Ab-initio characterization of iron-embedded nitrogen-doped graphene as a toxic gas sensor

Special binding sites in graphene are beneficial for near-surface interaction. These binding sites, which are supplied by single-atom catalysts, change the electronic characteristics of graphene and its derivatives, greatly expanding its potential use as gas sensors. Iron–nitrogen–carbon is reflected as one of the most effective substitutes for platinum in oxygen reduction reactions. The selection for carbon-enclosed FeN4 moieties, which serve as catalytically active centers, is among the top priorities. Current research focuses heavily on carbon-enclosed FeN4 moieties from a gas sensing perspective. In the present work, transition metal atom iron supported on nitrogen-doped graphene (FeN/G) was analyzed by density functional theory. The effect of gas adsorption on the structural and electronic properties was investigated with adsorption energy, charge transfer, work function, and band structure. The results indicate the chemisorption nature of carbon monoxide (CO), nitrogen oxide (NO), and nitrogen dioxide (NO2) with strong adsorption energies of − 1.641 eV, − 2.081 eV, and − 1.345 eV. They induced spin polarization when adsorbed on the graphene support, which drastically modulated the electronic characteristics of the substrate. While other gas molecules of carbon dioxide, hydrogen disulfide, and ammonia (CO2, H2S, and NH3) with adsorption energies of − 0.154 eV, − 0.371 eV, and − 0.460 eV were physisorbed and served as electron donors, sulfur dioxide (SO2) exhibited weak chemisorption at a value of − 0.620 eV. Nitrogen-containing gas molecules of NO, NO2, and NH3 showed band gap shortening with increasing conductivity as compared to bare iron embedded graphene supported structure. Based on the investigation, the structure has potential application for the detection of NO and NO2 and other gases.

Metal-decorated graphene has also been suggested as a good sensing material [13,24,44]. The carbon atoms of graphene are replaced or covalently bonded by foreign atoms upon doping with heteroatoms such as oxygen, boron, nitrogen, sulfur, and phosphorus [45][46][47]. Nitrogen (N) doped graphene materials provide high reversible stability and selectivity over CH 4 , H 2, and N 2 [48]. Furthermore, an exciting class of catalysts is recently emerging as single-atom catalysts (SACs) with monodispersed single atom supported by a solid substrate [49]. Different metal oxide substrates of TiO 2 , CeO 2, and FeO x are being employed which have the drawback of poor stability and low conductivity. Metal single-atom catalysts (MSACs) replace the declining activity of high-cost platinum (Pt) and Pt-based catalysts for practical applications [50]. Due to superior and highly effective bonding topologies, N-doped carbon nanomaterials combined with transition metals (M-N-C, M = Fe/Co/Mn, etc.) have fascinated a lot of attention [51]. In 2018, Huang and coworkers [52] successfully synthesized a distinctive class of SACs using transition metals (M = Ni, Co, Fe) embedded in N doped holey graphene (MNHGFs) by thermal annealing process. H 2 O 2 , metal precursor, and aqueous suspension of graphene oxide are hydrothermally treated into self-assembled 3D graphene hydrogel. The dried gel is then annealed in NH 3 to obtain MNHGFs. The structure provides enriched defective sites, a tremendous number of vacancies for nitrogen incorporation and anchoring metal atoms, and the least geometrical distortion to graphene lattice. This structure (MNHGFs) has identical MN 4 C 4 moieties in which M and C are adsorption sites for intermediates. MN 4 C 4 consists of a single divacancy defect in graphene by the removal of two neighboring carbon atoms at the center. Four nitrogen atoms replace four carbon atoms surrounding the defect making MN 4 C 4 a porphyrin-like structure. Similarly, co-coordinated iron and nitrogen-doped graphene (FeN/G) possess FeN 4 moieties in the structure utilized for higher desired activity. The kinetically and energetically stable FeN 4 sites are more preferential with smaller formation energy [53]. Theoretically, these structures are based on divacancy moieties, and have been explored for catalytic [54][55][56][57], electronic and magnetic properties [58,59]. However, to the best of our knowledge, MN 4 C 4 has not been investigated for gas sensing applications.
To effectively utilize the capabilities of MN 4 C 4 , this study exploits Fe in gas sensing by density functional theory. The FeN/G structure configuration has motivated us to adopt density functional theory for exploring gas sensing properties. We investigated binding sites, adsorption energies, charge transfer, band gap, work function, and electronic band structures of adsorbed gas molecules (CO, CO 2 , NO, NO 2 , H 2 S, SO 2 , NH 3 ) on FeN/G monolayer. The calculated properties prove to be good magnetic sensors with high selectivity, stability, and sensitivity.

Computational methods
In the present work, the calculations were performed with Vienna Ab-initio Simulation Package (VASP) centered on density functional theory (DFT). The generalized gradient approximation (GGA) with Perdew-Burke-Ernzerhof (PBE) functional was employed to treat exchange-correlation potential. Plane wave basis set with a value of energy cutoff of 500 eV was adopted. The convergence criteria for energy (10 -6 eV) and forces (0.002 eV/Å) with a conjugate gradient approach was achieved for energy minimization. Special K points based on the Monkhorst-Pack scheme were generated with a 6 × 6 × 1 grid. Spin polarization was conducted to examine the magnetic possibilities of the structure. Vander Waals (vdW) correction with D3 method was employed.
The projected density of states (PDOS) and projected band structure were plotted to evaluate the contribution of atoms in forming unoccupied and occupied states near the Fermi level. Charge distribution was analyzed by the Bader charge analysis program [60]. The interaction between adsorbate (gas molecule) and the substrate (FeN/G) was calculated by the following equation. The most stable structure was figured by adsorption energy given as follows: where the total energy of the substrate adsorbate system in the equilibrium state is E substrate−adsorbate . E adsorbate is the energy of adsorbate (gas) and E substrate (layer) is the energy of the substrate. The adsorption process will be exothermic if the value is negative implying a stable and favorable adsorption structure [61].
The charge density difference was computed by the following equation; ρ total is the charge density of the adsorbate substrates system, ρ substrate and ρ adsorbate are the charge densities of substrate and adsorbate [62].
The efficiency of sensing devices is measured in terms of work function. The energy needed to transfer an electron from the Fermi level to the vacuum level is defined as work function (WF) [63]. Zero band gap graphene possesses a work function of 4.49 eV [64]. Doping, hybridization, and surface functionalization alter the work function of graphene [65]. The gas adsorption creates surface charge redistribution on the substrate [66]. The amount of charge gained or lost between the adsorbate upon adsorption influences the work function [29]. The lower value of work function enhances the sensitivity of the sensor thereby increasing the charge density. Weak interaction between the adsorbate and substrate has little effect on work function [67]. Strong chemical interaction between the gas adsorbate and the (2) Δ = total − substrate − adsorbate sensing substrate leads to higher sensitivity and selectivity of the gas sensor [68].
Adsorption energies, bond length between gas and layer, bond length of gas molecules before and after adsorption, charge transfer, band gaps and work function are summarized in Table 1.

Structural and electronic properties of FeN/G
The optimized structure of iron-embedded nitrogen-doped graphene contains total 31 atoms and a layer thickness of 0 Å. The structure (FeN/G) consists of one iron (Fe) atom, 4 nitrogen (N) atoms and 26 carbon (C) atoms. The obtained crystal system is oblique with a lattice parameter of 9.755 Å and a space group of P2/m. A single divacancy defect is produced in graphene by the removal of two adjacent carbon atoms. Structurally, four nitrogen atoms replace the four carbon dangling bonds of graphene which surround the divacancy (removal of two adjacent C atoms). It makes a porphyrin-like structure with a stable Fe atom at the center. The Fe, N and C atoms all lie in a plane. The N being harder than C strongly binds to harder transition metals such as Cr, Ni, Ag, Co, Pt, Fe and Pd. So, doping of N leads to stability of atomically dispersed transition metal in the vacancy of graphene. Figure 1a shows the optimized structure of FeN/G in which all atoms lie in the same plane. FeN/G structure is more favorable energetically as compared to all other structures of Fe-GN 2 , Fe-GN 3 , Co-GN 4 , and Mn-GN 4 . Carbon divacancy creation, the substitution of N atoms, and the incorporation of a metal atom into the center of nitrogen atoms make a more stable structure possessing a single Fe atom surrounded by four N atoms [69]. Thus, the four FeN bonds are smaller than those of the transition metal adsorption on defective graphene [58,70,71].
According to Bader charge analysis, 0.91 e is transferred by iron (Fe) atom exhibiting positive charge on it. These electrons are distributed to neighboring four N atoms with Table 1 Calculated adsorption energy in eV, D sys (Å) the distance between the doped atom and atom adsorbed, distance between the molecule after and before adsorption, Band gap in eV, charge transfer and nature of adsorbed gas and work function (eV)  a negatively charge of about 0.70 e. C atoms show dual behavior of accepting and losing charge. Due to this transfer of electrons, Fe-N bonds show a covalent feature. So, the higher value of electron distribution at the Fe-N bond helps in stabilizing the Fe atom [62] as illustrated in Fig. 1b. This explanation is in accordance with electron localization function (ELF). The system under consideration is thermodynamically stable. ELF is used to visualize electronic distribution in three-dimensional space. It gives information of the nature of bonding exists between the atoms, local accumulation and depletion of charge and the localization of lone pairs. It is an indicator used to describe Pauli repulsion between electrons. The atomic interactions are of two types: chemical bonding with shared electrons and physical bonding with unshared or closed shell interaction [72,73]. Asymmetry of spin channels in the system exhibits magnetic behavior due to Fe. The partial density of states (PDOS) of FeN/G in Fig. 1c explains the contribution of four Fe-N bonding orbitals with the hybrid 2p orbitals of N and 3d xy and 4 s orbitals of Fe. Whereas, the remaining 3d orbitals of Fe will play role in the nonbonding state and interacts with the adsorbate [74]. 3d electrons of Fe make bonds with N-doped graphene by utilizing 4 s electrons of N. While the remaining partially filled 3d orbitals facilitate the electrontransfer. A strong hybridization with the total density of states arises between Fe and N doped graphene around the Fermi level. Fe atom imparts ferromagnetism to graphene doped with N [75,76]. As a result, it contributes to the splitting of the density of states of two spins, which is beneficial for magnetic sensor applications [77].

Adsorption energies and geometry
The adsorption of a range of hazardous gas molecules including CO 2 , CO, NO 2 , NO, NH 3 , H 2 S, and SO 2 are investigated on the most stable configuration of the FeN/G monolayer. Each gaseous molecule is adsorbed to FeN/G structure with a different configuration. The most favorable site for energy minimization is the Fe atom. The structural and electronic properties of adsorbed systems are analyzed.
The parallel adsorption of CO 2 molecule is observed on Fe embedded N doped graphene as depicted in Fig. 2a with top and side views. The Fe-C bond length is 1.686 Å after adsorption of the CO 2 molecule on the FeN/G surface. The bond length of C-O is 3.778 Å and O-O is 1.394 Å. The adsorption energy of the CO 2 molecule is − 0.154 eV indicating weak physisorption on FeN/G. H 2 S has gained much attention in different scientific fields. The emission of highly toxic and corrosive gas damages the health and environment which is irreversible. Due to its substantial toxicity, it is fascinating to analyze H 2 S adsorption on various materials. The location of the sulfur (S) atom plays a key role in the adsorption. The configuration of the H 2 S molecule is perpendicular to the plane with the S atom facing toward the substrate plane. Figure 2b exhibits the adsorption of V-shaped H 2 S molecule on FeN/G monolayer with an adsorption energy of − 0.371 eV. The S atom of H 2 S binds to the Fe atom while H atoms are away and rotated around the axis to the right side. The bond length between Fe-S is 2.141 Å. This distance between S of H 2 S and Fe is greater than the adsorption of H 2 S on Fe-doped graphene (2 Å) showing weak interaction between these two atoms [78]. A slight elongation from 1.348 to 1.37 Å occurred between the bond lengths of S-H with less structural changes upon adsorption. Adsorption of NH 3 molecule is investigated for a vertical configuration where three H atoms are away from the FeN/G surface with N atom facing towards the substrate. The bonding of the NH 3 molecule to the Fe atom via the N atom upon an interaction is depicted in Fig. 2c. The adsorption energy − 0.460 eV for NH 3 indicates its physical adsorption on the FeN/G monolayer. It can be seen that this adsorption energy is higher than NH 3 adsorption on graphene (− 0.11 eV), phosphorene (− 0.18 eV), MoS 2 (− 0.246 eV), N doped graphene (− 0.12 eV) [39]. The bond length of Fe-N is 1.973 Å showing an increase near the interaction locality.
The most stable configuration for CO adsorption on FeN/G is vertical with C facing downward. It makes Fe-C bond and the O atom away from the substrate plane.  [58] graphene. The adsorption energies of the considered gases are more than the N-doped graphene but less than Fe-doped graphene and are comparable to other metal-doped graphene substrates (see Table 2). Additionally, the GGA (specifically PBE) method and the supercell approach are found to be the most popular methods for exploring doped graphene used in toxic gas sensors [24].

Charge density analysis
The sensing quality of the gas sensor is evaluated by the alteration of resistance, occurring in charge transfer, induced by gaseous molecule adsorption on the monolayer. This transfer can be visualized in Fig. 3 from the differential charge density distribution. The charge accumulation and depletion sites are displayed in green and cyan colors. The Bader analysis is preferred to calculate the charge transfer between adsorbed gas molecule and the monolayer substrate. From Bader charge analysis, the Fe and the C lose electrons (cyan color), which are gained by the N and the O atoms (green color). Due to its paired electrons, the CO 2 molecule serves as electron donor with a charge transfer of 0.02 e to the FeN/G monolayer. The charge analysis is in accordance with the Fig. 3a. The differential charge density visualizes less charge (i.e. 0.11 e) transferring from gas to monolayer. As seen in Fig. 3b, the charge protrudes from H towards N atoms of FeN/G, while the charge accumulates at the Fe-S bond. The charge density in Fig. 3c depicts the charge accumulation take place at H-N and Fe-N bonds. Three H atoms of NH 3 lose 1.39 e charge to N. N atom of NH 3 donates 0.23 e to the monolayer via Fe atom. Fe atom distributes this charge to surrounding N atoms. The charge transfer is further confirmed by the Bader analysis, where the charge moving from H atoms to N atoms of the monolayer indicates the electron donor nature (1.17 e) of the NH 3 molecule.
More negative adsorption energy values are indicative of chemisorption, which involves more charge transfer between the molecule and the substrate [92]. The charge density (Fig. 3d) shows the charge transmission from FeN/G to adsorbed CO gas in which the Fe atom acts as an electron transfer carrier. The charge accumulation (green color) takes place in the vicinity of the O atom and Fe-C bond. The dominant Fe atom donates 1.00 e charge to its surroundings (N and C) while C atom of CO loses 0.84 to the O atom. O atom receives 1.06 e which means that the molecule is receiving − 0.23 e charge from the substrate (Fig. 3d). A net charge of 0.31 e is accepted by NO molecules in Fig. 3e

Electronic band structure and PDOS
Several studies have revealed that the dopant increases the adsorption capability of gas molecules which further enhances the sensitivity of the substrate by evaluating adsorption energies, charge densities, band structure and DOS [85,92,93]. To understand the interaction of gas molecule to the substrate, band structure and PDOS  [91] are computed after adsorption. Due to very weak physical adsorption, a slight change occurs ( Fig. 4a and S1a) between the band structure and (PDOS) of CO 2 adsorbed FeN/G. The band structure in Fig. 4a shows the introduction of red color oxygen density of states below and above the Fermi level (0 eV). The band gap slightly shifts from 0.033 (bare FeN/G) eV to 0.035 eV (adsorbed). FeN/G is not suitable for CO 2 detection. The detail of PDOS is given in supplementary information (SI). A slight increase in band gap (0.037 eV) occurs after H 2 S adsorption. The states of H 2 S lie above and below the Fermi level and can be seen in Fig. 4b and S1b (see more detail in SI). The spin up and spin down states are identical. This structure indicates the physisorption nature of H 2 S which can be utilized for gas sensing. The contribution of green-colored H atoms can be visualized in the conduction band above the Fermi level ( Fig. 4c and S1c), which proves the enhancement in conductivity of the adsorbed system and decreases the band gap. The contribution also comes from the overlapping of p orbital of N and d orbital of Fe. The lone pair of NH 3 facilitates the interaction between the surface and adsorbate [94,95].
The plots in Fig. 4d and S1d illustrate the band structures and PDOS of CO adsorption on FeN/G. The band gap of CO has increased to 0.055 eV as compared to bare FeN/G (0.033 eV). Figure 4d visualizes the contribution of O atoms of CO above the Fermi level. The results indicate that the chemisorption nature of CO-FeN/G has potential for CO gas sensing application. The electronic band structure of FeN/G after NO adsorption and PDOS are depicted in Fig. 4e and S1e. Visualization of NO states can be done within − 2.5-2 eV (Fig. 4e and S1e). NO possesses an unpaired electron in 2π* orbital making the molecule more reactive for chemical bonding. Chemical adsorption of NO decreases the band gap of the substrate to 0.010 eV (71%) indicating high conductivity of the substrate. The hybridization of orbitals of Fe and NO occur in the band structure.
According to Fig. 4f and S1f, NO 2 adsorption can be observed above the Fermi level (0 eV). The system's conductivity increases after the adsorption of NO 2 which reduces the band gap of bare FeN/G (0.033 eV) to 0.006 eV. NO 2 prefers to absorb on FeN/G from two oxygen atoms. The gas can receive electrons from the metal-embedded graphene due to the excessive positive charge on N. This result can be explained by the π-back donation effect (see supplementary information). Remarkable changes can be examined in the electronic structure due to transport of more electrons which leads to higher sensitivity of NO 2 gas sensor [29,32,67]. It can be inferred from Lowdin charge results that this system can be an excellent candidate for NO 2 sensing [96]. Figure 4g and S1g, show the plots of electronic band structure and PDOS of the SO 2 adsorbed system. In Fig. 4g and S1g, SO 2 adsorption states can be observed above and below the Fermi level (0 eV). The band gap increases to 0.143 eV after adsorption. A pronounced change occurs in the band structure near the Fermi level (− 0.5-0.5 eV) resulting in S p orbital hybridization with Fe p orbital. It is inferred that SO 2 on FeN/G shows weak chemisorption.

Work function
Work function is an effective way to detect gases. The calculated WF for bare FeN/G and adsorbed gases are enlisted in Table 1. The WF for bare FeN/G is computed to be 3.929 eV. Metal's work function linearly depends upon the charge density [97]. The WF of chemisorbed gases (CO, NO, NO 2 and SO 2 ) showed greater values from 4.184 to 5.294 eV than bare FeN/G (3.929 eV) as charge acceptance from the substrate creates less localized electron distribution on the surface. This creates more difference in negative potential at the surface thereby shifting the Fermi level to the vacuum level (upward) at increasing negative potential [94,97,98]. The values of WF of weakly physisorbed gases of H 2 S and NH 3 are 3.925 eV and 3.762 eV. Weakly physisorbed donor gases (CO 2 and H 2 S) did not show a significant change in WF as the presence of more localized electrons on the FeN/G surface creates less negative potential. With less change in the negative potentials, the shifting of the Fermi level will be in a downward direction. Therefore, WF can be tuned by the adsorption of gas molecules.

Conclusion
The interaction of gases with single-atom catalysts may be advantageous for tuning the structural and electronic properties of doped graphene. For this purpose, calculations of DFT were performed to investigate the adsorption of poisonous gases on iron-embedded nitrogen-doped graphene moieties. It was probed that SO 2 , CO, NO, and NO 2 show chemisorbed nature with bare FeN 4 and accept charge from the graphene substrate. Adsorption of NO, NO 2, and CO introduced spin polarization in the Fe-embedded graphene system with the highest adsorption energy of NO (− 2.081 eV). CO 2 , H 2 S, and NH 3 were explored to be physisorbed with electron-donating behavior. The adsorbed systems of CO, CO 2 , H 2 S and SO 2 present band gap widening and band gap reduction occurs in NO, NO 2 and NH 3 . Work function were computed for bare (3.929 eV) and adsorbed systems which show less values for physisorbed gases and higher values for chemically adsorbed gases. These findings suggest that FeN 4 -supported graphene monolayer has a strong potential as a gas sensor particularly, in detecting NO and NO 2 molecules.

Funding
The authors have not disclosed any funding.
Data availability Enquiries about data availability should be directed to the authors.