Adsorption performance of M-doped (M = Ti and Cr) gallium nitride nanosheets towards SO2 and NO2: a DFT-D calculation

The structure, adsorption characteristics, electronic properties, and charge transfer of SO2 and NO2 molecules on metal-doped gallium nitride nanosheets (M-GaNNSs; M = Ti and Cr) were scrutinized at the Grimme-corrected PBE/double numerical plus polarization (DNP) level of theory. Two types, MGa-GaNNSs and MN-GaNNSs, of doped nanostructures were found. The MGa sites are more stable than the MN sites. The results showed that adsorption of SO2 and NO2 molecules on TiGa,N-GaNNSs is energetically more favorable than the corresponding CrGa,N-GaNNSs. The stability order of complexes is energetically predicted to be as NO2–TiGa-GaNNS > NO2–TiN-GaNNS > SO2–TiGa-GaNNS > NO2–CrN-GaNNS > SO2–TiN-GaNNS > NO2–CrGa-GaNNS > SO2–CrN-GaNNS > SO2–CrGa-GaNNS. The electron population analysis shows that charge is transferred from MGa,N-GaNNSs to the adsorbed gases. The TiGa-GaNNS is more sensitive than the other doped nanostructures to NO2 and SO2 gases. It is estimated that the sensitivity of TiGa-GaNNS to NO2 gas is more than to SO2 gas.


Introduction
At present, air pollution is a signicant factor limiting economic progression. 1 The emission of toxicant gases into the air is a serious matter due to the dangers of these air pollutants. 2 The source of air pollutants might be extensive in the Earth's environment. 3 Sulfur dioxide (SO 2 ) and nitrogen dioxide (NO 2 ) are noteworthy gaseous pollutants, discharged from natural and industrial procedures which have major environmental effects. [4][5][6] Thus, specic harmful gas detecting will be a major advantage to daily life for all people. [7][8][9] For the rst time in 2005, boron nitride (BN) nanosheets were forecast. 10 The honeycomb samples of BN sheets have analogies similar to graphene with equal numbers of alternating boron and nitrogen atoms that exhibit remarkable properties. 11 The electronic properties of BN sheets can be modied by B or N vacancies, Stone-Wales defects and doping heteroatoms. [12][13][14][15][16] In recent years, different studies have been done via surface quantum engineering of BN nanosheets. 17,18 For BN modication, the doped BN nanosheets were explored for developing a sensor for detecting harmful gases. [19][20][21] Recently, III-V nanostructures have attracted great attention for their potential applications in novel electronic, [22][23][24] optical, [25][26][27] and electrochemical devices. [28][29][30] One of the III-V nanostructures were gallium nitride nanosheets (GaNNSs) which have been theoretically predicted [31][32][33] and then experimentally discovered. 34,35 It was found that the GaNNSs have many remarkable properties such as a high surface area to volume ratio, high thermal stability and a tunable band gap indicating that GaNNSs have advantages in electronic usage such as effective gas sensor applications and so on. 36 There are some experimental studies focusing on the GaN based NO 2 and SO 2 sensors. [37][38][39][40] Bishop et al. 41 suggested a double Schottky junction NO 2 gas sensor based on BGaN/GaN. Triet et al. synthesized Al 0.27 Ga 0.73 N/GaN-based Schottky diode sensors for SO 2 gas detection. 42 For example, the adsorption capabilities of gallium nitride nanosheets towards noxious gases (such as HCN, NH 3 , H 2 S, H 2 , CO 2 and H 2 O) have been described. 43 Therefore, most of the research studies have focused on nanomaterials for increasing the adsorption of adsorbates on GaNNSs. For this purpose, the electronic properties of GaNNS can be modied by doping which generates more reactive adsorption sites. 44,45 Transition metals such as Ti, Cr, Fe, Ni and Zn have been theoretically explored as dopants in GaNNSs to increase the adsorption properties towards CO harmful gases. 46 The adsorption of H 2 S, NH 3 and SO 2 molecules on pure and doped GaNNSs has been considered using rst-principles calculations. The results show that the metal doped GaNNSs are more suitable for gas molecules detection compared with the pure ones. 47 The doping effect of metal atoms on the electronic properties of GaNNSs was studied for tuning the optoelectronic properties, gas adsorption, hydrogen storage and catalytic reaction. [48][49][50][51] The electronic and optical properties of GaNNSs as a function of thickness and strain with predictive calculations were scrutinized. 52 Based on the results reported about the magnetic properties of GaNNSs, the metallic and ferromagnetic properties of GaNNSs can be attained by semihydrogenation. 53 The chemical oxidation of GaNNSs was explored by using rst-principles calculations 54 that show the oxygen adsorption mechanism can be useful for application in novel semiconducting materials. So, it would be attractive to continue investigating the promising applications of GaNNSs in gas sensors.
To the best of our knowledge, this is the rst report on the adsorption of SO 2 and NO 2 molecules on the surface of Ti and Cr doped GaNNSs. The inuence of transition metals doping on the adsorption behavior of SO 2 and NO 2 on the metal doped GaNNSs for exploring the possibility of using the doped GaNNSs as candidates for removing and sensing of these molecules was considered herein at the Grimme-corrected PBE/double numerical plus polarization (DNP) level of theory.

Computational details
In this theoretical research, the double numerical plus polarization (DNP) basis sets were selected implemented in the DMol 3 package. 55,56 The periodic spin-unrestricted DFT calculation is employed using generalized-gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functional. 57 The density functional semi-core pseudopotentials (DSPP) were generated by tting all-electron relativistic DFT results. 58 To consider the van der Waals (vdW) interactions, an empirical dispersion-corrected density functional theory (DFT-D) was used in the calculations. The Brillouin zone integration was sampled using a 10 Â 10 Â 1 Monkhorst-Pack grid. A convergence tolerance of energy of 1.0 Â 10 À5 Ha, maximum force of 0.001 Ha perÅ and maximum displacement of 0.005Å were employed in all the geometry optimizations. To get reliable results, the real space global orbital cutoff radius was set as high as 5.2Å and the smearing of electronic occupations to be 0.005 Ha.
To calculate the adsorption energies (AE) of the SO 2 and NO 2 molecules on the pure and metal doped GaNNSs, the following equation is given: where E T , E S and E m are the energies of gas-M-GaNNSs complexes, M-GaNNSs and SO 2 or NO 2 molecules, respectively.

Results and discussion
3.1. Adsorption of SO 2 and NO 2 gas molecules over pure GaNNSs The optimized geometries of adsorbed molecules and gallium nitride nanosheets are displayed in Fig. 1. As demonstrated in Fig. 1, the calculated bond lengths of X]O (X ¼ N and S) in free SO 2 and NO 2 molecules are 1.482Å and 1.201Å, respectively, and that of the Ga-N bond length in the optimized geometry of GaNNS is 1.861Å.
To nd the most stable complexes obtained from adsorption of SO 2 and NO 2 gas molecules on the GaNNS, several congurations of SO 2 and NO 2 molecules on top of the GaNNSs are explored. The most stable adsorption complexes are illustrated in Fig. 1. Aer optimization, the C 2 axis of the SO 2 molecule is parallel to the GaNNS and that of the NO 2 molecule is perpendicular to the nanosheet. As presented in Table 1, the nearest distances between the SO 2 and NO 2 molecules with SO 2 -GaNNS and NO 2 -GaNNS are 1.782Å and 2.298Å, respectively.
The values of the adsorption energies (AEs) are À27.22 and À11.86 kcal mol À1 for SO 2 -GaNNS and NO 2 -GaNNS complexes, in good agreement with the smaller SO 2 -GaNNS distance obtained. Hence, the SO 2 and NO 2 molecules are chemically adsorbed on the GaNNSs. The adsorption energy for the SO 2 molecule on the GaNNS is comparable with those found for graphene (À6.45 kcal mol À1 ) 59 and boron nitride nanosheet (À7.14 kcal mol À1 ). 21 For adsorption of NO 2 on graphene, the calculated adsorption energy is À11.06 kcal mol À1 . 41 The Hirshfeld charges on the Ga and N atoms in pristine GaNNS are 0.39e and À0.39e, respectively, which change to 0.40e and À0.38e in SO 2 -GaNNS, and 0.39e and À0.39e in NO 2 -GaNNS. The charges on S and O change from 0.38e and À0.19e  Table 1 The calculated adsorption energy (AE), equilibrium distance between molecules and nanosheet (D), charge of Ga and N atoms (Q), charge transfer (CT) and band gaps for the most stable adsorption complexes

Band gap (eV)
Pure GaNNS --0.39 Ga  in free SO 2 to 0.33 e and À0.25e in SO 2 -GaNNS, respectively. Besides, the charges on N and O are 0.17e and À0.09e which change to 0.11e and À0.10e in NO 2 -GaNNS. This reveals that oxygen atoms in SO 2 -GaNNS and NO 2 -GaNNS complexes have the main contribution to charge transfer between the gas and nanosheet. The charge analyses show that the 0.17e and 0.09e charges are shied from the GaNNSs to the SO 2 and NO 2 molecules, respectively, in good agreement with greater AE found for the SO 2 -GaNNS complex. The negative AEs demonstrate the orbital interactions between the gases and GaNNS. The Mulliken electron populations of the total and each of the s, p and d orbitals before and aer interactions are given in Table 2. Inspection of the s, p and d orbital contributions in the free gases and in the SO 2 -GaNNS and NO 2 -GaNNS complexes indicate that the p orbital of the S atom in SO 2 -GaNNS and O atom in NO 2 -GaNNS have the most contribution in the interaction of molecules with the d orbital of Ga and p orbital of N atoms in the GaNNS. Comparison of the total electron population of orbitals shows that the population increases by 0.352e for SO 2 and 0.169e for NO 2 aer interaction of the gas with the surface. This indicates that the adsorbates will get electrons from the GaNNSs. The change in the electronic population of the orbitals in SO 2 -GaNNS is greater than for NO 2 -GaNNS, in good agreement with the greater AE and Hirshfeld charge transfer values found for SO 2 -GaNNS compared with NO 2 -GaNNS.

Ti and Cr doped GaNNSs
In order to investigate the effect of metal doping on the geometrical and electronic properties of the GaNNSs, one of the central atoms in the nanosheet was substituted by Ti and Cr metal atoms. Hereaer, M Ga -GaNNS and M N -GaNNS denote that Ga and N atoms in GaNNS have been substituted by M metal atoms, respectively.
The optimized structures of M N(Ga) -GaNNSs are illustrated in Fig. 2. The average bond distances between the metal atoms and the neighboring atoms are given in Table 3. The results show that the M-Ga bonds in M N -GaNNS nanostructures are longer than the M-N bonds in M Ga -GaNNSs. For example, the Ti-Ga and Cr-Ga bonds are longer than the Ti-N and Cr-N bonds by about 0.92 and 0.62Å, respectively. Accordingly, it is predicted that binding of the metal to the nanosheet is stronger for M Ga -GaNNS than M N -GaNNS. Fig. 2 presents the three bond angles A 1 , A 2 and A 3 around the M atoms of the NS and their average values are listed in Table 3. The averages of the three bond angles are 120.0 , 119.9 , 83.1 and 87.1 in Ti Ga -GaNNS, Cr Ga -GaNNS, Ti N -GaNNS and Cr N -GaNNS, respectively.
The binding energies (BEs) of Ti Ga -GaNNS, Ti N -GaNNS, Cr Ga -GaNNS and Cr N -GaNNS are À330.5, À236.1, À246.9 and À61.6 kcal mol À1 , respectively (Table 3). It is found that the BEs increase in the order M Ga -GaNNSs > M N -GaNNSs so that the value for the Ti Ga -GaNNS structure is greater than other ones. Therefore, the Ga sites for M doping are energetically more appropriate  The modied surface of Ti-doped GaNNSs facilitates the doped region to interact with approaching SO 2 and NO 2 molecules because of the higher chemical reactivity of the doped M atom. The results show that the SO 2 /Ti distance of SO 2 -Ti Ga -GaNNS complex is larger than SO 2 -Ti N -GaNNS ones. Also, the NO 2 /Ti distance for the NO 2 -Ti N -GaNNS complex is larger than for NO 2 -Ti Ga -GaNNS, indicating that the interaction in these complexes is stronger than in other ones.
The range of adsorption energies for SO 2 and NO 2 adsorbed on Ti-doped GaNNSs was between À58.36 to À61.06 and À70.68 to À76.83 kcal mol À1 , respectively. The negative value of the AE indicates that adsorption of SO 2 and NO 2 on Ti doped GaNNSs is an exothermic process. It is found that SO 2 and NO 2 molecules are adsorbed on Ti N -GaNNSs in the sequence NO 2 -Ti N -GaNNS > SO 2 -Ti N -GaNNS and on the Ti Ga -GaNNSs in the order NO 2 -Ti Ga -GaNNS > SO 2 -Ti Ga -GaNNS. Besides, it is found that the SO 2 and NO 2 adsorption energy values on Ti Ga -GaNNSs are greater than on Ti N -GaNNSs. The obtained results indicate that the adsorption capability of Ti Ga -GaNNSs is greater than that of Ti N -GaNNSs. Our results show that SO 2 and NO 2 molecules are chemically adsorbed on all Ti Ga,N -GaNNSs.
The Hirshfeld population analysis presents that the charges are transferred from the Ti Ga,N -GaNNSs complexes to the SO 2 and NO 2 molecules. In other words, SO 2 and NO 2 act as electron acceptors. There is a correlation between charge transfer values and adsorption energy in the process of adsorption of SO 2 and NO 2 on the GaNNSs. Comparison of charge transfer values between M-doped GaNNSs and SO 2 and NO 2 molecules demonstrate that the value for adsorption of NO 2 is greater than that of the corresponding SO 2 one, with the exception of that obtained for Cr Ga -GaNNS. This indicates that other parameters than charge transfer are responsible for the stability of the complexes. The electron populations of orbitals given in Table 2 show that population of d-orbitals as well as total population of the M metals decrease upon the interaction of gases with Ti Ga,N -GaNNSs. Besides, total electron population of orbitals in gases increases aer adsorption of gases on the surface. This nding reveals that gases will take the electrons from Ti Ga,N -GaNNSs. Aer adsorption of gases, total electron populations of orbitals of NO 2 (0.522e for NO 2 -Ti Ga -GaNNS and 0.500e for NO 2 -Ti N - Fig. 3 The most stable adsorption configurations of SO 2 or NO 2 on Ti-doped GaNNSs.   Cr N -GaNNS complex is larger than that for the SO 2 -Cr Ga -GaNNS one. Also, the NO 2 /Cr distance for the NO 2 -Cr N -GaNNS complex is larger than that for NO 2 -Cr Ga -GaNNS, indicating that interaction in these complexes is stronger than for other ones. The adsorption energies for SO 2 adsorbed on Cr Ga -GaNNS and Cr N -GaNNS are À40.46 and À53.28 kcal mol À1 and those for NO 2 are À54.79 and À60.81 kcal mol À1 , respectively. The negative value of the AE indicates that adsorption of SO 2 and NO 2 on Cr doped GaNNSs is an exothermic process. It is found that the ability of Cr N -GaNNS towards adsorption of SO 2 and NO 2 molecules is in the sequence NO 2 -Cr N -GaNNS > SO 2 -Cr N -GaNNS and that of Cr Ga -GaNNS is in the order NO 2 -Cr Ga -GaNNS > SO 2 -Cr Ga -GaNNS. In addition, it is found that SO 2 and NO 2 adsorption energies on Cr N -GaNNS are greater than on Cr Ga -GaNNS. The obtained results indicate that the adsorption capability of Cr N -GaNNS is greater than Cr Ga -GaNNS. Our results show that SO 2 and NO 2 molecules are chemically adsorbed on all M-doped GaNNSs.
The Hirshfeld population analysis shows that the charges are transferred from the Cr Ga,N -GaNNS complexes to the SO 2 and NO 2 molecules. As can be seen in Table 4, the CT values are 0.22e, 0.31e, 0.27e and 0.26e in NO 2 -Cr Ga -GaNNS, NO 2 -Cr N -GaNNS, SO 2 -Cr Ga -GaNNS and SO 2 -Cr N -GaNNS, respectively. This nding reveals that the charge transferred from the nanosheet to the gas in NO 2 -Cr N -GaNNS is greater than in other complexes, in good agreement with the greater AE obtained for these complexes. It should be noted that other parameters than charge transfer can affect the adsorption of gases.
Analysis of the electron population of orbitals involved in the interaction between gases and nanosheets given in Table 2 reveals that the total electron population of Cr decreases by À0.040e, À0.097e, À0.071e and À0.172e in NO 2 -Cr Ga -GaNNS, NO 2 -Cr N -GaNNS, SO 2 -Cr Ga -GaNNS, SO 2 -Cr N -GaNNS, respectively, in good agreement with the greater AE found for NO 2 (SO 2 )-Cr N -GaNNSs compared with NO 2 (SO 2 )-Cr Ga -GaNNSs. In addition, the results show that the population of d-orbitals of Cr decreases and those of the NO 2 and SO 2 gases increase upon interaction with Cr Ga,N -GaNNSs. This nding demonstrates that gases will get electrons from Cr Ga,N -GaNNSs, in good agreement with the computed Hirshfeld charge transfer from the surface to adsorbed gases.

HOMO and LUMO based electronic properties
There is an obvious difference between the electronic properties of doped and un-doped GaNNSs. As can be seen in Table 5, compared to pristine GaNNS, the energy of the highest occupied molecule orbital (HOMO) increases and that of the lowest unoccupied molecular orbital (LUMO) decreases in doped GaNNS so that the amount of increase in HOMO is greater than decrease in LUMO. Aer adsorption of NO 2 , the energies of the HOMO and LUMO decrease, but the LUMO energy shows a further decrease. In the case of SO 2 , adsorption of gas on the Ti-doped GaNNS decreases both the HOMO and LUMO, but its adsorption on the Cr-doped GaNNS increases them. These changes in HOMO and LUMO energy levels lead to a change in the HOMO-LUMO gap and, in turn, in the electronic properties of GaNNS.
The results indicate that the band gap energies in both M Ga,N doped GaNNSs are smaller than the pure GaNNS, making it more conductive. The results given in Table 5 demonstrate that the band gap value of pristine GaNNS is 2.52 eV that changes to 2.11 eV in SO 2 -GaNNS and 0.29 eV in NO 2 -GaNNS. Because of the greater decrease in the LUMO level in NO 2 -GaNNS with respect to that of SO 2 -GaNNS, the change in the band gap for SO 2 -GaNNS is lesser than for NO 2 -GaNNS. Therefore, it is predicted that GaNNS is more sensitive to NO 2 gas than SO 2 gas. So, the large changes in band gap value for GaNNS (2.52 to 0.29 eV) with NO 2 gas molecule adsorption can lead to a signicant change in electrical conductivity.
The electronic properties of doped GaNNSs are affected by the adsorption of SO 2 and NO 2 molecules. Upon adsorption of SO 2 and NO 2 molecules on the Ti Ga,N -GaNNS complexes the energy gap decreases in comparison with the pristine GaNNS. The energy gap values are in the sequences SO 2 -Ti N -GaNNS (1.11 eV) > NO 2 -Ti N -GaNNS (0.95 eV) and NO 2 -Ti Ga -GaNNS (2.28 eV) > SO 2 -Ti Ga -GaNNS (1.39 eV). Reduction of the band gap for SO 2 -Ti N -GaNNS is more than for NO 2 -Ti N -GaNNS and that for NO 2 -Ti Ga -GaNNS is more than for SO 2 -Ti Ga -GaNNS. Therefore, it can be concluded that the sensitivity of Ti N -GaNNS to SO 2 gas Fig. 6 The densities of states (DOSs) of GaNNS and SO 2 (NO 2 ) adsorbed on pristine GaNNSs.
This journal is © The Royal Society of Chemistry 2020 RSC Adv., 2020, 10, 27805-27814 | 27811 is greater than to NO 2 gas. Besides, for Ti Ga -GaNNS, it is predicted that the sensitivity to NO 2 gas is more than to SO 2 gas. It is a well-known issue that reduction of the energy gap enhances the electrical conductivity. Thus, the electrical conductivities are predicted to be in the order SO 2 -Ti N -GaNNS > NO 2 -Ti N -GaNNS and NO 2 -Ti Ga -GaNNS > SO 2 -Ti Ga -GaNNS.
Also, aer adsorption of SO 2 and NO 2 molecules on the Cr Ga,N -GaNNS complexes the band gap decreases in comparison with the pristine GaNNS. The band gap values are in sequence NO 2 -Cr N -GaNNS (0.91 eV) > SO 2 -Cr N -GaNNS (0.28 eV) and NO 2 -Cr Ga -GaNNS (0.65 eV) > SO 2 -Cr Ga -GaNNS (0.53 eV). The reduction in band gap for SO 2 -Cr Ga -GaNNS is more than for NO 2 -Cr Ga -GaNNS and that for NO 2 -Cr N -GaNNS is more than for SO 2 -Cr N -GaNNS. In consequence, the conductivities of SO 2 -Cr Ga -GaNNS and NO 2 -Cr N -GaNNS are greater than NO 2 -Cr Ga -GaNNS and SO 2 -Cr N -GaNNS, respectively. Also, from the changes in band gap energy values, it is forecast that the sensitivity of Cr N -GaNNS to NO 2 gas is more than to SO 2 gas. Fig. 7 The densities of states (DOSs) of SO 2 or NO 2 adsorbed on doped GaNNSs.