First-principle investigation of CO, CH4, and CO2 adsorption on Cr-doped graphene-like hexagonal borophene

It is important for life safety and scientific research to design new sensing materials for detecting CO, CH4, and CO2 from the environment. We theoretically designed a new Cr-doped graphene-like hexagonal borophene (CrB6) as potential sensor material for these gases. Carrying out first-principle density-functional calculations, we calculated the adsorption energy, band structure, adsorption distance, charge transfer, charge density difference, density of states, and partial density of states of CO, CH4, and CO2 gas molecules absorbed on CrB6 monolayer. The calculated results show that the adsorption behavior of CO is different from those of CH4 and CO2. CO adsorbed on CrB6 monolayer prefers chemisorption with the adsorption energy of − 2.59 eV while CH4 and CO2 adsorbed on CrB6 monolayer prefer physisorption with the adsorption energy of − 0.72 and − 0.69 eV. As a result, the different adsorption behaviors have significant influence on the band structures and density of states of CrB6 monolayer. We hope that our results can help experimentalists synthesize better sensor materials based on hexagonal borophene.


Introduction
Recently, the gas sensors have been attracting great interest in the identification and detection of toxic gases [1][2][3][4][5][6]. Among hazardous gases, the common air pollutants CO and CO 2 are mainly produced in industry and automobile exhaust, which poses a potential threat to the natural environment and human security. For example, CO is a colorless, tasteless, and difficult to distinguish toxic gas [7]. An individual exposed to the low concentration (~ 35 ppm) of CO would suffer from headache, dizziness, and nausea [8]. However, when the concentration of CO is higher than 150 ppm, CO inhaled by human body will combine with hemoglobin, destroying the ability of blood to transport oxygen, even leading to human death [9]. CO 2 and CH 4 are two representative greenhouse gases (GHG). The continuous rise of CO 2 concentration becomes the most important cause of global warming due to fossil fuel combustion and vegetation destruction. Recent researches demonstrated that CH 4 is 25 times greater than CO 2 at trapping heat in Earth's atmosphere [10]. Therefore, seeking for potential materials as highly effective gas sensors to detect CO, CO 2 , and CH 4 is highly demanded.
Since the discovery of graphene in 2004, two-dimensional (2D) materials have been the key research area in materials due to its high surface-to-volume ratio, good conductivity, distinctive surface morphology, and low Johnson noise [11][12][13][14]. The high sensitivity and excellent performance of the 2D materials to gas molecules make them promising for gas sensing application [15,16]. Therefore, lots of 2D materials have been extensively studied for gas adsorption and detection both in theoretical and experimental aspects, such as Fe-doped graphene, silicene, MoS 2 , C 2 N, and phosphorene [17][18][19][20][21]. Although the layered 2D materials process outstanding mobility and sensing performance, some intrinsic drawbacks still exist in 2D materials. For example, the main shortcoming of graphene is its zero-gap, which makes it difficult to adsorb more gases [22]. Besides, silicone shows poor stability and a relatively low mobility was found in MoS 2 [23,24]. All these shortcomings force us to actively look for new 2D materials with good performance as gas sensors.
Due to the distinctive electronic properties of boron, the structure and adsorption characteristics of 2D boron materials have been widely studied [25,26]. Recently, Mannix et al. experimentally proved single-layered borophene sheet (BS) can be successfully synthesized on single-crystal Ag (111) substrates under ultra-high vacuum conditions [26]. There are also many theoretical studies which predicted a variety of possible 2D configurations of BS. For example, buckled triangular BS [27,28], α/β-BS [29], and graphenelike hexagonal BS (HBS) [30,31]. Among these BS, HBS is the most promising candidate because it provides superconductivity and can be applied in fabricate Dirac fermion devices [32]. But the HBS was found to be unstable by Evans et al. [33], because the π-bonds cannot be formed in HBS due to boron atom with one electron less than carbon atom [29]. Metal doping is considered to be one of the most effective methods to improve the stability of HBS. Li, Be, Mg, Cr, and Mn have been attempted to be doped in HBS [34][35][36][37][38]. These metal atoms can provide electrons to the π-valence orbitals of HBS, maintaining the stability of HBS.
In this paper, we theoretically designed a 2D Cr-doped graphene-like hexagonal borophene (CrB 6 ) in which Cr atoms are doped partially on the center of boron ring to make hexagonal borophene stable. And then, using first-principle density-functional calculations, some properties of CO, CH 4 , and CO 2 gas molecules absorbed on CrB 6 monolayer, such as adsorption energy, band structure, adsorption distance, charge transfer, charge density difference, density of states, and partial density of states, have been studied to explore the possibility of CrB 6 monolayer as gas sensor material. Our calculated results show that the three gas molecules prefer to be adsorbed on Cr atom. What's different is that the adsorption of CO is relatively strong chemisorption with adsorption energy of 2.59 eV and the adsorptions of CH 4 and CO 2 are relatively weak physisorption with adsorption energy of 0.72 and 0.69 eV, respectively. Considering the reversibility property of gas sensor, the CrB 6 monolayer is more suitable for a promising candidate for CH 4 and CO 2 sensor. This paper is composed as follows. In "Computational details," the computational soft and approach are described. In "Results and discussions," some properties of CrB 6 monolayer with/without CO, CH 4 , and CO 2 gas molecules, such  as geometric structure, adsorption energy, band structure, adsorption distance, and charge transfer, are discussed. At last, the conclusion about CrB 6 monolayer as gas sensor is given in "Conclusions."

Computational details
We used the DMol [3] module of Material Studio software [39] to perform the density-functional theory calculations for the optimized structures and the electronic properties of CrB 6 monolayer. The Perdew-Burke-Ernzerhof (PBE) [40] generalized gradient approximation (GGA) which is embedded in DMol [3] was chosen. And the double-numerical properties plus polarization (DNP) was selected as basis set. To make the calculated results accurate, the global orbital cutoff radius in real-space was set as 5.2 Å. In the convergence tolerance, the energy, force, and displacement were set as 10 -5 Ha, 0.002 Ha/Å, and 0.005 Å, separately. For the calculation of the optimized structures, the Monkhorst-Pack k-mesh was set to 3 × 3 × 1 and for the calculation of energy band and density of states, the k-point was set to 6 × 6 × 1. To prevent the adjacent layers from interacting, a vacuum layer of 20 Å was added in the direction of vertical substrate plane. To accurately evaluate the interactions between gases and CrB 6 monolayer, the Grimme (DFT-D2) dispersion correction [41] was applied in the calculations of the adsorption of CO, CH 4 , and CO 2 on CrB 6 monolayer. The adsorption energy is defined as the change of the total energy before and after adsorption, the size of which can be used to determine the stability of the structure after adsorption. The adsorption energy (E ads ) of these gas molecules on CrB 6 monolayer is defined as follows: where E total is the total energy of the gas molecule adsorbed on CrB 6 monolayer, E monolayer is the energy of isolated CrB 6 monolayer, and E gas is the energy of a single gas molecule. According to our definition, a larger negative E ads represents the more stable adsorption of gas molecule on CrB 6 monolayer.
To calculate the diffusion barrier of Cr atom on the hexagonal borophene, the transition states were located by computing the minimum energy path (MEP) [42,43] using the nudged elastic band method which starts by inserting a series of image structures between the initial and final states of the reaction.

Structural and electronic properties of CrB 6 monolayer
The optimized unit cell of CrB 6 is shown in Fig. 1a. The calculated lattice parameters of CrB 6 unit cell are 35 Å, which is slightly shorter than the lattice parameter of FeB 6 [44]. The bond lengths of B-B and Cr-B in Cr-doped six-membered rings are 1.85 Å and 1.91 Å, respectively. The bond length of B-B in B 6 six-membered rings is 1.65 Å. Unlike the completely planar structure of FeB 6 monolayer, the Cr atom is not in the plane of borophene and the distance from the Cr atom to the plane is 0.49 Å. Besides, the band structure of the CrB 6 is also calculated and shown in Fig. 1b. It can be seen that the CrB 6 monolayer has a small band gap of 0.851 eV, which indicates that the CrB 6 exhibits semiconductor characteristic. As a promising gas sensor/capture material, excellent dynamical stability is essential. The structural stability of CrB 6 can be examined by phonon dispersion. As shown in Fig. 1c, there is no imaginary frequency, which means that the structure of CrB 6 monolayer has a good dynamical stability.
To estimate the stability of Cr atom on the hexagonal borophene, we calculated its binding energy (E b ). The E b is given by: where E CrB6 is the total energy of the CrB 6 monolayer, E B6 is the energy of the hexagonal borophene, and E Cr is the energy of a single Cr atom. The calculated E b is 10.17 eV which is much higher than the cohesive energy (4.10 eV) of bulk BCC Cr [45]. We also calculated the diffusion barrier (E db ) of Cr atom on the hexagonal borophene. The diffusion path and the E db are shown in Fig. S1. The calculated E db is 2.25 eV which is much larger than that (0.01 eV) on graphene [46]. These results indicate that Cr atom can be bound stably on the hexagonal borophene.

Adsorption of gas molecule on CrB 6 monolayer
To fully comprehend the feasibility of CrB 6 as a gas sensor material, we researched the adsorption behaviors of CO, CH 4 , and CO 2 molecules on the CrB 6 monolayer. Three possible adsorption sites are considered by us, and they are T Cr site (the top site on Cr atom), B site (above the B-B bond bridge), and H site (above the center of boron ring), respectively, as shown in Fig. 2.
We used a 2 × 2 × 1 supercell, consisting of 28 atoms, to calculate the E ads of gas molecules on CrB 6 monolayer. In order to find the most stable adsorption configuration, we  . 4 The side views of charge density difference plot of a CO, b CH 4 , and c CO 2 on the most stable adsorption site placed the gas molecules with different orientations on the three possible adsorption sites in CrB 6 monolayer. For each gas molecule adsorption on CrB 6 monolayer, the optimized structures of the two largest E ads are presented in Fig. 3.
And the E ads , charge transfer (Q), and the distance between the nearest atom of gas molecules and CrB 6 monolayer (d) are listed in Table 1. For CO, it is preferably adsorbed on the T Cr site. The CO is vertical to the CrB 6 monolayer and the distance between C and Cr is 1.87 Å which is shorter than the sum of radii of C (0.70 Å) and Cr (1.35 Å) [47]. Such short C-Cr bond length indicates that the interaction between C and Cr atoms is very strong, leading to the large E ads (− 2.59 eV) and Q (− 0.03 e). For CH 4 , it is also preferably adsorbed on the T Cr site, corresponding to the E ads of − 0.72 eV. The C atom is on the top of the Cr atom and the nearest distance from H atom to the Cr atom is 1.98 Å. And for CO 2 , the adsorption sites of the two largest E ads are all on the T Cr site. The difference is the orientation of CO 2 . One is vertical to the CrB 6 monolayer, denoted by T Cr-V ; the other is almost parallel to the CrB 6 monolayer, denoted by T Cr-P . For CO and CH 4 , the shorter d and larger Q indicate a larger E ads (see Table 1). However, contrary to CO and CH 4 , the E ads of CO 2 on T Cr-P is larger than that on T Cr-V , although the value of d (Q) of CO 2 on T Cr-P is longer (less) than that on T Cr-V . The reason may be attributed to the distance (2.67 Å) between C in T Cr-P and Cr being shorter than that (3.28 Å) between C in T Cr-V and Cr, which increases the interaction between CO 2 on T Cr-P and the CrB 6 monolayer. Thus, the T Cr-P site provides the good adsorption energy (− 0.69 eV) for CO 2 , which is similar to carbon nanocones [48] and open edge graphene [49]. In fact, according to the evaluation standard proposed by Rouquerol et al., the surface binding energy of gas molecules determines the type of gas adsorption [50]. Usually when the E ads < 1 eV, physisorption takes place between gas molecules and surface, but the chemisorption occurs when the E ads > 1 eV. Therefore, CO 2 and CH 4 belong to physisorption on CrB 6 monolayer. In contrast, CO gas molecule on substrate is chemisorption. Similar results are found in the previous studies where CO molecule is chemisorbed on the transition metal-functionalized germanene [51], aluminene nanosheet [52], and doped silicon nanowires [53]. Figure 4 shows the charge density difference between the gas molecule and CrB 6 monolayer in the most stable adsorption site, which is defined by where ρ total, ρ monolayer , and ρ gas are the charge density distributions of the gas molecule adsorbed on CrB 6 monolayer, pristine CrB 6 monolayer, and an isolated gas molecule, respectively. The charge accumulation is represented by yellow, whereas blue represents the charge depletion region. It (3) Δ = total − monolayer − gas can be seen that there are a lot of electron depletion/accumulations between CO and CrB 6 monolayer, which reflects the chemisorption between CO and CrB 6 monolayer, while there are less electron depletion/accumulations between CH 4 /CO 2 Fig. 5 The band structures of a CO, b CH 4 , and c CO 2 adsorbed on the most stable adsorption site and CrB 6 monolayer, which is consistent with the physisorption between CH 4 /CO 2 and CrB 6 monolayer.
To examine the thermal stability of these gas molecules adsorbed on CrB 6 , the ab initio molecular dynamic (AIMD) simulations were performed within a Nosé-Hoover thermostat [54] scheme of the NVT canonical ensemble and lasted for 2.0 ps with a time step of 2.0 fs. The results of AIMD simulations are shown in Figs. S2-S4. As can be seen from the snapshots, no broken bond and distortion are found in CrB 6 monolayer, which indicates that CrB 6 monolayer has practical value for gas sensor. For CO gas molecule, the simulation temperatures were set to 300 K and 700 K. It can be seen that the changes (1.69 ~ 2.19 Å) of C-Cr bond length at 700 K are larger than those (1.78 ~ 2.03 Å) at 300 K, which indicates that the desorption of the chemisorbed CO could occur at certain high temperature. For CH 4 and CO 2 gas molecules, the simulation temperatures were set to 300 K and 400 K. It can be seen that the distance of CH 4 gas molecule from Cr atom is changed from 2.27/2.28 to 2.81/2.91 at 300 K/400 K while the distance of CO 2 gas molecule from Cr atom is changed from 2.00/2.38 to 2.01/2.79 at 300 K/400 K. Thus, compared with CO, the desorption of the physisorbed CH 4 and CO 2 could occur at lower temperature.

Band structures
To investigate the adsorption effect of three gas molecules on CrB 6 , the band structures of CO, CH 4 , and CO 2 adsorbed on the most stable adsorption site are shown in Fig. 5. It can be seen that the band gap of CrB 6 monolayer will increase when the gas molecules are adsorbed on the surface of CrB 6 monolayer. Compared with the band gap (0.851 eV) of CrB 6 monolayer, the band gap (0.901 eV) of CrB 6 monolayer absorbed by CO increases obviously while the band gap (0.862/0.868 eV) of CrB 6 monolayer absorbed by CH 4 /CO 2 increases slightly. These results agree well with the type of gas adsorption on CrB 6 monolayer. Similar conclusions have been reported in a previous study [17].

Density of states and partial density of states
To further explore the effect of adsorbed gas molecules on the electronic structures of CrB 6 monolayer, we analyzed the density of states (DOS) and partial density of states (PDOS) of the gas molecules adsorbed on the most stable adsorption site, which are shown in Fig. 6. As can be seen from Fig. 6a-c, the DOS of CrB 6 monolayer in CH 4 on CrB 6 is the same as that in CO 2 on CrB 6 in the Fig. 6 The DOS and PDOS of a, d CO; b, e CH 4 ; and c, f CO 2 molecule adsorption on the most stable adsorption site range of − 3 to 3 eV, while the DOS of CrB 6 monolayer in CO on CrB 6 is obviously different from the former in the range − 3 to 0 eV, which indicates the effect of the physisorption on DOS of CrB 6 monolayer is less than the effect of the chemisorption. It is interesting that there are more overlaps between the DOS of the three gas molecules and the DOS of the CrB6 in the range of − 10 to − 4 eV in both chemisorption and physisorption.
As can be seen from Fig. 6d-f, we found that the main contribution of the DOS of CrB 6 monolayer with the adsorbed gas molecule comes from the Cr-3d orbitals through comparing with the corresponding DOS. In Fig. 6d, comparing with the PDOS of CrB 6 monolayer with and without CO, we observed that the peaks of Cr-3d orbitals near the Fermi level become obviously weak after CO is absorbed on CrB 6 monolayer, which indicates   Table 3 Recovery times(s) of CH 4 and CO 2 under the two adsorption configurations exposed to vacuum at 300 K and 500 K Gas CH 4 (T Cr ) CO 2 (T Cr-p) CH 4 (H) CO 2 (T Cr-v) T = 300 K 1.25 3.90 × 10 −1 7.31 × 10 −9 1.2 × 10 −2 T = 500 K 1.81 × 10 −5 9.01 × 10 −5 2.08 × 10 −10 1.12 × 10 −7 that the electrons transfer from the Cr-3d orbitals in the conduction band of CrB 6 monolayer to the CO molecule due to the formation of C-Cr bond, while in Fig. 6e and f, the peaks of Cr-3d orbitals near the Fermi level show little change after CH 4 /CO 2 is absorbed on CrB 6 monolayer because of the physisorption for them. However, the changes of Cr-3d orbitals in the valence band are almost similar after the three gas molecules were absorbed on CrB 6 monolayer, which indicates that the Cr-3d orbitals in the valence band are not sensitive to the type of gas adsorption. Besides, it can be found that the DOS overlaps between CO/CH 4 /CO 2 and CrB 6 monolayer are contributed by the C-2p, H-1 s, and O-2p orbitals, respectively.
By calculating the work function (WF) of the adsorption system, we can study the sensing performance of the gas sensor. WF is a sensor surface-related property that is sensitive to conduction from the substrate [55]. The adsorption of gas molecules causes the WF change of the substrate, so the work function is an important basis for determining the sensitivity and selectivity of gas sensors. ϕ is defined as the minimum energy required to move an electron from the Fermi level to infinity and is calculated as [56]: where E vac represents the electrostatic potential at infinity and E Fermi is the Fermi energy. The calculated WF image is shown in Fig. 7. The change in WF (∆ϕ), which is calculated by subtracting the WF of the pristine CrB 6 from the WF of the system after gas adsorption, is listed in Table 2. The calculated ∆ϕ after adsorption of CO, CH 4 , and CO 2 by CrB 6 are 0.25 eV, − 0.11 eV, and 0.03 eV, respectively. Negative values represent that the WF of the adsorption system is lower than the pristine CrB 6 . The WF changes of CH 4 and CO are larger than 0.10 eV [57], which proves that CrB 6 has excellent selectivity and sensitivity to CH 4 and CO.
The WF change of CH 4 and CO is larger than 0.1 eV and higher than the WF change of 0.06 eV for CO and 0.05 eV for CH 4 in PtX 2 (X = P, As) [58]. The above proves that CrB 6 has excellent selectivity and sensitivity to CH 4 and CO.
To test the recoverability of the sensor, we also investigated the recovery time of CrB 6 . The recovery time is closely related to the E ads and is given by the following formula [59]: where E ads is the gas adsorption energy, K B is the Boltzmann constant (8.62 × 10 −5 eV K −1 ), T is the temperature, and ν is the attempt frequency taken as 10 12 s −1 . In Table 3, we can see that the recovery time of CH 4 and CO 2 at the T Cr position at 500 K is 1.8 × 10 −5 s and 9.01 × 10 −5 s, respectively, and the recovery time increases at 300 K, while both are within the detectable range. It can be seen that CrB 6 has valuable gas recovery performance.

Conclusions
In summary, to search new sensor material for detecting CO, CH 4 , and CO 2 from the environment, we theoretically designed a 2D CrB 6 monolayer in which Cr atoms are doped partially on the center of boron ring to make hexagonal borophene stable. Performing first-principle density-functional calculations, the adsorption energy, band structure, adsorption distance, charge transfer, charge density difference, density of states, and partial density of states of CO, CH 4 , and CO 2 gas molecules absorbed on CrB 6 monolayer have been investigated to check the possibility of CrB 6 monolayer as gas sensor material. The adsorption energy and adsorption distance reveal that CO prefers to be chemically adsorbed on Cr atom while CH 4 and CO 2 prefer to be physically adsorbed on Cr atom. The analyses of density of states and partial density of states show that the conduction bands of CrB 6 monolayer near the Fermi level are affected obviously by the chemisorption but are affected less by the physisorption. Moreover, these gas molecules can lead to the increase in band gaps in different extents after they are absorbed on CrB 6 monolayer. Considering the reversibility property of gas sensor, the CrB 6 monolayer is more suitable for a promising candidate for CH 4 and CO 2 sensor and deserves further experimental exploring.