Oxygen dissociation on the C3N monolayer: A first-principles study

The oxygen dissociation and the oxidized structure on the pristine C3N monolayer in exposure to air are the inevitably critical issues for the C3N engineering and surface functionalization yet have not been revealed in detail. Using the first-principles calculations, we have systematically investigated the possible O2 adsorption sites, various O2 dissociation pathways and the oxidized structures. It is demonstrated that the pristine C3N monolayer shows more O2 physisorption sites and exhibits stronger O2 adsorption than the pristine graphene. Among various dissociation pathways, the most preferable one is a two-step process involving an intermediate state with the chemisorbed O2 and the barrier is lower than that on the pristine graphene, indicating that the pristine C3N monolayer is more susceptible to oxidation than the pristine graphene. Furthermore, we found that the most stable oxidized structure is not produced by the most preferable dissociation pathway but generated from a direct dissociation process. These results can be generalized into a wide range of temperatures and pressures using ab initio atomistic thermodynamics. Our findings deepen the understanding of the chemical stability of 2D crystalline carbon nitrides under ambient conditions, and could provide insights into the tailoring of the surface chemical structures via doping and oxidation.


Introduction
The emergence of a wide variety of two-dimensional (2D) materials and the advancement of their promising applications in electronics [1][2][3], catalysis [4][5][6], gas sensors [7][8][9], energy conversion and storage [10][11][12] inspired by the great success of graphene [13,14], has been accompanied by an increasing attention on their chemical stability under ambient conditions. Especially, the O2 dissociation involved in the oxidation of 2D materials when exposed to air is the inevitably critical issue in nanomaterial manipulation and device engineering. The presence of chemisorbed oxygen on the pristine surface of 2D materials tunes the bandgaps [15][16][17][18], provides active sites for chemical reactions [19] and assists the surface functionalization [20,21], sometimes is related to the structural degradation and breakdown [22,23]. Furthermore, we found that the chemisorbed oxygen groups can surprisingly convert carbon-based materials, such as graphene and carbon nanotube, into dynamic covalent materials [24][25][26] and even induce the self-adaptivity in response to the adsorption of biomolecules [24]. Although the atomic-thick 2D materials have a large surface-volume ratio and are prone to show high surface reactivity, the O2 dissociation on the surface of 2D materials usually depends on the chemical bonding characteristics, thus differs from one to another [14,27,28].
Recently, a hole-free and graphene-like 2D honeycomb structure with the stoichiometric formula, C3N, has been successfully synthesized [29,30] and demonstrated to exhibit ultrahigh stiffness [31] and thermal conductivity [32], and excellent electrical properties [33,34], offering potential applications in photo-or electro-catalysts [35,36], gas adsorption medium [37] and electrode materials for batteries [38]. Compared with graphene, the C3N monolayer can be regarded as a nitrogen-doped graphene structure with nitrogen atoms uniformly distributed and all atoms sp 2 hybridized. It is expected that the C3N could exhibit higher surface activity toward small gas molecules like O2 than graphene at ambient conditions due to the nitrogen atoms [39,40]. However, detailed discussions on the O2 dissociation on the C3N monolayer and the oxidized structure are still lacking, despite that recent work has pointed out that the C3N monolayer is chemically inert to O2 molecule [41].
In this work, we performed the first-principles calculations on the oxygen dissociation on a pristine C3N monolayer. We have systematically explored possible adsorption sites of an oxygen molecule and the atomic oxygen, various oxygen dissociation pathways and the oxidized structures. It is demonstrated that the pristine C3N monolayer shows more O2 physisorption sites and exhibits the stronger O2 adsorption than the pristine graphene. Among eight O2 dissociation pathways, the most preferable pathway is a two-step process involving an intermediate state with the chemisorbed oxygen molecule where the barrier is lower than that on the pristine graphene, indicating that the pristine C3N is more susceptible to oxidation than the pristine graphene. These results can also be generalized into a wide range of temperatures and pressures by analyzing the adsorption Gibbs free energy and surface phase diagram according to the ab initio atomistic thermodynamics. In addition, we find that the electronic properties can be altered significantly by the oxidized structures with two chemisorbed O atoms, from the metal to the semiconductor with the largest band gap of 0.67 eV. These results deepen the understanding of the chemical stability of 2D crystalline carbon nitrides under ambient conditions, provide insights into the tailoring of surface chemical structures, and may guide the design of high-efficient catalysts via doping and oxidation. The pristine C3N monolayer is modeled within a 3×3×1 supercell, as shown in Fig. 1, including 54 carbon and 18 nitrogen atoms. The optimized lattice constants of C3N, denoted by a and b, are a = b = 4.86 Å, which are consistent with the experimental value [29]. The average lengths of C-C and C-N bonds are 1.40 Å and 1.41 Å, respectively. The Hirshfeld charges of C and N atoms are +0.01e and -0.03e. The calculated values of 3 , 2 and are -635.29 eV, -9.85 eV and -1.59 eV and are used throughout this work.

Computational details
All the calculations were performed based on the density functional theory as implemented in the Vienna Ab-initio Simulation Package (VASP) [42,43]. The exchange-correlation interaction is described by the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximations (GGA) [44], and the interactions between valence electrons and ion-core are described by the projected augmented wave (PAW) method [45,46]. Grimme's DFT-D3 method is employed to describe the nonlocal dispersive interactions [47]. The energy cutoff of plane wave is 450 eV, and the convergence criteria are 1×10 -5 eV and 0.02 eV/Å for the energy and the force, respectively. The vacuum layer along the z-axis direction is 20 Å to avoid the interaction between periodic images. The Monkhorst-Pack scheme is used to sample the k-point [48] mesh in the Brillouin zone. For the structure optimization, the 3×3×1 k-point mesh is used. For the density of states (DOS) calculations, we use a larger 12×12×1 k-point mesh to ensure the accuracy. The size of 3×3×1 supercell containing 54 carbon, 18 nitrogen and 2 oxygen atoms is used in all the calculations, and the system is fully relaxed until the convergence criteria are satisfied. The climbing image-nudged elastic-band (CI-NEB) method [49] is used to search the O2 molecule dissociation pathway and estimate the reaction barrier connecting the optimized physisorbed and chemisorbed states of C3N monolayer. All the transition states (TS) are confirmed by the single imaginary frequency output from the default frequency calculation algorithm.

Quantitative analyses
(I) The adsorption energy, , is defined by where @ 3 is the total energy of the C3N monolayer with the adsorbate (O2 molecule or atomic O), 3 is the energy of a pristine C3N monolayer and is the energy of an adsorbate.
(II) The cohesive energy, ℎ is defined by [27] where and are the numbers of carbon and nitrogen atoms, and represent the energies of atomic carbon (C) and atomic nitrogen (N), respectively.
(III) The O2 dissociation on the C3N monolayer is described by the reaction O2 + C3N → 2O@C3N. According to the method developed by Nørskov et al. [50], the Gibbs free energy change of this reaction at a certain temperature T can be estimated by [51,52] where 2 @ 3 , 2 and 3 are the energies of the absorbed system, an isolated O2 and the pristine C3N monolayer, respectively. ∆ is the zero-point energy difference of an O2 molecule between in the gas phase and in the adsorbate state obtained from vibrational frequency calculation. ∆ is the entropy change of an O2 molecule due to the adsorption.
(IV) The thermodynamical stability of oxidized states at the experimental conditions can be determined by the ab initio atomistic thermodynamics. This approach is formulated by Reuter and Scheffler [53][54][55], and has been an effective tool to explore the interfacial oxidization [56][57][58][59]. For the oxidized state of C3N monolayer, the adsorption Gibbs free energy of two chemisorbed O atoms onto the C3N monolayer at the temperature T and O2 partial pressure 2 is given by ∆ � , 2 �, which is expressed as where 2 @ 3 ( , 2 ) and 3 ( , 2 ) are the Gibbs free energies of the adsorbed C3N monolayer, the bare C3N monolayer and 2 ( , 2 ) is the chemical potential of an O2 molecule. The 2 ( , 2 ) is in the following form The 2 -T profile for a given ∆ ( , ) can be plotted through [55] where the values of parameters = 2 , = 3 , 0 = 0.18 and ℏ 0 = 196 . The first term in the curly bracket is from the translational free energy of an O2 molecule together with the contribution of 2 term. The remaining terms are from the rotational, vibrational and nuclear free energy contributions.

Physisorption of an oxygen molecule
The adsorption of an O2 molecule is usually considered to be the first step of O2 dissociation on the surface of nanomaterials. Hence, we search for the favorable physisorption configuration for an O2 molecule on the pristine C3N monolayer. The adsorption configuration is obtained by initially placing the O2 molecule at the height of about 3.0 Å from the C3N monolayer and orienting the O2 molecule parallel, vertical or with a tilt angle to the basal plane. As shown in Fig. 2, eight stable adsorption configurations have been found, and can be classified into two types: (I) adsorption sites on the six-membered carbon ring (Figs. (a-d)) and (II) the ones on the six-membered carbon-nitrogen ring (Figs. (e-j)). In the optimized adsorption configurations, the O2 molecule is almost adsorbed in parallel to the basal plane with the height of ~ 3.0 Å and Ead ~ -0.35 eV, consistent with the values in Refs. [37] and [61] which indicate the physisorption. The O-O bond length is 1.27 Å, larger than the 1.23 Å for the isolated O2 molecule, an indication of the weak attraction between the O2 molecule and the C3N monolayer. The orientation of stable physisorption configurations shows some symmetries: on the carbon ring, the O2 molecule prefers to be adsorbed on the (a) para-carbon, (b) ortho-carbon, (c) meta-carbon and (d) hollow sites; on the carbon-nitrogen ring, the O2 molecule is more easily captured on the (e) orthocarbon-nitrogen, (f) para-nitrogen, (g) hollow, (h) para-carbon, (i) meta-carbon and (j) meta-carbon-nitrogen sites. Compared with the O2 adsorption height of ~ 3.0 Å and Ead ~ -0.1 eV on the pristine graphene [40,62], the O2 molecule is more preferably physisorbed onto the C3N monolayer and the stable adsorption configurations are enriched due to the presence of N atoms.

Chemisorption of an oxygen atom
We further explore the chemisorption site for an O atom on the pristine C3N monolayer as the O2 molecule will dissociate into two chemisorbed O atoms. As shown in Fig [63], higher than that of -3.61 eV on the C3N monolayer, indicating that the epoxy configuration is more stable on the C3N monolayer.
The presence of N atoms enriches the variety of chemical bonds on the surface of C3N monolayer, such as the dangling C-O and N-O bonds, which are thermodynamically unstable on the pristine graphene. The dangling O atom at the TC and TN sites and the epoxy at the BC-C site cause the carbon atom to move out of the plane, inducing the local structural deformation compared to the pristine C3N monolayer. At the TC site ( Fig. 3(a)), a buckling of 0.60 Å is formed, with two equally C-C bonds elongated from 1.40 Å to 1.53 Å and a C-N bonds elongated from 1.41 Å to 1.56 Å. The dangling C-O bond of 1.31 Å is not strictly pointing along the normal and tilts slightly toward the N atom with the O-C-N angle of 111.8°. Both the geometric configuration and negative adsorption energy of the atomic O at the TC site are close to the descriptions reported in Refs. [64] and [65]. A more symmetric configuration can be seen at the TN site (Fig. 3(c)). The dangling N-O bond is along the normal and the buckling is 0.50 Å. The three C-C bonds are all equally elongated to 1.48 Å, with the formation of three equal angles of 110°. At the BC-C site ( Fig. 3(b)), two carbon atoms bonded to the O are pulled out to the height of 0.31 Å. The existence of stable dangling C-O or N-O bonds and epoxy enriches the interfacial structures of the C3N monolayer and may lead to various dissociation pathways of O2 molecule.

The oxygen molecule dissociation pathways
The cohesive energy, Ecoh, is usually used to measure the strength of chemical bonds within the 2D materials and quantify the oxidation resistance. We find that Ecoh of the pristine C3N monolayer is 6.99 eV/atom, close to that of graphene and h-BN (~ 7 eV/atom) [66][67][68][69]and larger than that of germanene and phosphorene (~ 4 eV/atom) [70][71][72], which indicates that the pristine C3N monolayer is relatively inert to O2 and exhibits decent oxidation resistance at ambient conditions.
In order to quantify the O2 dissociation process in detail, we focus on the possible dissociation pathways of O2 starting from all the stable physisorption configurations on the pristine C3N monolayer. As the physisorption of an O2 molecule can be classified into two groups, we will discuss the O2 dissociation on the carbon and carbon-nitrogen rings of the C3N monolayer individually. In the following discussions, only the O2 or two O atoms, and the adsorbed carbon or carbon-nitrogen ring are shown for clarity.  [65], where the barrier is 1.04 eV and the energy of M state is 0.69 eV with respect to the R state. In the next step, by passing a low barrier of 0.05 eV, the O2 molecule dissociates into two dangling C-O bonds and the distance between two O atoms reaches the maximum of 2.68 Å. This two-step dissociation of O2 is also found on the pristine graphene where the barrier from the physisorbed state on the para-carbon site to the M state is 2.0 eV [73], indicating that the pristine C3N monolayer shows better catalytic properties on O2 dissociation than on the pristine graphene.  Fig. 3(a)). This is mainly due to the electrostatic repulsion between two negatively charged O atoms of -0.33 e, -0.34 e and -0.32 e for P states in Paths I, II and III. The O…O distances for P states are 3.14 Å, 3.56 Å and 2.68 Å which are larger than the corresponding C…C distances of 2.60 Å for meta-carbon atoms, 2.88 Å for para-carbon atoms and 1.63 Å for ortho-carbon atoms, also an indication of repulsion between two dangling O atoms. In addition, the buckling and the local structure deformation around the bonded carbon or nitrogen atoms can be seen in side views of TS and P states in Fig. 4.  The remark difference of relative energies of P states also implies the stability of two dangling bonds on the carbon-nitrogen ring generated from the O2 dissociation process. Two dangling O atoms prefer to stably covalent to the atoms in the following order: paracarbon atoms > meta-carbon atoms > meta-carbon-nitrogen atoms > ortho-carbon-nitrogen atoms > para-nitrogen atoms, as indicated by the corresponding values of Ead listed in Tab.

Electronic band structure and DOS of the oxidized C3N monolayer
The oxidized structures with two chemisorbed O atoms also exhibit various band structures and DOS. The pristine C3N monolayer is an indirect semiconductor with the bandgap of 0.39 eV, consistent with the value given by Zhou et al [31]. As shown in Fig. 6, the valence bands of C3N monolayers with two O atoms at the para-carbon, ortho-carbon sites of the carbon-ring, and para-carbon site of the carbon-nitrogen ring cross the Fermi level. This indicates that these oxidized C3N monolayers become metallic, due to the orbital coupling between two O atoms and bare C3N monolayer at the valence band edge. While for O atoms at the meta-carbon site of the carbon ring and para-nitrogen site of the carbon-nitrogen ring, the orbital hybridization mainly occurs at lower energies far from the Fermi level and their band gaps are widened to 0.41 eV and 0.67 eV, respectively. The narrower band gaps of 0.06 eV, 0.28 eV and 0.18 eV can be seen for O atoms at the ortho-carbon-nitrogen site, meta-carbon-nitrogen site and meta-carbon site of the carbon-nitrogen ring, an indication of the enhanced electronic activity. These results demonstrate that the electronic properties of C3N monolayer can be altered significantly due to the presence of two chemisorbed O atoms, from the metal to the semiconductor with the largest band gap of 0.67 eV.

Free energy for the oxygen dissociation
To describe the oxygen dissociation at room temperature, we analyze the free energy change ∆G of TS and P state with reference to the initial state (O2 + C3N) along eight possible O2 dissociation pathways. As shown in Tab. 3, ∆GTS and ∆GP at T = 300 K increase by 0.1 ~ 0.2 eV compared to ∆ETS and ∆EP at T = 0 K, due to the difference of zero-point energy and that of entropy contribution (see PS. 3. in SI for ∆GTS and ∆GP at other temperatures). We can see among these dissociation pathways at T = 300 K, the two-step dissociation process occurring at the ortho-carbon of the carbon ring shows the lowest barrier of 0.90 eV and two chemisorbed O atoms at the para-carbon of the carbon ring shows the lowest free energy of -1.28 eV. This indicates that the most preferable dissociation pathway is still the two-step process and two chemisorbed O atoms at the paracarbon site of the carbon ring still corresponds to the most stable dissociation structure.

Phase diagram of O2 adsorption at experimental conditions
To understand the thermodynamic stability of oxidized C3N structures at experimental conditions, we introduce the adsorption Gibbs free energy ∆ � , 2 �, which measures the Gibbs free energy of the oxidized state with respect to the reactant (O2 + C3N) at the temperature T and O2 partial pressure 2 . A more negative ∆ indicates a more stable oxidized structure. According to the expression ∆ � , 2 � ≈ − 2∆ � , 2 � (see details in Sec. 2.3.) deduced from ab initio atomistic thermodynamics, we can see that the formation of oxidized C3N monolayer with two chemisorbed O atoms is accompanied by adsorbing an O2 molecule onto the C3N surface yielding an energy descend of | |, that is balanced by the free energy ascend of |2∆ | due to the loss of an O2 in the surrounding gas phase. ∆ is usually negative since that entropy contributions from translation and rotation are dominant and their values are positive. for the two chemisorbed O atoms at the para-carbon site of a carbon ring is lower than the values for other configurations, indicating that this configuration is the most favorable oxidized structure. We thus focus on this oxidized structure. It can be seen that ∆ > 0 for ∆ < -0.745 eV and a more negative ∆ results in a more positive ∆ . This means that when ∆ < -0.745 eV, the O2 molecule prefers to stay in the gas phase and a clean C3N surface is obtained. While the oxidized structure with two O atoms adsorbed at the para-carbon site of a carbon ring is more stable when ∆ > -0.745 eV as ∆ < 0. Thus, the value of ∆ = 1 2 = -0.745 eV is a critical point which decides the existence of clean C3N monolayer or the oxidized C3N monolayer. This condition can be converted into a line in the 2 − phase diagram separating the phases of clean and oxidized C3N monolayer, as shown in Fig. 7(b). monolayer. In the legend of (a), the former three lines represent the O2 dissociation sites at the carbon ring and the remaining lines denote the sites at the carbon-nitrogen ring.
Whether the O2 dissociation on the C3N monolayer is feasible under realistic conditions depends on the height of barrier, which can be estimated by ∆ using the value of Ead corresponding to the transition state. We focus on the two-step O2 dissociation reaction since this process shows the lowest barrier of all eight possible reaction pathways, and choose the O2 dissociation on the graphene for the comparison. The O2 dissociation reaction is considered to be feasible when the barrier height is lower than 0.5 eV. This means that the critical value ∆ ≈ − 2∆ = 0.5 eV. As = 0.75 eV for C3N and 2.39 eV [40] for graphene, we obtain ∆ � , 2 � = 0.125 eV and 0.945 eV, respectively. As shown in Fig. 8, the minimal O2 partial pressure 2 needed for the feasible O2 dissociation decreases with the increase of temperature T, indicating that lower O2 partial pressure is sufficient to activate the O2 dissociation on the C3N or graphene at higher temperatures. However, at a certain temperature T, the O2 is easier to be dissociated on the C3N monolayer than on graphene since the value of 2 is much smaller. At the atmospheric pressure of 1 atm and T = 300 K, the 2 ~ 0.2 atm, which is much smaller than the value of 2 shown in Fig. 8, suggesting that the spontaneous O2 dissociation on the C3N or graphene under environmental conditions is very difficult.

Conclusions
In summary, we have performed the first-principles calculations to systematically investigate various adsorption sites of an oxygen molecule and an atomic oxygen, eight oxygen dissociation pathways and the associated oxidized structures on the pristine C3N monolayer. In comparison with the pristine graphene, the pristine C3N monolayer shows more O2 physisorption sites and exhibits the stronger O2 adsorption. The O2 molecule can be adsorbed onto several sites at the carbon ring (ortho-, meta-and para-carbon atoms, hollow) or at the carbon-nitrogen ring (para-and meta-carbon, ortho-and meta-carbonnitrogen, para-nitrogen atoms and hollow). The adsorption energies at these sites are close and over the range of 0.34 -0.36 eV which are two times lower than that on the pristine graphene.
The O2 dissociation pathways on the pristine C3N monolayer depends on the initial physisorbed sites and the oxidized structures, and the most preferable one is a two-step process involving an intermediate with the chemisorbed O2 onto the ortho-carbon atoms of the carbon ring and the dissociation barrier is 1.10 eV, which is lower than about 2 eV for the similar process on the pristine graphene. Other O2 dissociation pathways are direct routes where O2 directly dissociates into two chemisorbed O atoms by forming two stable dangling C-O or N-O bonds, overcoming the barriers over the range of 1.3 -4.4 eV. These results indicate that the pristine C3N monolayer is more susceptible to oxidation than the pristine graphene.
The presence of nitrogen atoms in the pristine C3N monolayer assists the formation of stable dangling C-O or N-O bonds, leading to the enriched oxidized structures after oxygen dissociation. For the dissociation state, two O atoms prefer to be stably chemisorbed onto the carbon or nitrogen atoms in the form of dangling C-O or N-O bonds. The oxidized structure with two dangling C-O bonds on the para-carbon atoms of the carbon ring shows the lowest adsorption energy of -8.16 eV and is more favorable than other structures. Moreover, the electronic properties can be altered significantly, from the metal to the semiconductor with the largest band gap of 0.67 eV.
The detailed description of O2 dissociation and the oxidized structure on the pristine C3N monolayer can be generalized to a wide range of temperatures and pressures by analyzing the adsorption Gibbs free energy and surface phase diagram according to the ab initio atomistic thermodynamics. This provides insights into the tailoring of the surface chemical structures to manipulate the physical and chemical properties. For instances, the surface functionalization of the pristine C3N monolayer via the chemisorbed oxygen atoms is an effective method to tune the electronic and magnetic properties which sensitively depend on the surface oxygen coverage [74]. The dangling C-O bond on the pristine C3N monolayer can be utilized to enhance the adsorption of metal atoms on its surface to assist the single-atom catalysts [75]. It thus could be beneficial for the investigations on the catalysis and material engineering relative to the C3N or other carbon nitrides derivatives.