Computational design of single-atom catalysts embedded on reduced graphitic carbon nitride monolayers

The design of efficient single-atom catalysts (SACs) with optimal activity and selectivity for sustainable energy and environmental applications remains a challenge. In this work, comprehensive first-principles calculations are performed to validate the feasibility of single TM atoms (3d, 4d, and 5d series) embedded in two different conformations of graphitic carbon nitride (g-C3N4) monolayers. Additionally, we investigate the effect of nitrogen vacancies in the g-C3N4 monolayers on the absorption of SACs considering three potential absorption scenarios that correspond to different experimental conditions. Our results point to the most stable configurations with the lowest formation energies and indicate that the absorption of single TM atoms on-vacancy and on-center sites are more favorable than via-substitution. In addition to the thermodynamic stability, electrochemical stability is also investigated through the calculation of the dissolution potential of the SACs. Within the scenarios considered in this study, we find that Pt, Pd, Rh, Au, Ru, Ir, Cu, Co, Fe, and Ni will produce the most robust SACs on both (edge and bridge) N vacancy site of reduced g-C3N4. Our findings provide guidance for the design and development of g-C3N4 sheets decorated with single TM atoms for technological applications such as pollutant degradation, CO2 reduction, N2 fixation, selective oxidation, water splitting, and metal ion-based batteries.


Introduction
Currently, more than 90% of chemical processes carried out in the chemical industries rely on catalysts, and there is a continuously increasing demand for new catalytic technologies to ensure a sustainable future [1,2].Recently, a new category of catalysts known as single-atom catalysts (SACs) has emerged [3,4].This innovative class of catalysts demonstrates exceptional catalytic reactivity, ultrahigh atomic utilization, and stability in various reactions and applications such as hydrogen evolution reduction (HER) [5], oxygen reduction reaction (ORR) [6], CO 2 reduction reaction [7], fuel cells [8,9], and rechargeable batteries [10][11][12], among others.However, the structural stability of SACs is often influenced by the ability of the supporting materials to accommodate the dispersed atoms [13].One of the main challenges in SACs is a propensity of single atoms to aggregate rather than remain atomically dispersed during synthesis and catalytic processes [14].
Two-dimensional (2D) materials, with their large surface area and efficient metal anchoring sites, have been identified as promising candidates in order to prevent the aggregation of single atoms [15,16].Various 2D substrates (nitrogen-doped graphene [17], borophene [18], hexagonal boron nitride [19], transition metal dichalcogenides [20], and transition metal carbides [21]) have been used as suitable supports for SACs.Within the group of 2D substrates, graphitic carbon-nitride (g-C 3 N 4 ) has been identified as a promising substrate for anchoring single atoms due to its unique six-fold cavities, low cost, and accessibility, making it a good candidate for realizing TM-SACs [22,23].It has been recently reported that TM-doped g-C 3 N 4 catalysts are potential candidates for various applications such as nitrogen electroreduction [24], nitrogen fixation [25,26], efficient photocatalysts, and electrocatalysts [23,27,28].
In addition, Zhou [29] and Niu et al [30] have reported that anchoring of Pd and Rh catalysts on a reduced g-C 3 N 4 substrate leads to a strengthened metal-support interaction and a promising bifunctional catalyst with low HER and ORR overpotentials, respectively.These works seem to indicate that reduced g-C 3 N 4 with nitrogen vacancies exhibits an enhanced binding affinity to capture TM atoms compared to pristine g-C 3 N 4 and that reduced g-C 3 N 4 should be a more favorable substrate for SACs [31].However, most theoretical studies have mainly focused on the deposition of TM atoms on pristine planar and corrugated g-C 3 N 4 surfaces.Additional theoretical efforts have been made to modify g-C 3 N 4 for applications in nitrogen fixation and photocatalytic water splitting [30][31][32].Due to its importance in SACs applications, it is necessary to further investigate the energetics, thermodynamic, and electrochemical stability of single TM atoms adsorbed on various types of nitrogen vacancies in both planar and corrugated g-C 3 N 4 surfaces.
In this study, we perform a systematic density functional theory (DFT) screening of the structure and energetic, thermodynamic, and electrochemical stability of TM atoms (3d, 4d, and 5d series) adsorbed on nitrogen defective planar and corrugated g-C 3 N 4 .Our calculations point to the most stable configurations with the lowest formation energies and find that the absorption of single TM atoms on-vacancy and on-center sites are generally more favorable than the via-substitution absorption scenarios.Furthermore, our calculations indicate the most efficient SACs to prevent metal clustering and dissolution.We determine that the top 10 most stable TMs (Pt, Pd, Rh, Au, Ru, Ir, Cu, Co, Fe, and Ni) can generate the most resilient SACs on reduced g-C 3 N 4 surfaces.Our theoretical findings can guide experimental studies of robust SACs on g-C 3 N 4 substrates.

Computational details
Spin-polarized DFT calculations were performed by using the Vienna Ab Initio Simulation Package (VASP) [33,34].The electronic exchange and correlation interactions are treated using the generalized gradient approximation functional of Perdew, Burke, and Ernzerhof (PBE) [35].For all structural optimizations, we performed full optimization without any cell or atomic position constraints, with energy and force thresholds of 10 −5 eV and 0.01 eV Å, respectively.The SACs on g-C 3 N 4 were built using 2 × 2 × 1 supercells with more than 20 Å vacuum along the c direction to reduce interactions between periodic images.A 500 eV cut-off energy was used for the planewave expansion [36] and k-point meshes of 3 × 3 × 1 and 8 × 8 × 1 were adopted for structural optimization and electronic structure calculation, respectively.Grimme's scheme (DFT-D3) was included to address long-range van der Waals interactions [37].The analysis of atomic charges and electron transfer in these systems was performed using the Bader charge population analysis [38] and VASPKIT was used to analyze the results from VASP [39].The thermal stability is further examined by conducting ab-initio molecular dynamics simulations (AIMD) at room temperature (300 K) and high temperature (800 K) within the NVT ensemble on 2 × 2 × 1 supercells.

Structural and electronics properties of pristine g-C 3 N 4
As illustrated in figures 1(a), 2D graphitic carbon nitride (g-C 3 N 4 ) with tri-s-triazine as the primary building block can exist in two different conformations, planar (p) and corrugated (c).The pg-C 3 N 4 sheet keeps a perfectly flat structural morphology with the same lattice constants of 7.13 Å in both, a and b, directions, while cg-C 3 N 4 has a buckled structure (h = 1.40 Å as indicated in figure 1(b)) with slightly different lattice vectors along the a and b directions (6.93 Å and 6.96 Å, respectively).
It has been shown before that the corrugated conformation is slightly more stable than the planar one (about 41.42 meV/atom) [40,41].Our calculated structural parameters such as lattice constant, buckling height, bond length and relative energy for these two conformations of g-C 3 N 4 are in excellent agreement with the results previously reported in the literature (table S1).To further confirm the electronic structure of the planar and corrugated conformations of g-C 3 N 4 , we computed their electronic band structure at the PBE level of theory.Both p and c g-C 3 N 4 sheets show a semiconducting nature with indirect and direct band gaps of 1.22 eV and 1.99 eV, respectively (see supplementary information section S1).These band gap values are in very good agreement with previously reported theoretical band gaps (1.20 eV and 1.96 eV, respectively) [42].

Geometries and stability of SACs adsorbed on g-C 3 N 4 3.2.1. Pristine p and c g-C 3 N 4 monolayer
In order to effectively utilize SACs, the formation of a strong bond between the metal atom and the substrate is crucial to prevent metal clustering [43].Thus, we computed the binding energy and the formation energy of a single TM atom on both pristine g-C 3 N 4 conformations (p and c) to conduct a thorough screening based on their structural and thermodynamic stability.We investigated 24 TM atoms (figure 1(c)), and the sixfold cavity was found as the most stable site for anchoring TMs on g-C 3 N 4 sheets, in agreement with previous reports [23,24].Our computational results indicate that most of the TM atoms move slightly aside from the center of the sixfold cavity upon structure optimization except for a few elements: Hf, Mo, Nb, Sc, Ta, Ti, W, Y, and Zr, in both planar and corrugated g-C 3 N 4 .The differences in atomic radii and electronegativities of the TMs and surface atoms can account for the variation in the preferred anchoring sites within the sixfold cavity.The energy difference (total energy from DFT) between the TM atoms adsorbed in the planar and corrugated conformations is, in general, relatively small at about 0.2 eV/cell with the majority of adatoms favoring a corrugated structure upon adsorption except for a few outliers (see supplementary information section S2).It should be noted that upon TM adsorption the p conformation of g-C 3 N 4 tend to relax to a quasi-corrugated conformation that deviates from the original planar structure [23,44].
Bader population analysis was utilized to further confirm the strong interactions between the TM atoms and the g-C 3 N 4 substrate.In both conformations p and c, a significant amount of charge ranging from 0.35 to 2.09 e − is transferred from the TM atom to the substrate (see supplementary information table S2), agrees well with previous reported range (0.51 to 2.08 e − ) [45].It has been discussed previously that charge transfer from the metal adatom can enhance its electrocatalytic activity [46,47].
To explore the SACs stability, we obtain the metal binding energy With this definition, more negative binding energies represent a stronger binding strength between the adatom and the substrate.The calculated binding energies (figure 2(a)) for the TM atom absorbed on the pg-C 3 N 4 sheet are significantly higher than those corresponding to the c conformation.The strong binding energies (stronger than −7 eV) found here indicate a strong interaction between the g-C 3 N 4 substrate and the anchored SAC.For comparison, the obtained binding energies for corrugated Fe@g-C 3 N 4 , Co@g-C 3 N 4 and, Ni@g-C 3 N 4 are 3.39 eV, 3.94 eV, and 4.12 eV, respectively, as listed in table S3.These binding energy values are in very good agreement with previously reported energy ranges of 3.73-4.74eV and 3.75-4.68eV, 3.86-4.20eV, respectively [24,49,50].Next, to analyze the thermodynamical stability of these SACs relative to the pure metal bulk, we calculate the formation energy of a single TM atom adsorbed on the g-C 3 N 4 sheet relative to the cohesive energy of the TM bulk as

F p c b p c Coh
where the cohesive energy is defined as Tm Single and -E Tm Bulk is the total energy of the TM atom in the most stable pure bulk form and n is the number of atoms in the unit cell in the bulk.A negative E F indicates that SAC configuration are thermodynamically not prone to aggregate into the corresponding bulk phases [51].This definition has been applied in previously published works [49,52,53].As summarized in figures 2(b)-(c), we obtain 17 TMs with formation energies between −0.43 eV and −5.06 eV in the planar conformation and 5 TMs with a formation energy between −0.32 eV and −3.05 eV in the corrugated one, indicating a good thermodynamic stability for these metals.
In addition to the thermodynamic stability, we also analyzed the dissolution possibility of the metal adatom by calculating the dissolution potential defined as [30,54]  against / E F c p for the 24 TMs analyzed in this study, considering both the p and c conformations of g-C 3 N 4 .Based on the definition above, / U diss c p > 0 indicates a strong binding on g-C 3 N 4 and that their dissolution can be avoided under electrochemical conditions.Following these two stability criteria, Au, Pd, Cu, Zn, Ni, Fe, and Co on the pg-C 3 N 4 substrate show both thermodynamic ( / E F c p < 0) and electrochemical ( / U diss c p > 0) stabilities, rendering these TM adatoms experimentally feasible for a variety of applications.It is encouraging to note that some of our predicted stable of SACs on g-C 3 N 4 (Co [22], Ni [56], Fe [57] Pd [58] and Au [59]) have been recently synthesized which confirms that the SACs predicted to possess high thermodynamic and electrochemical stabilities hold great potential for synthesis.

Reduced p and c g-C 3 N 4 monolayer
It has been shown in previous studies that reduced sheets can exhibit an enhanced binding affinity for capturing TM atoms when compared to their pristine counterparts due to changes in their atomic arrangement and local chemical environment [31,60].In particular, monolayers with vacancies have proven to be a more suitable substrate for single-atom catalysts (SACs) [61].According to a previous work presented by Niu et al, N vacancies are more favorable than C vacancies in g-C 3 N 4 [30].Therefore, as shown in Figures 1(a)-(b), we here focus our work on three types of N vacancies on the p (c) conformation of g-C 3 N 4 : the edge site, ¢ N 1 ( ¢¢ N 1 ), the bridge site, ¢ N 2 ( ¢¢ N 2 ), and the center site ¢ N 3 ( ¢¢ N 3 ).To explore the stability of these various N vacancies, the vacancy formation energy where / E V c p and / E c p 0 are the total energies of g-C 3 N 4 with vacancy and pristine, respectively, and ( ) m N 2 is the N chemical potential defined as the total energy per atom of the N 2 molecule.The optimized structures and the calculated / E VF c p are presented in supplementary information section S3.We generally observe that the removal of a N atom results in a significant structural distortion that is more pronounced in the c conformation than the p conformation.Consequently, the buckling height increases to 2.82 Å ( ¢¢ N 1 ), 5.58 Å ( ¢¢ N 2 ), and 2.79 Å ( ¢¢ N 3 ) compared to the 1.4 Å in pristine cg-C 3 N 4 .In the case of the p conformation, all atoms remain in a plane, as in their pristine counterpart since there are no forces acting in the direction perpendicular to the plane.Vacancy formation energies for the ¢ N 1 and ¢ N 3 types are almost the same and much smaller than that of ¢ N 2 for reduced pg-C 3 N 4 , while the E VF c of the ¢¢ N 1 type are 3.07 eV and 1.14 eV smaller than the corresponding ¢¢ N 2 and ¢¢ N , 3 respectively, suggesting that the ¢¢ N 1 would be the more likely formed in the reduced cg-C 3 N 4 sheets.Next, we explore the structure stability of SACs on N-reduced p and c conformations of g-C 3 N 4 .Here we consider three potential single TM's absorption scenarios, (I) on-vacancy: represents the absorption of the TM on top of the vacancy site after full relaxation of the reduced surface of the g-C 3 N 4 sheet (i.e.fully relaxed structure after a N vacancy is generated).Here, the term vacancy site refers to the location where the nitrogen (N) vacancy is created.(II) on-center: represents the absorption of the TM on the top of the central cavity of the fully relaxed surface of the reduced g-C 3 N 4 sheet.(III) via-substitution: represents a scenario in which the TM directly substitutes a N atom with a single TM atom within the g-C 3 N 4 sheet.This last scenario corresponds to the experimental setup in which simultaneous reduction and single metal atom deposition occurs [63].The calculated binding energies of TMs adsorbed on the reduced p ( ¢ N , 1 ¢ N , 2 and ¢ N 3 ) conformation of the g-C 3 N 4 surface via the three adsorption scenarios considered here are shown in supplementary information (section S4).The converged structures andU diss p versus E F p profiles of ¢ N 1 reduced pg-C 3 N 4 sheets are presented in figure 3.Both on-vacancy and via-substitution absorption scenarios on the pg-C 3 N 4 surface provide one N and two C coordination sites for a TM adatom, which can help anchoring the SACs.A single TM on-center adsorption site preserves the ¢ N 1 vacancy with a pentagonal ring at the edge of the cavity for the pg-C 3 N 4 sheet (figure 3(c)).From our results we find that among the 24 thermodynamically stable TMs adsorbed on the ¢ N 1 site, 19 TMs adsorbed on-vacancy and 20 TMs adsorbed on-center are electrochemically stable with dissolution potentials in the range of 0.19-3.31V and 0.07-4.48V, respectively.The via-substitution absorption (figure 3(b)) is less thermodynamically and electrochemically stable, which can be attributed to their negligible structural deformation compared to the on-vacancy and on-center absorption sites.
Similar to ¢ N , 1 the reduced pg-C 3 N 4 surface with ¢ N 2 and ¢ N 3 vacancies (shown in figures 4 and 5) also shows more favorable absorption on-vacancy and on-center sites than via-substitution.Our results show that the TM is N , 2 and ¢¢ N 3 ) cg-C 3 N 4 sheets are presented in supplementary information (section S5).In contrast to the planar conformation and considering ¢¢ N 2 vacancies, we find that only Rh and Ir are simultaneously thermodynamically and electrochemically stable in the via-substitution absorption scenarios.Moreover, our calculations indicate that for ¢¢ N 1 and ¢¢ N 3 reduced cg-C 3 N 4 , no TMs is electrochemically stable.Here, r -TM@g C N 3 4 and r , TM r , C r N represent the total charge density of the TM@g-C 3 N 4 system and the superposition of the individual atomic (TM, C, N) charge density, respectively.The charge densities (represented in figure 7) reveal a noticeable charge transfer between the TM atoms and the adjacent N atoms, indicating a strong interaction between the lone pair electrons of the neighboring N atoms and the isolated TM.The charge is mainly accumulated around the TM atom and in the hexagonal rings for both ¢ N 1 and ¢ N 2 reduced TM/g-C 3 N 4 system.Partial DOS and charge densities plots for ¢ N 1 reduced TM/g-C 3 N 4 system are reflected in section S7 of supporting information.Among the SACs adsorbed on the reduced surfaces, the highest charge accumulation (light blue region) is observed for Fe with charge transfers of 0.92, and 0.81 e − for ¢ N 1 and ¢ N 2 vacancy types, respectively.We find that the charge transfer values of the TMs on reduced g-C 3 N 4 are lower than the values of their pristine counterpart.This reduction in charge transfer can be attributed to the reduced number of neighboring N atom, resulting from alterations in the structure during the N atom reduction process.TM catalysts with a lower oxidation state typically exhibit enhanced capability to capture the adsorbates, resulting in higher catalytic activity [23,65].Hence, it is anticipated that single TM atoms supported on reduced g-C 3 N 4 surfaces will show greater catalytic activity compared to TM atoms supported on pristine g-C 3 N 4 surfaces.
The thermal stability of the most stable SACs on both ¢ N 1 and ¢ N 2 reduced g-C 3 N 4 is also evaluated by performing ab-initio molecular dynamics simulations (AIMD) at a room temperature (300 K) and high temperature (800 K).A total time process of 5000 fs with a time step of 1 fs was implemented using 2 × 2 × 1 supercells (56 atoms).The variations of the total energy and temperature and the final structure snapshots at 5000 fs for Co, Fe, and Ni on ¢ N 1 and ¢ N 2 reduced pg-C 3 N 4 are depicted in figure 8.These structures do not display significant structural distortions or detachment of the SAC during the simulation interval, indicating the thermal stability up to 800 K of the TMs on reduced pg-C 3 N 4 .Their total energies and temperature as a function of time also show slight variations in the 5000 fs interval.Results of AIMD simulation for all other TMs on ¢ N 1 and ¢ N 2 reduced pg-C 3 N 4 are presented in supplementary information, section S8.It should be noted that the total energy for the Au and Ir SACs on the ¢ N 2 reduced pg-C 3 N 4 is slightly reduced after 1ps in the AIMD simulations.

Conclusions
In summary, we have performed a systematic computational screening of 24 TMs embedded on two different conformations (denoted as p and c) of graphitic carbon nitride monolayers.Upon single TM atom adsorption,  the planar conformation of the g-C 3 N 4 sheet can be modified to an energetically stable quasi-corrugated configuration which highlights a potential structural modification with implications for various applications.Our findings pave the way for understanding the most favorable scenarios via on-vacancy and on-center for TM absorption based on the analyses of binding energy, formation energy, and dissolution potentials.Our calculations show that the bridge-type vacancy ( ¢ N 2 ) in the reduced planar g-C 3 N 4 monolayer is the most energetically, thermodynamically, and electrochemically stable for single TM atom deposition.Our results indicate that due to enhanced atom adsorption, which can prevent clustering and dissolution, the top TMs Pt, Pd, Rh, Au, Ru, Ir, Cu, Co, Fe, and Ni are the most resilient single-atom catalysts (SACs) on ¢ N 1 (except Cu) and ¢ N 2 reduced g-C 3 N 4 surfaces.In addition, our AIMD simulations indicate a thermal stability up to 800 K of these SACs which will hopefully stimulate efforts in the experimental synthesis of TMs on reduced g-C 3 N 4 surfaces for novel SACs applications.

4
represent the total energies per unit cell of the p or c g-C 3 N 4 with a single adsorbed TM atom, the isolated TM atom, and the pristine p or c conformation of g-C 3 N 4 , respectively.

Figure 1 .
Figure 1.Top and side views of (a) p and (b) c conformations of a g-C 3 N 4 monolayer with a single TM atom embedded in the central cavity.(c) A table with the transition metals screened in this work.
denotes the standard dissolution potentials of the TM bulk, while n e represents number of electrons transferred during the dissolution process (taken from [55]).In figures 2(b)-(c), we present / U diss c p

Figure 2 .
Figure 2. (a) The computed binding energies (E b ) of TM atoms adsorbed in the central cavity of pristine g-C 3 N 4 .Dissolution potentials (U diss ) versus formation energy (E F ) of TM atoms on pristine (b) p and (c) c g-C 3 N 4 sheets.

Figure 3 . 1 ¢¢
Figure 3. Top and side views of the optimized SACs and dissolution potentials (U diss versus formation energy (E F ) of single TM atoms adsorbed (a) on-vacancy, (b) via-substitution, and (c) On-center for the ¢ N 1 reduced surface of the planar g-C 3 N 4 monolayer.

Figure 4 .
Figure 4. Top and side views of the optimized structures of SACs and dissolution potentials (U diss versus formation energy (E F ) of single TM atoms (a) on-vacancy (b) via-substitution (c) On-center for ¢ N 2 the reduced planar surface of the g-C 3 N 4 monolayer.

Figure 5 .
Figure 5. Top and side views of the optimized structures for SACs and dissolution potentials (U diss ) versus formation energy (E F ) of TM atom adsorption (a) on-vacancy, (b) via-substitution, and (c) on-center for ¢ N 3 reduced planar g-C 3 N 4 monolayer.

3. 2 . 3 .
Thermodynamic and electrochemical stable TMs on reduced pg-C 3 N 4 monolayer The most stable configurations in terms of thermodynamic and electrochemical stability for the TMs adsorbed on the pg-C 3 N 4 surface are presented in figure 6.The N bridge-type vacancy ( ¢ N 2 ) with anchored TM is the most thermodynamically as well as electrochemically stable among all of N vacancies.In general, the most stable adsorption sites are on-vacancy except for V, Zr, Sc, Y, and Hf which favor on-center sites for adsorption.We observe that TM formation energies (dissolution potentials) of anchored TM atoms on reduced pg-C 3 N 4 are smaller (larger) in the range of −3.10 to −7.36 eV (0.04 to 3.92 V) than the corresponding values in pristine pg-C 3 N 4 (E F ranging from 1.89 to −5.06 eV and U diss ranging from −0.64 to 1.48 V).The top 10 most stable TMs (Pt, Pd, Rh, Au, Ru, Ir, Cu, Co, Fe, and Ni) with a formation energy range between −4.90 and −5.50 eV and a dissolution potential range between 2.0 and 4.0 V are therefore identified as the most stable SACs configurations in ¢N 2 reduced pg-C 3 N 4 .Similarly, in ¢ N 1 type vacancies Pt, Pd, Rh, Au, Ru, Ir, Co, Fe, and Ni are identified as the most stable SACs (figure3(a)).We next examine the projected density of states (PDOS) of the most stable SACs adsorbed on ¢ N 1 and ¢ N 2 reduced g-C 3 N 4 .TM-induced gap states (mainly contributed by d electrons) emerge at the Fermi level of both ¢ N 1 and ¢ N 2 reduced TM/g-C 3 N 4 implying it could be a promising catalyst[64].The reduced g-C 3 N 4 substrate with adsorbed TMs exhibits a semiconductor nature with lower band gap values than pristine cg-C 3 N 4 , suggesting that the adsorption of TMs may slightly increase the conductivity of the monolayers (see supplementary information, section S6).To gain more insight into the chemical bonding of the stable SACs on reduced g-C 3 N 4 , we plot deformation charge densities distribution, obtained as r

Figure 6 .
Figure 6.Calculated (a) formation energies and (b) dissolution potentials of TM adsorption on pristine and reduced pg-C 3 N 4 .

Figure 7 .
Figure 7. Deformation charge density distribution of TM atom (Pt, Pd, Rh, Au, Ru, Ir, Cu, Co, Fe) with ¢ N 2 reduced pg-C 3 N 4 layer.The light blue and yellow colors denote the charge accumulation and depletion regions, respectively.The isosurface value is 0.025 e Å 3 .

Figure 8 .
Figure 8. Fluctuations of total energy of TM (Co, Fe and Ni) SACs on ¢ N 1 (upper-panel) and ¢ N 2 (lower-panel) reduced pg-C 3 N 4 layer during the ab-initio molecular dynamics simulations (AIMD) simulations at 300 K (black color) and 800 K (red color) in the NVT ensemble.Inset structures represent the snapshot at the end of a 5 ps simulation at 800 K.