First-principles study on α/β/γ-FeB6 monolayers as potential gas sensor for H2S and SO2

The adsorptions of toxic gases SO2 and H2S on 2D α/β/γ-FeB6 monolayer were investigated using density functional theory calculations. To analyze the interaction between gas molecule H2S/SO2 and α/β/γ-FeB6 monolayer, we calculated adsorption energy, adsorption distance, Mullikan charge, charge density difference, band structure, the density of states, work function, and theoretical recovery time. The adsorption energies show that H2S/SO2 is chemisorbed on α/β-FeB6 while H2S/SO2 is physiosorbed on γ-FeB6 monolayer. As a result, γ-FeB6 has a short recovery time for H2S (5.71×10−8 s)/SO2 (1.94×10−5 s) due to modest adsorption. Therefore, γ-FeB6 may be a promising candidate for reusable H2S/SO2 sensors at room temperature. Although H2S is chemisorbed on α/β-FeB6, as the working temperature rises to 500 K, the recovery time of α/β-FeB6 for H2S can decrease to 1.13×10−1 s and 2.08×10−1 s, respectively, which are well within the detectable range. So, α/β-FeB6 monolayer also may be a good candidate for H2S gas sensor. Calculations were performed at GGA-PBE/DNP level using the Dmol3 module implemented in the Material Studio 2018 software package.


Introduction
Hydrogen sulfide (H 2 S) and sulfur dioxide (SO 2 ) are two colorless toxic gases that are very harmful to humans.For H 2 S, it can cause human eyes and nose irritation, headaches, sore throat, cough, pulmonary edema, coma, convulsions, and even death as its concentration increases from 10 to 700 ppm [1,2].For SO 2 , humans can absorb it through the respiratory system and skin contact and will have life-threatening danger at concentrations of 100 ppm [3].To minimize the harmful effect of toxic gases on human health, gas sensors should be used to detect and monitor the air quality.Especially, H 2 S/SO 2 sensors are most needed for use in wastewater treatment plants [4], oil refineries [5], power stations [6], and industries where both gases are commonly produced.With the help of H 2 S/SO 2 sensors, operators can quickly detect any deviations from safe gas conditions, which allows them to take corrective measures immediately before any harm occurs.Hence, the use of H 2 S/SO 2 sensors plays an essential role in protecting workers' health.
2D materials have been regarded as promising candidates for gas sensors due to their unique properties of high surface-to-volume ratio and plentiful active sites.Moreover, 2D materials have become a large family that has numerous members with vastly different properties, which can provide a rich material library for the research of various gas sensors.For example, NO 2 , NH 3 , H 2 S, and other gases adsorption on graphene's surface can induce the perturbations of graphene electronic states, which makes graphene, graphene oxide, Chao Wang and Yuhang Zhang contributed equally to this article.
314 Page 2 of 12 reduced graphene oxide, and their functionalized materials be applied widely to gas sensors [7][8][9][10][11].The gas sensors based on the typical transition metal dichalcogenide MoS 2 can detect NO 2 [12], NH 3 [13], and SO 2 [14] with concentrations as low as 20 ppb, 1 ppm, and 1 ppm, respectively.The gas sensors made from Ti 3 C 2 T x , a 2D MXene material, showed a very low detection limit (50-100 ppb) of volatile organic chemical gases [15].The black phosphorene can also act as the active material for NO 2 gas sensor which responds to concentrations as low as 5 ppb [16].Besides these experimental studies, some 2D materials, such as WO 3 [17], C 2 N [18], silicene [19], germanene [20], and arsenene [21], have been also predicted to be ideal candidates for gas sensors using theoretical simulations based on first-principles calculations.Therefore, the abundant 2d materials bring tremendous opportunities for future research in gas sensor applications.
Recently, our group has studied theoretically the polymerization of the Fe@B 6 H 6 cluster and obtained a metal boride FeB 6 monolayer [38], which indicates Fe atom can stabilize the HBS.Interestingly, our FeB 6 monolayer is the same as the γ-FeB 6 monolayer which was searched by Zhang et al. [39] using the particle-swarm optimization method.In addition to γ-FeB 6 monolayer, Zhang et al. [39] also predicted α-FeB 6 and β-FeB 6 monolayers.Very recently, the transition metal embedded graphene as a promising material for gas sensors have been intensively investigated [40][41][42][43].Similarly, the graphene-like α/β/γ-FeB 6 monolayers can be regarded as borophenes with embedded Fe atoms.However, few studies have been reported on gas sensors based on them.In this article, through first-principles calculations, we studied some properties of SO 2 and H 2 S gas molecules absorbed on α/β/γ-FeB 6 monolayers, including adsorption energy, adsorption distance, Mullikan charge, charge density difference, band structure, density of states, and partial density of states, to fully explore the potential and possibility of α/β/γ-FeB 6 monolayers as gas sensor material.Our calculated results show that the adsorption energies of H 2 S adsorption on α-FeB 6 and β-FeB 6 are −1.014 and −1.163 eV, respectively, which are larger than that (−0.93 eV) of H 2 S on graphane decorated with Fe [44] and the recovery time of SO 2 adsorption on γ-FeB 6 is 1.94×10 −5 s which is shorter than 7.95×10 −4 s for SO 2 adsorption on PdSe 2 monolayer [45].Thus, our results suggested that γ-FeB 6 may be a promising candidate for reusable H 2 S/SO 2 sensors at room temperature while α/β-FeB 6 can be a good choice as reversible H 2 S sensor at 500 K.

Computational details
All first-principles calculations with density functional theory (DFT) were performed using the Dmol [3] module of the Materials Studio software [46,47].The 2×2×1 supercells of α/β/γ-FeB 6 monolayer, consisting of 28 atoms, and a large cubic cell with a boundary length of 20 Å for gas molecules were built for simulation.The Perdew-Burke-Ernzerhof (PBE) functional was adopted as the exchangecorrelation functional under the generalized gradient approximation (GGA).And the double-numerical properties plus polarization (DNP) were selected as basis set.The cutoff radius was chosen to be 5.3 Å to achieve high precision.The thickness of the vacuum layer in the z-direction was set to 20 Å to avoid interference between adjacent layers.The energy of the convergence criterion for geometric optimization of α/β/γ-FeB 6 monolayer, gas molecules, and α/β/γ-FeB 6 monolayer with gas molecule was selected to 1×10 −5  Ha.The force and displacement in the convergence criteria were 0.002 Ha/Å and 0.005 Å, respectively.The threshold of self-consistent-field (SCF) convergence was 1×10 −6 Ha.Convergence tests (Fig. S1) show that 6 × 6 × 1 k-point for sampling the Brillouin zone and smearing value of 3×10 −3  Ha can provide reliable results.
The adsorption energies (E ads ) of gas molecule adsorption on the α/β/γ-FeB 6 monolayer are calculated using the following formula: where E tot is the total energy of the system after gas adsorption, E sub is the energy of α/β/γ-FeB 6 monolayer, and E gas is the energy of the gas molecule.According to our definition, a larger negative E ads represents the more stable adsorption of gas molecules on α/β/γ-FeB 6 monolayer.To examine the effect of the van der Waals (vdW) interaction between α/β/γ-FeB 6 monolayer and H 2 S/SO 2 gas on the E ads , the vdW correction DFT-D2 proposed by Grimme [48] was engaged to describe long-range vdW interactions.The E ads with vdW and without vdW of the most stable adsorption configuration for H 2 S/SO 2 adsorption on α/β/γ-FeB 6 monolayer are listed in Table S1.It can be seen that the rations of vdW are in the range of 24-46%, which indicates that the vdW interactions cannot be negligible.Thus, the E ads used in the following study refers to the adsorption energy with vdW

Analyses of adsorption
To completely understand the feasibility of α/β/γ-FeB 6 as a gas sensor material, we researched the adsorption behaviors of H 2 S/SO 2 molecules on the α/β/γ-FeB 6 monolayer.According to the structure of α/β/γ-FeB 6 , we fully considered all the possible absorption sites for the gas molecules on them, as shown in Fig. 2. The T1 and T2 sites are located above the Fe atom and B atom, H1, H2, and H3 are located above the holes, and B1, B2, and B3 are located above the Fe-B and B-B bonds.We used a 2×2×1 supercell to calculate the E ads of H 2 S/SO 2 on α/β/γ-FeB 6 monolayer.To find the most stable adsorption configuration, we placed the gas molecules with different orientations on the six possible adsorption sites in α/β/γ-FeB 6 monolayer.It should be noted that the gas molecules were placed on both sides of α/β-FeB 6 monolayer due to their out-of-plane buckled structures.The top four optimized structures with the highest E ads are shown in Fig. S2-3.It can be seen that for H 2 S, the B or Fe atoms of α/β/γ-FeB 6 are the main adsorption sites that interact with the S or H atoms of H 2 S.Among them, the one with the shortest distance between the S atom and the Fe atom is the most stable adsorption configuration.For SO 2 , α/β-FeB 6 has two sites (two B atoms or two Fe atoms) to adsorb SO 2 at the same time.And the most stable adsorption configurations emerge from them.γ-FeB 6 interacts with SO 2 through the B or Fe atoms.Among them, the most stable adsorption configuration is SO 2 adsorbed near the Fe atom of γ-FeB 6 .3 illustrates the most stable adsorption configuration of H 2 S/SO 2 on α/β/γ-FeB 6 .It can be seen that the gas molecules are mainly adsorbed near Fe atoms except that SO 2 is absorbed on boron atoms in α-FeB 6 .For H 2 S, it is almost parallel to the surface of α/β/γ-FeB 6 and the S atom is almost directly over the Fe atom.The distances between the S atom and Fe atom (d S-Fe ) of α/β-FeB 6 are 2.244 Å which is similar to that (2.247 Å) of H 2 S on graphane decorated with Fe 44 .But the E ads (−1.014 eV for α-FeB 6 and −1.163 eV for β-FeB 6 ) are larger than that (−0.93 eV) of H 2 S on graphane decorated with Fe 44 , which indicates that there are stronger interaction between H 2 S and α/β-FeB 6 .The d S-Fe (2.319 Å) of γ-FeB 6 is longer than the d S-Fe of α/β-FeB 6 , which leads to smaller E ads (−0.508 eV).For SO 2 , the adsorption cases are different on α/β/γ-FeB 6 .The S/O atoms, the two O atoms, and the S atom of SO 2 are attached to two B atoms of α-FeB 6 , two Fe atoms of β-FeB 6, and a Fe atom of γ-FeB 6 , respectively.The bond lengths of 1.442 Å for O-B and 2.021 Å for S-B in α-FeB 6 are slightly longer than those (1.344Å for O-B and 1.880 Å for S-B) of SO 2 adsorption on borophene [49].The lengths of O-Fe bonds in β-FeB 6 are 1.968 Å and 1.958 Å which are close to that (1.97 Å) of SO 2 adsorption on FeN 3 -doped graphene [50].Such adsorption distances result in the orders of E ads of SO 2 : α-FeB 6 (−2.240 eV) > β-FeB 6 (−1.847 eV) > γ-FeB 6 (−0.578 eV).Usually, adsorption energies larger than 1 eV belong to chemisorption while those smaller than 1 eV belong to physisorption [51].Therefore, both H 2 S and SO 2 belong to chemisorption on α/β-FeB 6 while they are physisorption on γ-FeB 6 .
To analyze the effect of the gas molecules on α/β/γ-FeB 6 monolayer, their surface energy (γ surf ) are calculated according to the following equation [52]: where E surf is the energy of FeB 6 monolayer, E bulk i−atom is the energy in the bulk of the ith atom that constitutes FeB 6 monolayer, n i is the number of ith atoms of that species at FeB 6 monolayer and A is the surface area of FeB 6 monolayer.The calculated surface energies of α/β/γ-FeB 6 before (γ surf ) and after (γ surf-gas ) H 2 S/SO 2 adsorptions and their Fig. 3 The top and side views of the most stable adsorption configuration with adsorption energies and the nearest distances between H 2 S/SO 2 and α/β/γ-FeB 6 differences (∆γ surf = γ surf-gas − γ surf ) are listed in Table 1.The γ surf of α/β/γ-FeB 6 before H 2 S/SO 2 adsorptions are in the range of 1.419-1.948kcal/mol Å −2 , which is larger than the surface energies of MoS 2 (200-260 mJ m −2 [53,54] that is, 0.288-0.374kcal/mol Å −2 ).The γ surf follows the order α-FeB 6 < β-FeB 6 < γ-FeB 6 , which is consistent with the order of magnitude in Ref. 39.After H 2 S/SO 2 adsorptions, the γ surf-gas increases slightly.For H 2 S adsorption, the structures of α/β-FeB 6 change little (see Fig. 3a, b), which leads to the small ∆γ surf of α/β-FeB 6 while the Fe atom is slightly induced out of γ-FeB 6 plane (see Fig. 3c), which leads to the large ∆γ surf of γ-FeB 6 .For SO 2 adsorption, two B atoms are induced out of the α-FeB 6 surface (see Fig. 3d), resulting in the largest ∆γ surf .And the γ interacts with two Fe atoms of β-FeB 6 , causing slight surface distortion (see Fig. 3e), thus, having the second largest ∆γ surf .Similar to the γ-FeB 6 -H 2 S system, the Fe atom induced out of the γ-FeB 6 surface causes the smaller ∆γ surf .Therefore, the ∆γ surf can reflect the effect of H 2 S/SO 2 on the structures of α/β/γ-FeB 6 .
The charge density differences between H 2 S/SO 2 and α/β/γ-FeB 6 monolayer are shown in Fig. 4 where green and blue represent charge depletion region and charge gain region, respectively.It can be seen clearly that the S atoms of H 2 S adsorption on α/β/γ-FeB 6 are the charge depletion region while the S/O atoms of SO 2 adsorption on α/β/γ-FeB 6 are the charge gain region.Based on Mullikan population analysis, the calculated Mullikan charges before and after H 2 S/SO 2 adsorption on α/β/γ-FeB 6 monolayer are listed in Table 2.For H 2 S adsorption on α/β/γ-FeB 6 , the charges of S are −0.218/−0.294/−0.226,respectively.The similar charges of S contribute to the similar d S-Fe in these systems.Compared with the charge (−0.418) of S in free H 2 S molecule, the charges of S in H 2 S adsorption on α/β/γ-FeB 6 reduce 0.20, 0.124, and 0.192, respectively, which agrees well with the charge depletion of S atom in the analyses of density difference between H 2 S and α/β/γ-FeB 6 .The total charges transferred from H 2 S  Based on charge transfer, the β-FeB 6 is more suitable for SO 2 , which also corresponds to the larger ∆γ surf and E ads .

Band structures and density of states
To study the adsorption effect of H 2 S/SO 2 on α/β/γ-FeB 6 monolayer, the band structures of α/β/γ-FeB 6 monolayer with and without H 2 S/SO 2 are shown in Fig. 5.The pristine α-FeB 6 exhibit intrinsic metallic features and the metallicity is still maintained after adsorption of H 2 S/SO 2 .Compared with the band structure of α-FeB 6 , H 2 S/SO 2 adsorption makes α-FeB 6 produce some new energy levels in valence and conduction bands near Fermi energy, which indicates that there are some interactions between H 2 S/ SO 2 and α-FeB 6 .But for the other two substrates, β-FeB 6 and γ-FeB 6 are narrow band gap semiconductors with the band gap of 0.179 and 0.4 eV, respectively.After adsorbing H 2 S and SO 2 gas molecules, the band gaps of β-FeB 6 -H 2 S, β-FeB 6 -SO 2 , γ-FeB 6 -H 2 S, and γ-FeB 6 -SO 2 decrease to 0.03, 0, 0 and 0 eV, respectively.Compared with the band structure of β-FeB 6 , H 2 S adsorption makes β-FeB 6 produce some new energy levels in valence and conduction bands near Fermi energy due to the strong interaction between them, which leads to the decreased band gap.And SO 2 adsorption also makes β-FeB 6 produce some new energy levels near Fermi energy, and one new conduction band crosses to valence band through Fermi energy, which makes the band gap disappear.Compared with the band structure of γ-FeB 6 , H 2 S, and SO 2 adsorption induce downshifted valence bands of γ-FeB 6 and introduce some new energy levels crossing through Fermi energy, which eliminates the band gap.Thus, after adsorbing H 2 S and SO 2 gas molecules, the band gaps of β/γ-FeB 6 monolayer decrease and even disappear which can enhance their electric conductivities and detect the existence of these gases.The total density of states (TDOS) of H 2 S/SO 2 adsorption on α/β/γ-FeB 6 are shown in the upper panel of Fig. 6 (the enlarged version in Fig. S4-S9).It is clear that the discrete TDOS of isolated H 2 S/SO 2 have multiple overlaps with the TDOS of α/β/γ-FeB 6 at −5.12, −3.24, and −0.33 eV for H 2 S and at -8.31, -4.46, -1.52, -0.92, -0.29 eV for SO 2 , which results in the changes of TDOS of α/β/γ-FeB 6 after H 2 S/SO 2 adsorptions.Especially, some new electronic states near Fermi energy of β/γ-FeB 6 are observed, which causes the reduction or elimination of band gap of β/γ-FeB 6 -H 2 S/SO 2 systems (see Fig. 5).The partial density of states (PDOS) of the nearest atoms (see Fig. 3) in α/β/γ-FeB 6 -H 2 S/SO 2 systems are shown in the lower panel of Fig. 6.We mainly focus on the PDOS near Fermi energy since they can strongly affect the electronic property.For H 2 S, there are evident overlaps between S-3p orbitals of isolated H 2 S and Fe-3d orbitals of isolated α/β/γ-FeB 6 at −0.33 eV.After H 2 S adsorption on α/β-FeB 6 , the peak (−0.92 eV) of Fe-3d orbitals of α-FeB 6 shifts to −1.26 eV, and the peak (−0.62 eV) of Fe-3d orbitals of β-FeB 6 becomes lower and splits into two new peaks (−0.75 and −0.37 eV).The peak (−0.33 eV) of the S-3d orbital of α/β-FeB 6 disappears and obviously becomes wider, which indicates H 2 S molecule is chemisorbed on α/β-FeB 6 .After H 2 S adsorption on γ-FeB 6 , the Fe-3d and S-3d peaks that almost overlap at −0.33 eV cross Fermi energy and shift to 0.14 eV and the S-3d peak still exists, which indicates H 2 S is physiosorbed on γ-FeB 6 .Thus, the α/β-FeB 6 can bind H 2 S with the larger Eads while the γ-FeB 6 binds H 2 S with the moderate Eads.In addition, the changes of Fe-3d and S-3d peaks of α/β/γ-FeB 6 lead to the new bands in band structures (see Fig. 5b, e, h).
Similarly, after SO 2 adsorption on α-FeB 6 , the peaks (−1.52, −0.92, and −0.29 eV) of O-2p orbitals and the peaks (−0.92 and −0.29 eV) of S-3p orbitals disappear, which indicates SO 2 molecule is chemisorbed on α-FeB 6 .After SO 2 adsorption on β-FeB 6 , the peaks (−1.52, −0.92, and −0.29 eV) of O-2p orbitals become very lower and wider, which indicates SO 2 molecule is also chemisorbed on α-FeB 6 .Moreover, the O-2p and Fe-3d orbitals near Fermi energy can be assigned to the components of some new bands in band structures (see Fig. 5f).After SO 2 adsorption on γ-FeB 6 , we find that the peaks (−0.92, and −0.29 eV) of S-3p orbitals only decrease in height without any shift, which indicates SO 2 is physiosorbed on γ-FeB 6 .The peak (−0.31 eV) height of Fe-3d also decreases and shifts to −0.29 eV.One new peak of Fe-3d appears at 0.40 eV near Fermi energy, which contributes to the elimination of the band gap of the γ-FeB 6 -SO 2 system (see Fig. 5i).

Work function
The work function (WF) is the energy threshold that must be overcome to extract an electron from the Fermi level to the vacuum level [55].The WF of α/β/γ-FeB 6 with gas molecules is calculated using the following equation [56]: where E vac represents the electrostatic potential at infinity and E Fermi is the Fermi energy.The calculated WF curves are shown in Fig. 7 and the values of WF (ϕ) and the change of WF (∆ϕ) that is the difference between ϕ of α/β/γ-FeB 6 before and after gas molecule adsorption are listed in Table 3.

Recovery time and desorption energy
At last, we investigated the relation between recovery time (t) and desorption energy (Ed) in these systems at working (3) = E vac -E Fermi temperature.To leave the surface, H2S/SO2 gas molecule must overcome the Eads.The Ed is equal to the −Eads in value in this case.Thus, more negative Eads value leads to higher desorption energy which means that the desorption process is more difficult.According to conventional transition state theory [60] and Van't-Hoff-Arrhenius expression [61,62], t can theoretically be predicted by the following equation [60]: where K B is the Boltzmann constant 8.62 × 10 −5 eV•K −1 , and T is the working temperature (300 and 500 K).E ads is the gas adsorption energy calculated using smearing of 0.00095 and 0.0016 Ha which correspond to 300 and 500 K. ν is the attempt frequency, which is the vibration frequency of single bonds between the molecule and the surface.Here, we (4) = −1 e (−Eads∕KBT) Fig. 6 TDOS (upper panel) and PDOS (lower panel) of α/β/γ-FeB 6 before and after H 2 S and SO 2 adsorptions.A and I in the bracket in PDOS denote adsorbed system and isolated system, respectively assume that H 2 S and SO 2 have the same attempt frequency as NO 2 (10 12 s -1 ) [63] since the H 2 S, SO 2 , and NO 2 are triatomic gas molecules that have the same order of magnitude in vibration frequency [64].The calculated t of H 2 S/ SO 2 adsorption on α/β/γ-FeB 6 at T = 300 and 500 K are also listed in Table 3.It can be seen that the t of H 2 S/SO 2 adsorption on α/β-FeB 6 is very long at 300 K owing to their stronger chemisorption capacities of H 2 S/SO 2 .In contrast, ϕ (eV) ∆ϕ (eV) E ads (eV) @300K E ads (eV) @500K τ(s) @300K τ(s) @500K α-FeB 6 the t of H 2 S /SO 2 adsorption on γ-FeB 6 is very short at 300 K.For example, the t of H 2 S is 5.71×10 −8 s which is less than 2.98×10 −7 s for H 2 S adsorption on Janus-MoSSe [65] and the t of SO 2 is 1.94×10 −5 s which is shorter than 7.95×10 −4 s for SO 2 adsorption on PdSe 2 monolayer [45].Therefore, γ-FeB 6 may be a promising candidate for reusable H 2 S/SO 2 sensor.When the working temperature increases to 500 K, the t of H 2 S/SO 2 adsorption on α/β/γ-FeB 6 obviously decreases.Especially, the t of H 2 S adsorption on the α/β-FeB 6 decrease to 1.13×10 −1 s and 2.08×10 −1 s, respectively, which indicates that α/β-FeB 6 can be a good choice as a reversible H 2 S sensor due to recovery time within detectable range [66,67].

Conclusions
In

( 1 )
E ads = E tot − E sub − E gas Page 3 of 12 314 correction.While other calculations were not performed with vdW corrections.
structures of α/β/γ-FeB 6 The optimized structures of α/β/γ-FeB 6 monolayers are shown in Fig. 1.The lattice parameters of α-FeB 6 (a = b = 4.481 Å) and β-FeB 6 (a = b = 4.758 Å) are similar due to boron sheet composed of triangular lattice in them, while the boron sheet in γ-FeB 6 consists of honeycomb lattice, which leads to its larger lattice parameter (a = b = 5.380 Å).The B-B bond lengths in α/β/γ-FeB 6 vary over a small range.However, the variation in B-Fe bond lengths of α/β/γ-FeB 6 is large.For example, the B-Fe bond length (2.255 Å) of α-FeB 6 is obviously larger than that (1.863 Å) of γ-FeB 6 , which can be attributed to the different B atom configuration around the Fe atom.

Fig. 1 Fig. 2
Fig. 1 Top view and side view of the optimized structures of a α-FeB 6 , b β-FeB 6 , and c γ-FeB 6 monolayer with lattice constant and bond length.Blue and pink spheres are Fe and B atoms, respectively.The labeled bond length is in Å

Figure
Figure3illustrates the most stable adsorption configuration of H 2 S/SO 2 on α/β/γ-FeB 6 .It can be seen that the gas molecules are mainly adsorbed near Fe atoms except that SO 2 is absorbed on boron atoms in α-FeB 6 .For H 2 S, it is almost parallel to the surface of α/β/γ-FeB 6 and the S atom is almost directly over the Fe atom.The distances between the S atom and Fe atom (d S-Fe ) of α/β-FeB 6 are 2.244 Å which is similar to that (2.247 Å) of H 2 S on graphane decorated with Fe44 .But the E ads (−1.014 eV for α-FeB 6 and −1.163 eV for β-FeB 6 ) are larger than that (−0.93 eV) of H 2 S on graphane decorated with Fe44 , which indicates that there are stronger interaction between H 2 S and α/β-FeB 6 .The d S-Fe (2.319 Å) of γ-FeB 6 is longer than the d S-Fe of α/β-FeB 6 , which leads to smaller E ads (−0.508 eV).For SO 2 , the adsorption cases are different on α/β/γ-FeB 6 .The S/O atoms, the two O atoms, and the S atom of SO 2 are attached to two B atoms of α-FeB 6 , two Fe atoms of β-FeB 6, and a Fe atom of γ-FeB 6 , respectively.The bond lengths of 1.442 Å for O-B and 2.021 Å for S-B in α-FeB 6 are slightly longer than those (1.344Å for O-B and 1.880 Å for S-B) of SO 2 adsorption on borophene[49].The lengths of O-Fe bonds in β-FeB 6 are

Fig. 4
Fig. 4 Top and side views of the charge density difference between H 2 S/SO 2 and α/β/γ-FeB 6 monolayer.Green and blue represent charge depletion and gain, respectively

Table 2
Fig. 5 Band structures of α/β/γ-FeB 6 before and after H 2 S and SO 2 adsorptions conclusion, we have theoretically explored the potential of 2D α/β/γ-FeB 6 monolayer as H 2 S and SO 2 gas sensors by investigating adsorption energy, adsorption distance, surface energy, Mullikan charge, charge density difference, band structure, density of states, work function, and theoretical recovery time.Our results suggest that SO 2 and H 2 S are physiosorbed on γ-FeB 6 due to their smaller adsorption energies (−0.508-−0.578eV) while they are chemisorbed on α/β-FeB 6 due to their larger adsorption energies (−1.014-−2.240eV).The Mullikan charge analyses reveal that the significant charge transfer exists in α/β/γ-FeB 6 -H 2 S/SO 2 systems where α/β/γ-FeB 6 act as the electron acceptor for H 2 S while α/β/γ-FeB 6 act as electron donor for SO 2 , which is consist with the charge density difference analyses.The analyses of density of states further confirm that there are strong orbital overlaps between α/β/γ-FeB 6 and H 2 S/SO 2 , which changes obviously the band structures of β/γ-FeB 6 and reveals the origin of H 2 S/ SO 2 chemisorbed and physiosorbed on α/β/γ-FeB 6 .The results of recovery time indicate that γ-FeB 6 may be a promising candidate for reusable H 2 S/SO 2 sensor at room temperature while α/β-FeB 6 can be a good choice as a reversible H 2 S sensor at 500 K.