suggested there is some amount of oxygen in experimentally prepared pyridinic N. 72 With the initial structure shown in Fig. 2(a) and nal structures shown in Fig. 7 of pyridinic N, the activation barrier was calculated as shown in Fig. 8. Focusing on the nal structure and when the electroneutrality is maintained, the nal structure is about 1.05 eV larger than that of the previous structure. However, when a single electron was added into the entire system, the nal structure shows 0.12 eV larger activation barrier than the previous structure. This value (0.12 eV) is about one-tenth the size of the structure under electroneutrality. This indicates that the hydrogen sulde dissociation was signicantly enhanced by the reducing gas.
However, H 2 S is always stable as a molecule on oxidized N, and the dissociation reaction could not be reproduced. Although a previous study had raised the possibility that a water lm could cause H 2 S to dissociate, 86 the separation of H 2 S into HS À and H + by water molecules could not be reproduced by our investigation. Chemical reactions such as the above-described dissociation reaction do not occur because the interaction energy between H 2 S and oxidized N is À0.114 eV, which is so small that there might be contribution of hydrogen bonding as well as ionic bonding. However, as shown in Fig. 5(e), there is a slight overlap of electrons between the O p-orbital and the H porbital, making it difficult to precisely separate the effect of hydrogen bonding from that of ionic bonding. As mentioned above, we could not nd any tendency for H 2 S to react with oxidized N in a divergent manner. Therefore, we conclude that oxidized N does not contribute to the dissociation reaction for H 2 S, but rather has the effect of preventing the dissociation reaction.

Conclusions
In this study, the adsorption energies of H 2 S on pyridinic N and oxidized N have been precisely investigated by examining the interaction and deformation energies by DFT. Our result indicated that H 2 S gets adsorbed more preferably onto pyridinic N than onto oxidized N. This indicates that pyridinic N is a signicant material for the oxidation reaction of H 2 S. The above-mentioned difference is explicable because the interaction energy of H 2 S with pyridinic N is lower than that with oxidized N, which can be inferred from the difference in intermolecular forces and covalency properties. As for the deformation energy, it is remarkably small compared to the interaction energy, but oxidized N has a higher deformation energy than pyridinic N, which is due to the intermolecular force between the O atom in oxidized N and the H atom in H 2 S. It was also shown that the bond angle of H 2 S is larger on pyridinic N than on oxidized N due to charge transfer aer adsorption of H 2 S. Furthermore, the activation barrier for the dissociation of H 2 S (H 2 S $ H + + HS À ) on pyridinic N and oxidized N was investigated and found to be 1.05 eV on pyridinic N. Moreover, when one electron was added considering the reducing atmosphere, the activation barrier on pyridinic N was found to be 0.12 eV, which became very smaller. However, we could not reproduce the reaction of H 2 S dissociation on oxidized N, and concluded that only pyridinic N contributes to the H 2 S dissociation reaction.

Author contributions
T. F. and Y. S. designed this project. K. I. and A. T. S. provided valuable advice for proceeding this research. Also, H. S. gave useful viewpoint from experimental aspect. The manuscript was written through contributions of all authors. All authors have given approval to the nal version of the manuscript.

Conflicts of interest
There are no conicts to declare.
English language editing. In addition, the computation was carried out using the computer resource offered under the category of General Projects by Research Institute for Information Technology, Kyushu University.