The Adsorption of 1-Chloro-1,2,2,2-Tetrafluoroethane Onto the Pristine, Al-, and Ga-Doped Boron Nitride Nanosheet

Density functional techniques (DFT) were used to research the existence of intermolecular interactions between the gas molecule 1-Chloro-1,2,2,2-tetrafluoroethane (HCFC-124) and the single-walled boron nitride nanosheets doped with pristine, aluminum and galium (BNNS). PBE0, M06-2X, ωB97XD, and B3LYP-D3, functional calculations were applied for both isolated and complex structures to perform the optimization process. Along with split-valence triple-zeta basis sets of d-type and Cartesian-Gaussian polarization functions with 6-311G(d, p) basis set were performed in all. Electronic structure, total state density (DOS), natural bond orbital (NBO), quantum atom theory in molecules (QTAIM), and non-covalent interaction (NCI) analyses were investigated to study the intermolecular interaction of nanosheets with gas molecules. The results show that when the dopant atom was introduced to the BNNS, interactions at the HOMO–LUMO energy gap (HLG) were significantly altered. Eventually, optical properties are highly influenced by the mechanism of interaction in which, as a result of interaction with the proposed pristine nanosheets, the absorption spectrum (HCFC-124) receives a salient signal. This comparative study predicts that Al-doped BNNS is the most desirable material for designing a nanosensor that designs a sensitive nanosensor among all the absorbents.


Introduction
An extraordinary position in computational chemistry has been found in theoretical studies on nanoscale structures, and researchers have used various computational methods to analyze intermolecular interactions to design tools that have better precision and performance (Kamel et al. 2020;Santos et al. 2015;Ghafur Rauf et al. 2019;Li and Asadi 2020;Mohammadi and Hamzehloo 2018). For the construction of sensors with high measurement precision, extreme temperature insensitivity, very low response time and low production costs, a variety of nanomaterials were considered Abdullah 2020a, b, c, 2021a, b;Mohammadi et al. 2020a, b;Nemati-Kande et al. 2018. In theoretical studies, various methods have been used to boost the sensitivity of the adsorption process in nanomaterials, such as metal doping (Nemati-Kande et al. 2018Wilke and Breuer 1999;Botas et al. 2010;Saha and Deng 2009), surface defects (Bolton 2003;Wang et al. 1995;Wu et al. 2010), transition metal decoration (Srinivasu and Ghosh 2012;Yildirim et al. 2005), etc. Impurities added to the nanomaterial wall modify the energy difference, changing its morphology significantly as well.
A comprehensive study on the effect of transition metal decoration on boron nitride nanosheet (BNNS) (Lin et al. 2013) is given by Lin et al. In addition, the application of non-metals such as oxygen will activate the BNNS surface (Lei et al. 2014). The author proposed that doped nanomaterials have a higher efficiency compared to pure nanomaterials (Hjiri et al. 2014). In theoretical studies (Esrafili and Asadollahi 2018) the surface of boron nitride nanosheets. By the chemical vapor deposition process (Lin and Connell 2012), BNNSs are easily synthesized. BNNS is commonly used due to its exceptional mechanical, thermal, electrical and chemical properties, as well as its outstanding reactivity and selectivity (Guerra et al. 2019;Li et al. 2019;Yang et al. 2019). BNNS was defined by the broad band gap (5-6 eV) as an electrical insulator (Lin and Connell 2012;Li and Chen 2016;Falin et al. 2017 (Esrafili 2018b), and N 2 O  in several theoretical studies. This nanosheet and BNNS decorated with metal were also used in the development of several electronic devices (Dorn et al. 2020;Ai et al. 2019;Azamat et al. 2016;Esrafili and Saeidi 2017;Esrafili et al. 2016;Li et al. 2015;Lin et al. 2015). It can also be used in the coating and metal protection industry as a valuable commodity since it is impervious to gases and liquids and is also an electrical insulator (Li et al. 2014;Fu et al. 2016;Luo et al. 2017). In drug delivery systems, the interaction and bond properties of the anticancer drug doxorubicin (DOX), armchair single-walled carbon nanotube (SWCNT), and hydroxyl and carboxyl-functionalized SWCNT (-SWCNT) have been studied (Karimzadeh et al. 2021). The effects of mechanical properties and thermal conditions on the spontaneous adsorption into and on the surface of carbon nanotubes (CNTs) of doxorubicin (DOX) molecules were observed (Karimzadeh et al. 2020).
In the current analysis, HCFC-124 gas molecule interactions will be simulated with pristine BNNS and BN nanosheets doped with Al and Ga by density-functional theorem (DFT) with PBE0, M06-2X, xB97XD, and B3LYP-D3 methods. In order to study the intermolecular interaction of nanosheets with gas molecules, the electronic structure, total state density (DOS), natural bond orbital (NBO), quantum atom theory in molecules (QTAIM), Frontier molecular orbitals (FMO) and non-covalent interaction (NCI) analyses were investigated. Several physical parameters, such as Fermi energy, HOMO/LUMO offset, Band gap, chemical potential (l), chemical hardness (g), and electrophilicity (x) have been measured. Mulliken, Mayer, and Wiberg's natural atomic charges and intermodal charges are also determined to enhance the nature of intermolecular interactions between two fragments.

Computational Details
All of the nanosheet structures were optimized using twodimensional periodic boundary condition Kohn-Sham density functional theory (Bickelhaupt and Baerends 2000;Pople et al. 1992;Kohn and Sham 1965;Hohenberg and Kohn 1964) (PBC-DFT) method in vacuum. Various functionals such as PBE0 (Perdew et al. 1996a, b;Adamo and Barone 1999), M06-2X (Zhao and Truhlar 2008), xB97XD (Chai and Head-Gordon 2008), and B3LYP-D3 scheme of Grimme (2006) and Grimme et al. (2010Grimme et al. ( , 2011 together with split-valence triple-zeta basis sets with d-type Cartesian-Gaussian polarization functions [6-311G(d)] (Binning and Curtiss 1990;Curtiss et al. 1995;Frisch et al. 1984;Hay 1977;Blaudeau et al. 1997;Raghavachari et al. 1980;McGrath and Radom 1991;Raghavachari and Trucks 1989;Russo et al. 1994) were employed through the spin-restricted approach. There is no symmetry constraints were imposed. According to benchmark studies , such a basis set covers all we need in this study. A 3 9 3 9 1 k point sampling in the Brillouin zone integration (Ibach and Lüth 1995) with kinetic energy cutoff of 450 eV was hired. In this approach, when the number of unit cells increase the total energy will become minimal. All the molecular geometries were built in Gaussview 6.0.16 (Dennington et al. 2016) software package then fully optimized by the Berny (Baker 1987) method by Gaussian 16 Rev. C.01 (Frisch et al. 2016) linux-based software. The optimization process was performed using the default Gaussian convergence criteria. To configure the stability of each structure frequency calculation were done to determine the nature of the stationary points. In addition, the wave function stability calculation was also done to consider stability of the electrons. Natural bond orbital (NBO) calculations were carried out using the NBO v 3.1 software, which is coupled within Gaussian package to consider the charge-transfer interactions between occupied and unoccupied orbitals. To extract the result data of NBO, NCI, and QTAIM analyses, Multiwfn (Lu and Chen 2012) software was used and GaussSum (O'boyle et al. 2008) package depicted the DOS diagrams.
The energy of adsorption (E ads ) between two fragments (nanosheet and HCFC-124) can be considered as follows: where E sheet/HCFC-124 shows the total energy of the gas/nanosheet cluster. E sheet and E HCFC-124 are the energies of the isolated nanosheet and isolated gas molecule, respectively. Where DE is computed from Gaussian log file. Basis set superposition error (BSSE) was obtained from the Boys and Bernardi's counterpoise procedure (Boys and Bernardi 1970;Alkorta et al. 2011) as follows: According to Eq. (1), negative values of E ads (i.e., exothermic adsorptions) indicate that the formed complex is stable; otherwise, positive values of E ads is belong to a local minimum in which the adsorption of HCFC-124 and nanosheet is deterred by an energy barrier.

Geometric Surveys
The PEB0 functional, hybrid form of Perdew-Burke-Ernzerhof (PBE) (Perdew et al. 1996b), together with 6-311G(d) basis set were selected at the first stage to start the geometry optimization process of the isolated and complex structures. Although PBE0 is fast, it cannot describe the long-range interactions, dispersion effect, and charge transfer excitations; therefore, all of the structures were re-optimized using robust methods like M06-2X, xB97XD, and B3LYP-D3. Chai and Head-Gordon (2008) invented the xB97XD functional to account for the effect of long-range interactions as well as the dispersion corrections. Among Minnesota 06 suit, which is developed by Ma et al. (2010), the global hybrid functional with double non-local exchange (2X) amounts (i.e., M06-2X) is a highperformance method to study the non-covalent interactions.
To study the dispersion effect, the latest version of B3LYP-D3 known as D3 (BD) (GD3BJ) developed by Grimme et al. (Grimme 2006;Grimme et al. 2010Grimme et al. , 2011 would be a good option. In order to compare the effect of each of the mentioned corrections, in Table 1, the amounts of adsorption energy for HCFC-124/nanosheet complexes were obtained from PBE0, B3LYP-D3, M06-2X & xB97XD in 6-311G(d) method. The PBC-DFT framework at PBE0/6-311G(d) level was applied on a pristine B 18 N 18 unit cell with 10.004 Å in each dimension. Figure 1 shows the selected boron nitride nanosheet (BNNS). Then the unit cell expanded 3 times along with each axis and the optimization process repeated with the same level of theory. It should be noted that, to reduce the boundary effects, the terminal atoms were terminated by H atoms. For the case for Al-and Ga-doped nanosheets, after the optimized expanded BNNS obtained, one of the boron atoms substituted by Al or Ga elements and calculations were performed at PBE0/6-311G(d) level of theory. The re-optimization process was performed using 3 other functionals and same basis set. The values of bond length for BNNS, BNAlNS, and BNGaNS are depicted in Fig. 2. As is obvious from Fig. 2a, the B-N bond length is 1.45 Å . Also, Fig. 2b, c show the value of bond length for Al-N and Ga-N 1.71 Å and 1.74 Å , respectively. Due to the inner stress, the B-N bond length in the vicinity of Al ad Ga dopant atoms vary from 1.42 to 1.49 Å .
The adsorptions of HCFC-124 gas molecule onto the surface of pristine and Al-, Ga-doped BNNS were also carried out. To achieve this goal, the gas molecule should be placed on top of the nanosheet in different positions through different orientations. The purpose of such calculations is to find energy local minima. Figure 3 shows the Table1 The adsorption energies (E ads ) and Bond length (Å ) for HCFC-124/nanosheet complexes  Fig. 1 The boron nitride unit cell (32 atoms, 192 electrons, neutral, and singlet) prepared to perform two-dimensional periodic boundary condition density functional theory calculations Iran J Sci Technol Trans Sci (2021) (Fig. 1) including: T 1 , in the middle of hexagonal ring; T 2 , between B and N atoms; T 3 , N atom; and T 4 , B atom. The gas molecules were put on top of each T x sites through different distances and optimization process started at PM7/6-311G(d) level. It should be stressed that, overall, there are 240 initial orientations were prepared (i.e., 6 9 4 9 10 = 240. It means 6 different gas molecule heads were put on each of the 4 sites of nanosheet from 0.5 to 5.0 Å vertical distances with 0.5 Å intervals). Right after that, 12 minima were predicted. We select these 12 The relaxed structure of 1-Chloro-1, 2,2,2-tetrafluoroethane gas molecule obtained from B3LYP-D3/6-311G(d) level of theory complex structures to optimize using PBE0/6-311G(d) level of theory. Regarding the values of adsorption energies, finally, the most stable complexes were chosen and re-optimization were done using other functionals including M06-2X, xB97XD, and B3LYP-D3. The relaxed structures of all complexes which have been obtained from B3LYP-D3/6-311G(d) are depicted in Fig. 4. When the values of E ads are ''below the range of chemical interest'' (Foresman and Frisch 1996), such results provide identical results.
The adsorption energy obtained from xB97XD and B3LYP-D3 are closed to each other. The xB97XD functional shows the most negative E ads values according to Table 1. It seems these two functional are good options for further investigations in this study. The most negative value of E ads corresponds to the adsorption of gas onto the Al-doped BNNS, -1.586 eV which indicates that the reactivity of HCFC-124 gas is significant. Otherwise, the reactivity of gas and pristine BNNS shows the weakest interaction, among those doped sheets. We preferred to run the population analysis calculations with B3LYP-D3 to reduce the computation times. Therefore, all the interactions analyses were applied to the results of the B3LYP-D3/6-311G(d) level of theory.

Electronic Structure
The ''Conceptual DFT'' has been developed to consider the reactivity concept. Various properties can be obtained from HOMO-LUMO energy gap (HLG) (Bredas 2014) in such a way when an external potential apply to a system the energy, in the Hohenberg-Kohn theorems (Hohenberg and Kohn 1964) context, changes as follows: In the above Taylor expansion N is a global quantity and m(r) is a local function. Each term has a specific meaning in the chemical language as follows: Equation (4) shows the negative electronegativity (v) which is equal to chemical potential (l). Also the values of HOMO and LUMO are related to the ionization affinity and electron affinity, were computed based on Fukui function, response function, dual descriptor, etc. (Geerlings et al. 2003;Liu 2009). Equation (6) is related to the electrophilicity index (x) and Eq. (7) gives the softness(s) of the compound. The values of these properties are listed in Table 2. The energy gap (E g ) of BNNS has calculated about 5.78 eV at B3LYP-D3/6-311G(d) level of theory and the adsorption of HCFC-124 on it reduced the energy gap to 5.72 which shows although adsorption energy is about -0.9 eV the sensitivity is not significant. On the other hand, Al-and Ga-doped nanosheets meaningfully reduced the E g values. Table 2 Shows the LUMO values were largely stabilized then the E g has been reduced. For the case of BNAlNS this reduction in E g is higher than BNGaNS; therefore, the sensor response (S) is stronger according to the following equations: where A is a constant and r is electrical conductivity, k is Boltzmann's constant, and T is Kelvin temperature. The resistivity will be diminished when E g is being reduced, since the resistivity is proportional to the reciprocal of the conducting electron population. Hence, the resistivity for BNAlNS/gas adsorption is low and the electric current generated in the circuit will face the lowest resistance, hence the electrical conductivity will be appreciably increased. Density of state (DOS) map is useful in intuitively revealing density of distribution of molecular orbitals in different energy regions, and gap is directly visible from this map (Fig. 5).

NBO Analysis
The Natural bond orbital (NBO) method, developed by Foster and Weinhold (1980), Weinhold and Landis (2001) and Weinhold (2012), is one of the most respectful population analyses and uses to calculate the distribution of electron density in bonds between atoms. The term NBO refers to a bonding orbital with the maximum electron density. A density matrix, calculated from DFT, as well as atomic charge, is used to define natural bonding orbitals.
To complete the span of valance space in addition to bonding NBO (r), we need an antibonding NBO (r*) as follows: where h A and h B are natural hybrid valance orbitals, C A and C B are the corresponding polarization coefficients. In the present study, NBO calculations were performed to figure out various types of bond order including Mulliken (1955) (Eq. 12) and Mayer (1983Mayer ( , 2012 and Bridgeman et al. (2001) (Eq. 13) bond order as well as Wiberg bond index (WBI) in Löwdin orthogonalized basis (Wiberg 1968;Sizova et al. 2008) (Eq. 14). Thus, In the above Equations, P and S are density and overlap matrix, respectively. Mulliken and Mayer's bond orders are sensitive to the basis set, especially for the basis set including diffuse functions. On the other hand, Wiberg bond order with respect to the two other is less basis set dependence. Table 3 reports the values of obtained bond orders from different methods. According to the WBI which is more accurate than Mayer and Mulliken we can up to this conclusion that BNAlNS adsorbent is the most material in this study for adsorbing HCFC-124. The bond order value shows that the interaction of gas with BNNS can be classified as physisorption; otherwise, the interactions between Al-and Ga-doped BNNS with the gas molecules are more significant.
Natural electronic configuration (NEC) has computed using a Douglas-Kroll-Hess 2nd order scalar relativistic configuration analysis. At the higher B3LYP/6-311G(d) stage, HCFC-124 revealed that the transfer of electrons from the Clusters and in Table 4, tabulated. In fact, C 2 HClF 4 /BNNS, C 2 HClF 4 /BNAlNS, and C 2 HClF 4 / BNGaNS donate -0.01, 0.05 and 0.06e, respectively, to the outer cage. In comparison, from the Cl-2s (1.88) to the Cl-3p (5.15) atomic orbitals, there is a large charge transfer in electronic configuration. In addition, there are efficient Hybridizations that are compatible with the NBO study between the F-2S (1.84) and F-2p (5.50) orbitals. The fluorine atoms seem to prevent the intracluster from transfer of charges by grabbing the electrons from clusters. The electrostatic interactions, therefore, between the inner cluster and the outer cage, these endohedral derivatives  should be significant and partially contribute to their stability.

QTAIM Analysis
QTAIM analysis is used study bond types and intermolecular interactions. A critical point of the electron density, including minimum, maximum, or saddle point, can belong to: (1) Atomic critical point (ACP); (2) bond critical point (BCP); (3) ring critical point (RCP); and (4) cage critical point (CCP). The Electron density q(r) and the Laplacian electron density r 2 q(r) are playing important role in the QTAIM analysis since they determine the  (Matta 2006). The values of Lagrangian kinetic energy G(r) and potential energy density V(r) divulges the nature of the intermolecular interaction; therefore, the ratio of G(r)/ |V|(r) can be hired as an appropriate index in link classification. When G(r)/|V|(r) \ 0.5, the nature of the Table 5 QTAIM topological parameters for electron density q(r), Laplacian of electron density r 2 q(r), kinetic electron density G(r), potential electron density V(r), eigenvalues of Hessian matrix (k), and bond ellipticity index (e) at the BCPs of the HCFC-124 clusters with BNNS, BNAlNS, and BNGaNS

Systems
Bond q (a.u) r 2 r (a.u) G(r) (a.u) V(r) (a.u) G(r)/V(r) (a.u) k 1 k 2 k 3 e (a, t) interaction is covalent, and if G(r)/|V|(r) [ 1, the interaction is non-covalent. Large values of elliptical bond (e) represent an unstable structure and defined as follows (Bohórquez et al. 2011): where k 1 , k 2 are the Hessian's eigenvalues (or principal curvatures). According to virial theorem (Grabowski Fig. 7 The RDG vs. sign(k 2 )q(r) diagrams for a pristine b Al-doped, and c Ga-doped BNNSs. The diagrams were obtained from B3LYP-D3/6-311G(d) level of theory. Left panel shows isolated nanosheets and right panel shows HCFC-124/nanosheet complexes 2012), a relationship exists between G(r), V(r), and r 2 q(r) as follows: 1 4 r 2 qðrÞ ¼ 2GðrÞ þ VðrÞ ð 16Þ From Table 5, Laplacian electron density r 2 q(r) for HCFC-124 clusters with BNNS, BNAlNS, and BNGaNS are positive and the G(r)/|V|(r) * 1, due to the decrease in inter nuclear region of the charge. These results shows intermolecular interactions are classified as non-covalent. In the case of BNAlNS very strong interactions were observed. And finally the small values of e show that all of the structures are stable (Fig. 6).
The results of QTAIM, in the previous section, showed that the interactions between HCFC-124 and nanosheets are non-covalent; hence, it is useful to check them by a non-covalent analysis. Reduced density gradient (RDG) and signk 2 (r)q(r) are a pair of functions used in non-covalent interaction (NCI) (Johnson et al. 2010) analysis which can be implemented to visualize the region and the type of weak interactions. RDG is defined as follows (Johnson et al. 2010;Contreras-García et al. 2011): The two functions RDG and signk 2 (r)q(r) can be plotted to define specific areas. In this case, non-covalent interactions will be identified. The points that indicate strong interactions are located in the signk 2 (r)q(r) \ 0 region. Relatively weak van der Waals interactions are found in the signk 2 (r)q(r) & 0 region. And if points are in signk 2 (r)q(r) [ 0 region, it means that the interactions are of the type of repulsive (Johnson et al. 2010;Contreras-García et al. 2011). As it turns out, bond strength is closely related to the density matrix q(r) as well as signk 2 . Low RDG and low electron density regions should be consulted to determine whether non-covalent interactions occur between the two components involved in the adsorption process. Figure 7 shows the RDG vs. sign (k 2 )q(r) pictures for (a) pristine (b) Al-doped, and (c) Ga-doped BNNSs.
Considering an isosurface as a reference (e.g., RDG = 0.5), it can be seen that the spots are appeared in the signk 2 (r)q(r) & 0 zone after the adsorption of HCFC-124 molecule onto BNNS and BNGaNS; therefore, the interactions can classified as van der Waals. However, the interactions of HCFC-124 with BNAlNS were strong in nature. NCI analysis also confirms the results of the adsorption energy calculations, QTAIM analysis, and NBO analysis, namely that the interactions of HCFC-124 with the Al-and Ga-doped BNNS were strong.

Conclusion
The intermolecular interactions between the HCFC-124 gas molecule and BNNS, BNAlNS, and BNGaNS were studied by the DFT framework in vacuum condition. All molecular structures optimized at PBE0, M06-2X, xB97XD, and B3LYP-D3 functionals together with a 6-311G(d) basis set. Relaxed structures obtained from B3LYP-D3/6-311G(d) were chosen for population analysis calculations. Results of adsorption energy show that among the nanosheets, the interaction of BNAlNS and gas (about -1.59 eV) is higher than the other adsorbents. DOS analysis can also approve that the most reduction in energy gap (about 0.83 eV) is related to the gas/BNAlNS cluster. Different bond order analysis data repeats former results. To shed light on the nature of intermolecular interactions NBO QTAIM, and NCI analyses were implemented and the results of all the analyses were in agreement. From NBO analysis, the charge transfer was observed and NCI and QTAIM results show strong intermolecular interactions-specially for BNAlNS/gas cluster. To sum up, we can conclude injecting Al and Ga elements inside the BNNS can dramatically active its surface in favor of adsorbing HCFC-124 gas. Accordingly, these nanomaterials would be favorable for designing a sensitive nanosensor.