Deciphering the electrochemical sensing capability of novel Ga12As12 nanocluster towards chemical warfare phosgene gas: insights from DFT

The applications of 3D inorganic nanomaterials in environmental and agriculture monitoring have been exploited continuously; however, the utilization of semiconductor nanoclusters, especially for detecting warfare agents, has not been fully investigated yet. To fill this gap, the molecular modelling of novel inorganic semiconductor nanocluster Ga12As12 as a sensor for phosgene gas (highly toxic for living things and the environment) is accomplished employing benchmark DFT and TD-DFT investigations. Computational tools have been applied to explore different adsorption sites and the potential sensing capability of the Ga12As12 nanoclusters. The calculated adsorption energy (−21.34 ± 2.7 kcal mol−1) for ten selected complexes, namely, Pgn–Cl@4m-ring (MS1), Pgn–Cl@6m-ring (MS2), Pgn–Cl@XY66 (MS3), Pgn–O@4m-ring (MS4), Pgn–O@XY66 (MS5), Pgn–O@XY64 (MS6), Pgn–O@Y (MS7), Pgn–planar@Y (MS8), Pgn–planar@X (MS9), and Pgn–planar@4m-ring (MS10), manifest the remarkable and excessive adsorption response of the studied nanoclusters. The explored molecular electronic properties, such as interaction distance (3.05 ± 0.5 Å), energy gap (∼2.17 eV), softness (∼0.46 eV), hardness (1.10 ± 0.01 eV), electrophilicity index (10.27 ± 0.45 eV), electrical conductivity (∼1.98 × 109), and recovery time (∼3 × 10−12 s−1) values, ascertain the elevated reactivity and an imperishable sensitivity of the Ga12As12 nanocluster, particularly for its complex MS8. QTAIM analysis exhibits the presence of a strong electrostatic bond (positive ∇2ρ(r) values), electron delocalization (ELF < 0.5), and a strong chemical bond (because of high all-electron density values). In addition, NBO analysis explores the lone pair electron delocalization of phosgene to the nanocluster stabilized by intermolecular charge transfer (ICT) and different kinds of non-covalent interactions. Also, the green region existence expressed by NCI analysis (between the nanocluster and adsorbate) stipulate the energetic and dominant interactions. Furthermore, the UV-Vis, thermodynamic analysis, and density of state (DOS) demonstrate the maximum absorbance (562.11 nm) and least excitation energy (2.21 eV) by the complex MS8, the spontaneity of the interaction process, and the significant changes in HOMO and LUMO energies, respectively. Thus, the Ga12As12 nanocluster has proven to be a promising influential sensing material to monitor phosgene gas in the real world, and this study will emphasize the informative knowledge for experimental researchers to use Ga12As12 as a sensor for the warfare agent (phosgene).


Introduction
Warfare agents are a serious threat towards populations, mainly in urban areas.They are more toxic, reactive, and mostly produced in industries.Phosgene gas, having the molecular formula COCl 2 , is one of the most poisonous warfare agents and was used in World War I as a chemical weapon. 1 It can be used to produce polyurethanes, isocyanate, plastics, dyes, pesticides, and pharmaceutical products.It is also used in the industry as a protective gas to produce dimethyl diphenyl urea.The annual production of phosgene is about 2 million tons, which is used to produce ne chemicals and polymers.It is very dangerous to store, transport, and utilize phosgene gas due to its high volatility and toxicity. 2,3Phosgene gas attained a reputation for the rst time when its exposure caused about 80% of deaths due to all warfare agents during World War I.It can cause irritation in the mucosal membrane and lung damage when its concentration is below 3 ppm, but at high concentration above 150 ppm, it can cause latent non-cardiogenic pulmonary edema, and it is also life-threatening. 4,5n the recent 20 years, aer the discovery of carbon-based nanoparticles and nanoclusters, several efforts have been made to discover other nanoparticles that include metallic nanoparticles, ceramic-type nanoparticles, and semiconductor nanoparticles. 6These nanoparticles have gained more attention from researchers to detect, absorb, and destroy more toxic chemicals and warfare agents because of their unique properties. 7The porous surfaces, the large surface-to-volume ratio, and the optical, electrical, mechanical, and magnetic properties of these nanoparticles make them unique.The particles also have a large HOMO-LUMO gap and special chemical and physical properties. 8Therefore, they have a wide range of applications in the chemical industry, medicine, electronics, and aviation.The most important application of these nanoparticles and nanoclusters is because of their sensing property to detect and absorb poisonous and toxic gases and warfare agents. 9][12][13] Literature review has shown the adsorption of toxic gases, especially warfare agents, by many fullerene-like inorganic nanoclusters due to their large HOMO-LUMO gap. 14,15The adsorption, sensing, and detection of phosgene gas by different nanomaterials have been investigated.For instance, Ti, Ni, and Cu-decorated borospherene nanocluster, 16 Al 12 N 12 nanocluster as a potential sensor, 1 different angle oriented boron nitride (BN) nanocones with 60°, 120°, 180°, and 240°disclination angles, 17 Sc-doped BN nanoclusters, 18 pristine and Cudecorated B 12 N 12 nanocluster, 19 and Ca 12 O 12 , Mg 12 O 12 , and Al 12 N 12 nanomaterials 20 have been investigated to be good sensing nanomaterials for phosgene gas.
Several inorganic nanoclusters such as B 12 P 12 , 21 Ga 12 As 12 , 22,23 and Al 12 P 12 (ref.24) have been investigated to explore their potential applications in non-linear optics, 25,26 the photoelectrochemical solar energy conversion, 27,28 and in sensing devices for the detection of wide range of chemicals. 29,30These fullerene-like nanoclusters have been found to show intermolecular interactions with diazomethane 31 and for the adsorption of alkali and alkaline earth metals. 32They also exhibited interaction with halo-methane 33 and used it for the adsorption of toxic gasses. 19They have been employed for 4-aminopyridine drug delivery and the adsorption of the sorbic acid drug using density functional theory. 34,35ccording to the best of our literature investigation and knowledge, no specic investigations has been fully done regarding the sensing capability of the Ga 12 As 12 nanocluster for toxic chemical warfare agents because the detection of dangerous chemical warfare agents by a fast and accurate method is the need of current situation, which urged us to investigate the potential sensing of the Ga 12 As 12 nanocluster toward phosgene gas.For this purpose, the sensing and adsorption of phosgene gas with different orientations on different adsorption sites of Ga 12 As 12 nanocluster have been studied comprehensively by applying benchmark DFT and TD-DFT computations.
Various analyses such as HOMO-LUMO, natural bond orbitals (NBO), quantum theory of atoms in a molecule (QTAIM), non-covalent interactions (NCI), molecular electrostatic potential (MEP), density of state (DOS), and thermodynamic analysis have been conducted to investigate the intermolecular interactions and charge distributions between the Ga 12 As 12 nanocluster and phosgene gas and to elucidate the sensing capability of the Ga 12 As 12 nanocluster.With the evidence of the current investigations, it is optimistically proposed that the Ga 12 As 12 nanocluster will be utilized as an excellent and potential sensor for phosgene gas detection.

Computational studies
In the current research, the geometry optimization, frequency analysis, interaction energy, HOMO-LUMO energy gap, and Fermi level energy calculations of the Ga 12 As 12 nanocluster and its ten selected complexes (MS1-MS10) were performed using DFT and TD-DFT at the B3LYP-D3/6-31G(d,p) level of theory using GaussView and Gaussian 09 suite of programs. 36,37This B3LYP-D3/6-31G(d,p) level of theory was selected by comparing the bond length of the optimized structure of the nanocluster by different functionals with the already reported data. 32Utilizing the same functional, the NBO 38 and MEP analyses were performed to analyze the charge distributions of the nanocluster complexes and the net charge on phosgene gas.The DOS analysis of the nanocluster and complexes was performed using the Multiwfn 3.8 program. 39To nd out the electronic transition within the nanocluster and complexes, HOMO-LUMO plots have been obtained using the Avogadro-1.2.0 program. 40The topological analysis quantum theory of atoms in molecules (QTAIM) and non-covalent interactions (NCI) analysis was used to attain more insights into the nature of the inter-atomic interactions visual molecular dynamic (VMD) 1.9.4 program. 41he computations of QTAIM were done via Multiwfn 3.8 program. 39A mathematical method named thermodynamic analysis (TDA) was applied to study spontaneous and nonspontaneous behavior of the system based on the interaction of work and heat with chemical reactions and variations in the physical state through the law of thermodynamics. 42,43

Selection of the method
The Ga 12 As 12 nanocluster was optimized by applying three reported and widely used functionals of DFT, namely, CAM-B3LYP, 44 B3LYP-D3, 45 and uB97XD, 46 assigned with the 6-31G(d,p) basis set.The functional CAM-B3LYP demonstrates long-range interactions but does not provide dispersion correction and charge transfer excitations to a ne extent.To obtain long-range interactions and form dispersion correction, the uB97XD functional was developed by Head-Gordon et al. 46 The bond lengths of all the different sides of the nanocluster have been calculated and compared with the already reported data, as shown in Table 1.
The calculated bond lengths of the nanocluster optimized using DFT with the functional B3LYP-D3 known as D3 and GD3 with the 6-31G(d,p) basis set were found to be consistent with previously published studies. 31Thus, this functional developed by Grimme et al. was selected as the most suitable method to investigate the sensing capability of the studied system.In order to compare the bond lengths of the nanocluster structure optimized by three different functionals with the reported data, the names of all the sites of the nanocluster were proposed and are represented in Fig. 1.

Geometry optimization
The geometry optimization of the Ga 12 As 12 nanocluster, phosgene gas, and their possible complexes were carried out using DFT at the latest functional B3LYP-D3/6-31G(d,p) level of theory.The Ga 12 As 12 nanocluster contains eight symmetric 6membered rings and six symmetric 4-membered rings and has equal adsorption sites to sense any toxic and dangerous chemicals on their outer surface.The adsorption and sensing sites are classied as follows: on top of the X-atom, on top of the Y-atom, on top of the r-6 position, on top of the r-4 position, on top of the XY66 bond, and on top of the XY64 bond (Fig. 2a).Aer the optimization of the isolated nanocluster and phosgene gas, the gas is placed on the surface of the nanocluster on six different sites, as mentioned above, with three different orientations, namely, planar, oxygen toward the nanocluster, and chlorine toward the nanocluster.The gas is placed at a vertical distance between 4.7 and 5.0 Å on the outer surface of the nanocluster.
The optimized geometry of the phosgene gas and bond lengths of the nanocluster were calculated from the optimized structures of the isolated Ga 12 As 12 nanocluster obtained by the B3LYP-D3 and shown in Fig. 2b and c, respectively.By evaluating all possible doping sites of Ga 12 As 12 , a comprehensive investigation of the phosgene atoms interaction with Ga 12 As 12 was carried out.Ten designed complexes with phosgene (Pgn) gas named as Pgn-Cl@4m-ring (MS1), Pgn-Cl@6m-ring (MS2), Pgn-Cl@XY66 (MS3), Pgn-O@4m-ring (MS4), Pgn-O@XY66 (MS5), Pgn-O@XY64 (MS6), Pgn-O@Y (MS7), Pgn-planar@Y (MS8), Pgn-planar@X (MS9), and Pgn-planar@4m-ring (MS10) were optimized to the true minima, as evidenced by all real  Fig. 1 The proposed names of all the sites of the nanocluster to compare the bond lengths with the reported data.
Fig. 2 The adsorption sites of the nanocluster (a), the optimized structure of the gas (b) and the nanocluster (c).
frequencies.The nal B3LYP-D3 optimized structures of nanocluster complexes, the interaction distances with the phosgene gas, and their bond lengths variations have been calculated and shown in Fig. 3.The interaction distance along with the interacting atoms between the nanocluster and the phosgene gas is calculated and expressed in Table S1 (ESI †).The complex having less interaction distance represents a relatively stronger interaction between the gas and the nanocluster and expresses an excellent sensing response and vice versa.It has been observed that complexes MS5 and MS7 indicate the minimum interaction distances to express comparatively stronger interactions and reactivity while complexes MS2 and MS10 indicate maximum interaction distances between the phosgene gas and the surface of the Ga 12 As 12 nanocluster.The bond distances of the nanocluster aer the interaction of the gas are mentioned in Fig. 3 that can be compared with Fig. 2c to observe a variation as a result of interaction.

Adsorption studies
The interaction energy of the nanocluster complexes with phosgene gas has been calculated to improve its reliability and nd out all possible interactions.The interaction energy of the gas with nanocluster was calculated by eqn (1)-(3). 47,48ads = E complex − E nanocage − E gas (1) where E ads is the adsorption energy of the nanocluster for the gas, E INT is the counterpoise corrected interaction energy, E complex is the total energy of the gas/nanocluster cluster, and E nanocage and E gas are the energy values of isolated nanocluster and isolated gas, respectively.E BSSE denes the basis set superposition error of the respective complex obtained by the counterpoise approach that Bernardi and Boys established.
According to the above equation, the negative values of E ads represent the stability of the formed complex and the positive values of E ads represent the barrier in gas adsorption to the nanocluster.The interaction energy has been calculated by placing gas on the mentioned positions of the nanocluster.A minor difference in the interaction energy has been observed for the six possible positions for adsorption.Using gas with different orientations, such as planar, oxygen toward the nanocluster and chlorine toward the nanocluster, many identical results for E ads are obtained. 49One result of similar values is chosen to show interaction energies for corresponding adsorption sites with three different orientations of phosgene gas.Ten complexes have been selected out of eighteen due to having identical results of adsorption energy values; these results are shown in Table 2.
The selection of the site for adsorption has a minor effect on other sites of corresponding energy values as in the present work; the MS1 complex shows the highest adsorption response and better sensing capability toward phosgene gas while complex MS6 represents the highest counterpoise corrected interaction energy (E INT ) among all the complexes of the nanocluster.The adsorption position showing high interaction energy values indicates better sensing capability of the nanocluster's complex.Among all the adsorption sites with three different orientations, the maximum difference in their adsorption energies for all the complexes is about 5.392 kcal mol −1 .

Frontier molecular orbitals analysis
The highest occupied molecular orbitals (HOMO) and lowest unoccupied molecular orbitals (LUMO) have importance for a molecule and are named frontier molecular orbitals (FMOs).FMO analysis is very important as it determines the material's electronic behavior and optical characteristics. 50,51It also provides information about the material's electrical conductivity, electron distribution, stability, and sensing response. 52he reactivity and interaction of the gas with the nanocluster and many other properties are obtained from the HOMO-LUMO energy gap (E g ).The information about the transfer of charges and reactivity response of the system can be explored by the E g values.The least energy gap values express a high electronic distribution from the donor to acceptor orbitals, which enhance the electrical conductivity of the corresponding complex.It has been also evidenced from the literature survey that the smaller E g represents higher electrical conductivity, higher electron distribution, less stability, higher sensitivity, and vice versa. 53or the current investigation, the graph expressing the HOMO and LUMO relation of the complexes along with energy gap is shown in Fig. 5.It has been observed that the complex MS8 having less energy gap indicates high electronic distribution, less stability, high electrical conductivity, and high sensitivity, while complexes MS5 and MS7 have higher energy gap and exhibit less electronic distribution, high stability, low electrical conductivity, and low sensitivity as compared to all other complexes.The FMO orbitals of the nanocluster and complexes have been obtained by the Avogadro soware, and these are shown in Fig. 4 with the corresponding energy values and E g values for each complex.Similar to the E g values, the Fermi level energy and work function values also provide information about the stability and reactivity of the system.The work function is the amount of required energy for the loss of an electron from the Fermi level, where the Fermi level energy (E f ) is the amount of energy occupied by an electron at absolute zero temperature and can be calculated from the FMO orbitals, as given in eqn (4). 54rmi level energy The E f and work function (F) values for the studied complexes are also affected due to the interaction of gas and are found to be different from the isolated nanocluster values.The E f is calculated as the average of HOMO and LUMO energy values, and the work function (F) is taken as the negative of the Fermi level energy value because the electrostatic potential energy is equal to zero. 55The relation between work function and Fermi level energy is given by eqn ( 5) where V el (+,N) is electrostatic potential energy and it is zero, i.e., V el (+,N) = 0, F = −E f Literature review has shown that the variation in the work function (F) values due to the interaction of gas produces a sound by inuencing the gate voltage to detect gas. 56Also, the changes in the work function values demonstrate the transfer of charges between phosgene gas and the studied nanocluster.The  3.

Global indices of reactivity
The HOMO and LUMO energies provide information about various reactive, electrical, and optical properties of a molecule, such as electron affinity (A), ionization potential (I), and electronegativity (c), which is equal to the negative of chemical potential (m) expressed by Koopmans' theorem. 57,58The chemical hardness (h) is associated with the difference in electron affinity, and ionization potential and inverse of chemical hardness provide electrophilicity index (u). 59The soness (S) and DN max are also obtained by the equations provided in the ESI.† DN max is the maximum amount of electronic charge accepted by the system. 60These properties are calculated and listed in Table 4.The soness and hardness of the compound are obtained from the energy gap (E g ).The large energy gap represents the hardness of the compound, while the small energy gap shows the so compound, and these energy gaps also provide information about the reactivity and sensitivity of the compound. 61The capability of the species to attract electrons toward itself is called electronegativity (A) while the ionization potential (I) is the required amount of energy for the loss of electrons from the surface of the compound.
The literature survey shows that the system having higher values of ionization potential and chemical hardness indicates less reactivity and less sensitivity.In contrast, the system indicates high sensitivity and reactivity and less stability because of low ionization potential values and chemical hardness.Similar results have been observed in view of the chemical soness as the system indicates high sensitivity and less stability by having higher values of chemical soness and vice versa.Also, the electrophilicity index (u) values for the nanocluster and the complexes demonstrate the capability of the fragment to attain electrons.It also provides information about the stabilization energy to gain many electrons by the chemical species. 62,63In the current study, complex MS8 indicates comparatively higher sensitivity and reactivity because of the low chemical hardness (1.09 eV), high chemical soness (0.46 eV), and high electrophilicity index (10.71eV) among all the other complexes of the studied system to attain the high capability to attain electrons and high electronic distribution.In comparison, complexes MS5 and MS7 have high chemical hardness (1.12 eV), low chemical soness (0.45 eV), and low electrophilicity index (9.81eV) and therefore indicate less sensitivity among all other complexes.This information is also correlated with FMO analysis results and expresses the better sensing response of the nanocluster.Because the energy gap (E g ) of the HOMO and LUMO orbitals of the nanocluster has been calculated to be 2.23 eV, the interaction of phosgene gas on the surface of the nanocluster reduces the energy gap to 2.22, 2.21, 2.20, and 2.17 eV on different adsorption sites.The reduction in the energy gap values expresses the enhanced interactions and reactivity of the Ga 12 As 12 nanocluster toward phosgene gas.

NBO analysis
This analysis indicates natural bond orbitals (NBO) using stabilization energy named as 2 nd order perturbation energy. 64his energy is useful for studying intermolecular and intramolecular charge transfer. 65The information about the distribution of electrons between atoms within the molecular bonds was developed by Weinhold et al. 66 The information about the type of orbitals, interactions nature, and occupancy level present in between the occupied and virtual Lewis s orbitals are provided by NBO analysis. 42,67The stabilization energy is mathematically represented by eqn (6).
The diagonal elements are represented by E i and E j .The Fock matrix and donor occupancy are denoted by F(i,j) and q, respectively.The important transitions providing stabilization energy to the investigated systems are presented in Table 5 while the remaining transitions are mentioned in Table S2 (ESI †).RY (Rydberg) and Cr (center core pair) interaction values are not mentioned in the NBO data of the studied system because these values represent loosely bonded and weak interactions.The above-mentioned transitions (lone pair to surface) ensure the effective delocalization of the electrons of chlorine and oxygen atom of phosgene to the entire studied system.These results also explore that the donor-acceptor interactions are stabilized by intermolecular charge transfer (ICT) and different kinds of non-covalent interactions (NCI).These interactions and transfer of charges in between the molecules are because of the electron delocalization of the oxygen and the chlorine lone pair of the phosgene to the sigma and pi antibonding orbitals of the studied nanocluster.For these interactions, the complexes MS2 and MS10 have the highest stabilization energies, as mentioned in Table 5.The charge transfer transitions from LP to the ring provide the clue of binding, interaction, and sensing capability.Because of these bond evidences, it can be explored that the NCI and ICT network is present in the studied system, which represents a synchronism of NBO that results with NCI analysis and QTAIM analysis.

QTAIM analysis
The analysis based on the quantum theory of atoms in a molecule, abbreviated as QTAIM, is useful for the topological study of the system.The QTAIM theory has been derived from Bader's theory. 68ts purpose was to investigate the molecule more deeply because the geometrical and electronic investigation of the system does not provide enough information to study the intermolecular interactions of the system.The information about the critical point properties of the system is provided by QTAIM analysis.The formation of complexes aer interactions have been investigated by QTAIM analysis and the investigation data obtained are given in Table 6.The bond critical point, all electrons density r(r), electron density Laplacian, energy density, electronic charge density, and Hamiltonian and Lagrangian kinetic energies are the topological parameters denoted by BCP, r(r), V 2 r(r), E(r), V(r), H(r), and G(r), respectively, and obtained by QTAIM analysis. 69,70V 2 r(r) and r(r) is used to determine the critical bond points that represent the intermolecular bonds by the sharing of electrons between the atoms in a molecule. 71t has been shown in Table 6 that V 2 r(r) for all the complexes is positive.The positive Laplacian electron density indicates the strong electrostatic bond between the two bonded atoms. 72The all-electron density r(r) is used to determine the strength of the chemical bond between the gas and the cage.Its positive values show the closed shell interactions, and the higher value of all electron density values indicates the greater strength of the chemical bond and vice versa.
The comparatively strong chemical bond has been observed in complex MS7 and the weak chemical bond in complex MS8 due to the comparatively higher and lower values of electron density, respectively, while all the other complexes have intermediate values of electron density, as shown in Table 6.The division of the chemical bond of the complexes into strong covalent, partial covalent, and non-covalent is achieved by the values of both V 2 r(r) and H(r).For the strong covalent, V 2 r(r) < 0, H(r) < 0. For the partial covalent, V 2 r(r) > 0, H(r) < 0, and for non-covalent, V 2 r(r) > 0, H(r) > 0.
It has been shown in Table 6 that the complexes MS5, MS6, and MS7 indicate partially covalent interactions while all the Table 6 The topological parameters of the studied system after the interaction of phosgene gas.All the values are in atomic unit (a.u.) other complexes indicate weak covalent or non-covalent interactions.Furthermore, the energy densities of the bonds explain the nature and strength of interactions in the complex. 73The ratio between Hamiltonian kinetic energy values and absolute values of electronic charge density is represented as jV(r)j/G(r).
The ratio jV(r)j/G(r) less than 1 indicates the presence of ionic Fig. 6 The schematic structures of the studied complexes by QTAIM analysis to represent bond critical points between the nanocluster and the adsorbate.
bond or weak interactions (van der Waals interactions), while its value greater than 1 and less than 2 show mixed type of interactions.If the value of the ratio is greater than 2, then it indicates covalent bond. 74n the current study, complexes MS1 to MS4 and complexes MS8 to MS10 have less than 1 values of the ratio jV(r)j/G(r), and these complexes indicate van der Waals interactions, while the complexes MS5, MS6, and MS7 have mixed and covalent nature of interactions as the value of the ratio is >1 for these complexes (Fig. 6).
Another parameter, ellipticity, denes the stability of the interactions as its value > 1 represents the instability of the structure while its value < 1 shows the strength of the structure and interactions.In the current work, the ellipticity values of the complexes of the studied system ranges from 0.0111 to 3.5351 a.u.The maximum number of critical points are represented by complex MS8, indicating more interaction between the surface and the adsorbate.Another tool electron localization function (ELF) is useful for covalent bond analysis.The values of ELF range from 0.5 to 1.00, indicating the localization of bonding and non-bonding electrons, while its values < 0.5 indicate delocalized electrons. 75It is observed from Table 6 the values of ELF for all the complexes of the studied system are less than 0.5, and the electrons are delocalized for the studied system.All the above parameters indicate the excellent performance of the surface as an adsorbent material for sensing phosgene gas.

Density of states
The important parameter of solid physics, through which numbers of states are described in the unit intervals of energy for the provided chemical system, is called density of states.The DOS graph is useful for analyzing the nature of electronic structure with the conguration of molecular orbitals with their proposed energies.The Multiwfn soware was employed to calculate the DOS of the Ga 12 As 12 complexes.The comparison between the DOS plot of the nanocluster and the DOS plots of its complexes with phosgene gas demonstrates the sensitivity of complexes toward phosgene gas and the variation in the complexes' electronic properties.By the interaction of the nanocluster and the gas for each complex, a few new energy states appeared around E f , which caused an increase and decrease in the energy gap (E g ) values, as shown in Fig. 7.
The decrease in the E g values for complexes MS1, MS4, and MS8 has been calculated as 0.02 eV, 0.03 eV, and 0.05 eV, respectively, while for complexes MS2, MS3, MS6, MS9, and MS10, it is 0.01 eV, but the increase in the E g values for complexes MS5 and MS7 has been calculated as 0.01 eV.It has been shown that the maximum variation in the E g value is observed for complex MS8, which represents the maximum conductivity and sensitivity of the studied system.

NCI analysis
Non-covalent bonds are analyzed by applying the Multiwfn soware.Hydrogen bonding, van der Waals interactions, and electrostatic interactions are those mechanisms through which non-covalent interactions are carried out.In order to predict weak interactions, NCI analysis of basic functions such as electron density, reduced density gradient, and Hessian 2 nd density eigenvalue is utilized.The information about the type of interactions is given by isosurface plots that involve two functions, namely, the eigenvalue of Hessian 2 nd density and electron density plotted against RDG.
By the isosurface plot, the nature of interactions is dened based on the eigenvalue.The negative values of l 2 (r)r(r) and the high value of electron density represent strong non-covalent interactions, such as hydrogen bonding through the blue region, while the positive value of l 2 (r)r(r) through the red region represents weak non-covalent interactions such as steric effect and reduced electron density.
In the case of the green region, the value of l 2 (r)r(r) is zero, and it represents comparatively weak intermolecular interactions such as van der Waals interactions. 47,76In the current work, it has been evident through the plots shown in Fig. 8 that the existence of the blue region in between the nanocluster represents strong non-covalent interactions.
The existence of the green region in between phosgene gas and the nanocluster for all complexes indicates the presence of van der Waals interactions.Further, repulsive interactions such as the steric effect were also observed in between the atoms of the nanocluster and indicated by the red region.

Molecular electrostatic potential analysis
In order to analyze the limit of charge distribution in a molecule, molecular electrostatic potential (MEP) analysis is very useful.The system's physiochemical properties, such as chemical reactivity, partial charges, and dipole moment, are correlated with the system's geometry by MEP analysis. 29The analysis was done by DFT at the B3LYP-D3/6-31G(d,p) level of theory.The charge distribution is disclosed in Fig. 9.
Commonly, the electropositive end (electron decient area) is represented by the blue region, while the electronegative end (electron-rich area) is characterized by the yellow region and the green area existing between two extreme regions indicates the mean potential in the web version. 77The isolated nanocluster indicates equal charge distribution with both charges at a similar extent because of the symmetrical geometry.The nanocluster xed with phosgene gas produces insignicant charge separation by decreasing the blue region intensity on the nanocluster and shiing toward the gas in the case of complexes MS4, MS5, MS6, and MS7.In the case of other complexes, the intensity of the yellow region increases on the gas, as shown in Fig. 9.
The pure Ga 12 As 12 nanocluster has zero dipole moment because of the same number of electronegative and electropositive atoms, but aer the interaction of phosgene gas, the variation in dipole moment takes place due to the shiing of (blue and yellow region) charges between the nanocluster and the gas.In MEP analysis, to understand the interaction strength of phosgene gas with the nanocluster, the charge distribution is also correlated with dipole moment (D m ), which is further supported by Q T (the calculated net charge on phosgene gas) Paper RSC Advances analysis.For all complexes of the studied system, the irregular behavior of D m was observed.The maximum value of D m was observed for complex MS7, and it causes the shiing of the blue region toward the phosgene gas, as shown in the MEP plots.The 2 nd largest D m value has been noted for complex MS5, and some changes have been observed in its MEP plot.The calculated dipole moment values and Q T values are found to be consistent with each other, as shown in Table 7.The highest Q T value has been observed for complex MS7 with large D m and E INT values.The variation in Q T and D m values for different complexes has been observed because of extra charge distribution and due to which the shiing of blue and yellow regions has been observed.These observations indicate the excellent response of the nanocluster in the sensing and detection of phosgene gas.

UV-Vis analysis
The UV-Vis spectra of all the complexes of the Ga 12 As 12 nanocluster with phosgene gas have been calculated utilizing the TD-DFT method at the B3LYP-D3/6-31G(d,p) level of theory.The adsorption behavior of the isolated nanocluster has been calculated and compared with its complexes aer the adsorption of phosgene gas to demonstrate its sensing capability based on the UV-Vis adsorption technique.The strong overlapping due to the interacting moieties is indicated by enhanced absorption wavelength along with oscillator strengths (f), as mentioned in Table 7.
In the current work, the change in the adsorption spectra of the Ga 12 As 12 nanocluster due to the presence of phosgene gas has been explained.The combined adsorption spectrum of the nanocluster with its complexes has been shown in Fig. 10.The combined adsorption spectrum of the studied system is composed of eleven peaks located in the wavelength range of 400-850 nm.
The maximum absorbance of the isolated nanocluster is at 551.95 nm.The maximum absorbance of complexes MS2, MS9, and MS8 is red-shied because of the shiing to longer wavelengths 556.63 nm, 556.56 nm, and 562.11 nm, respectively, because of nanocluster interaction with phosgene gas.The red-shied absorbance indicates the reduced band gap and enhanced electrical conductivity and the sensing response of the studied system. 78Similar complexes have minimum excitation energy (DE) and high conductivity values.Herein, the comparatively maximum absorbance wavelength and minimum excitation energy value is represented by complex MS8 while the minimum absorbance wavelength and maximum excitation energy values are represented by complexes MS5 and MS7.This result is correlated with FMO analysis and chemical reactivity indices values where MS8 show the least energy gap, high soness, high electrophilicity index, and maximum conductivity and express high sensing response.It can also be noted the l max is also blue-shied for all the other complexes because of shiing toward shorter wavelength (551.83-542.17nm), and for complex MS1, the interaction of phosgene gas with the nanocluster creates considerable variation in the adsorption spectrum.The variation in molar adsorption coefficient values and red/blue shi absorbance wavelength aer phosgene adsorption indicate that the Ga 12 As 12 nanocluster has the potential as an excellent sensor for phosgene gas.

Sensing mechanism
The main purpose of the work is to investigate the capability of the nanocluster to detect and sense phosgene gas.The sensing mechanism is a parameter that characterizes conductivity and resistance changes before and aer gas interaction.The sensing response of the nanocluster is associated with the change in the conductivity of the nanocluster and the conductivity of its complexes.It could be determined by the given eqn ( 7) where s 2 is the electrical conductivities of the complexes and s 1 is the electrical conductivity of the nanocluster.The electrical conductivity is inverse of the electrical resistance, and both these parameters and recovery time is used to determine the sensing response.

Electrical conductivity
The movement of electrons from the valence bond to the conduction bond is termed as electrical conductivity. 79The changes in the electrical conductivity of the complexes are due to their different electronic characteristics.The electrical conductivity is determined by eqn (8). 55 where A, T, and k are Richardson constant (6 × 10 5 ), working temperature (298 K), and Boltzmann constant (8.318 × 10 −3 kJ mol −1 K −1 ), respectively. 80The given equation relates the electrical conductivity with the HOMO-LUMO energy gap values, and this shows that the increase in the energy gap values causes a decrease in the electrical conductivity of the complexes.Aer the adsorption of the gas, the energy gap values are changed due to variations in the HOMO and LUMO values of the complexes.The electrical conductivity of the studied system has been calculated to determine the sensing response of the complexes.The sensitivity of all the complexes of the nanocluster with phosgene gas has been calculated and shown in Table 8.Complex MS8, having less energy gap and high electrical conductivity, respond excellently in sensing, and this result is also correlated with FMO analysis, global indices of reactivity, and UV-Vis analysis.It can be evidence to express the mechanistic sensing capability of the nanocluster.The sensing response of the studied system is displayed by Fig. 11.

Recovery time
The time a sensor utilizes to return to its original shape aer the adsorption of the material is named its recovery time and denoted by s.It indicates the sensing performance of the material.The surface having a shorter recovery time performs better to sense the material and vice versa.It can be calculated by the given eqn (9). 81¼ A À1 e ÀE ads kT (9)   where A is the vibrational frequency of the complex, which is 10 12 s −1 , and T and k are working temperature and Boltzmann constant, respectively.82 E ads is the adsorption energy of the complex, and its negative values represent an exothermic reaction.The more negative values of E ads indicate strong interactions between the gas and the nanocluster.
The adsorption strength also affects the sensing capability of the material because it makes for difficult desorption of the gas Fig. 10 The UV-Vis adsorption spectrum of the studied system.8.Among all the complexes, complex MS8 has the shortest recovery time and represents the highest reactivity and sensitivity.This investigation is also correlated with UV-Vis analysis, chemical reactivity of indices, FMO analysis, and conductivity response to describe the mechanistic sensing response of the nanocluster.

Thermodynamics analysis
The interaction of work and heat with chemical reactions and variations in the physical state through the law of thermodynamics is studied by thermodynamic analysis (TDA).This mathematical method is applied to study the spontaneous and non-spontaneous behavior of the system and chemical equations. 42,43The current work is concerned with enthalpy change and Gibbs' free energy change.The relation between the internal energy of the system and enthalpy change is represented by the equation DH = Q + PV.The positive and negative values of the enthalpy change depend upon the absorbance and release of heat.The enthalpy change is positive due to the absorbance of heat by the system, and the reaction is endothermic.In contrast, the enthalpy change is negative due to the release of heat by the system, and the response is exothermic.The relation of enthalpy change with Gibbs' free energy change is expressed by eqn ( 10) where T is the system's temperature and DS is the entropy change of the system.The information related to the spontaneity of the system is provided by the change in Gibbs' free energy.The spontaneous reaction and non-spontaneous reaction are represented by the negative and the positive values of DG, respectively.When the value of Gibbs' free energy change is zero, then the reaction is at an equilibrium state, has the tendency to maximum entropy, and is expressed by eqn (11).
The enthalpy changes and Gibbs' free energy change of the complexes have been calculated from the optimized geometries of the complexes using the following eqn ( 12)- (15).
where E 0 , H Corr , G Corr , D f H 0 , and D r G 0 represent electronic energy, thermal correction for H, thermal correction for G, standard enthalpy changes, and change in the Gibbs' free energy of formation, respectively.The other thermodynamic properties of the system, such as zero-point energy, heat capacity, and entropy change, have been calculated by DFT at the B3LYP-D3/6-31G(d,p) level of theory at a constant working temperature (298 K).
In the current work, the calculated enthalpy changes and Gibbs' free energy changes of the nanocluster and phosgene gas complexes are clearly shown in Table S3

Conclusion
The capability of the semiconductor Ga 12 As 12 nanocluster to sense and adsorb the warfare agent phosgene gas is examined employing comprehensive DFT insights.Utilizing computational tools, geometry optimization, adsorption studies, frontier molecular orbitals analysis, global indices of reactivity, NBO analysis, topological QTAIM analysis, NCI analysis, MEP analysis, UV-Vis analysis, thermodynamics analysis, and the density of states of ten selected complexes of the studied system has been investigated.The adsorption studies represent the maximum adsorption response of the nanocluster with −21.34 ± 2.7 kcal mol −1 adsorption energy and the least interaction distance (3.05 ± 0.5 Å) with phosgene gas.FMO analysis revealed that complex MS8 has the least energy gap (2.17 eV) and indicates less stability and high conductivity.DOS analysis has also been performed in support of FMO analysis, which explores the distribution patterns of HOMO-LUMO orbitals.The global indices of reactivity indicate comparatively the highest soness (0.46 eV), least hardness (1.09 eV), high electrophilicity index (10.71eV), and high reactivity of complex MS8 among all the complexes of the studied system.The ionization potential values of the studied system have been reduced by the adsorption of phosgene gas, and these factors indicate the enhanced reactivity and sensitivity of the studied system.Furthermore, NBO results explore that the donor-acceptor interactions are stabilized by intermolecular charge transfer (ICT) and different kinds of non-covalent interactions.These interactions and transfer of charges in between the molecules are because of electron delocalization of the oxygen and chlorine lone pair of the phosgene to the sigma and pi anti-bonding orbitals of the studied nanocluster because of high stabilization energy values.The topological parameters of QTAIM analysis provide information about the presence of partially covalent and non-covalent interactions and delocalized electrons between the nanocluster and phosgene gas.NCI analysis indicates green region existence, and its results are also compatible with the information obtained by NBO and QTAIM analysis.MEP analysis provides conrmation about the charge distribution by shiing the yellow region toward the nanocluster and shows that the calculated dipole moment and Q T values of the studied system are found to be consistent with each other.UV-Vis analysis expresses the maximum absorbance (redshi) and minimum excitation energy of complex MS8, and this information is also correlated with the results of FMO analysis and global indices of reactivity.The sensing mechanism indicates the shortest recovery time (2.42 × 10 −12 ), high conductivity (1.99 × 10 9 ), and excellent sensing response (0.0107) of nanocluster's complex MS8 toward the phosgene gas.It is also correlated with FMO analysis, global indices of reactivity analysis, and UV-Vis analysis.Furthermore, thermodynamics analysis shows spontaneous thermodynamic behavior and exothermic interaction process of the studied nanocluster with phosgene gas.Thus, it can be concluded from all these investigations that the Ga 12 As 12 nanocluster is a promising inuential sensor for phosgene gas detection, MS8 has proven to be the best isomer of the studied system, and this research will emphasize the informative knowledge for experimental researchers to use Ga 12 As 12 as a sensor for chemical defence and environmental monitoring in industry and military safety.It can be used further for chemical agent neutralization upon detection and forensic investigation to analyze traces of chemical warfare agent aer chemical attack.

a
XY64 sides of the nanocluster.b XY66 sides of the nanocluster, ML = mid le, MR = mid right, T = top, TL = top le, TR = top right, RB = rim B, RC = rim C.

Fig. 3
Fig.3The optimized structures of the complexes of the studied system calculated at the B3LYP-D3/6-31G(d,p) level of theory.

Fig. 4
Fig.4The HOMO and LUMO plots along with their calculated energy gap (E g ) values for the studied nanocluster and complexes.

Fig. 8
Fig.8The pictorial display of the non-covalent interactions of the studied system.

Fig. 9
Fig.9The MEP diagrams of the Ga 12 As 12 nanocluster and complexes under study.

Fig. 11
Fig.11The sensing response of the studied system.

Table 1
The calculated bond lengths (Å) of the Ga 12 As 12 nanocluster at three different functionals comparison with the already reported data

Table 2
The adsorption energy (E ads ) and counterpoise corrected interaction energy (E INT ) values of the complexes and basis set superposition error (E BSSE ) calculated at the B3LYP-D3/6-31G(d,p) level of theory a a E INT and E ads are in kcal mol −1 and BSSE in hartree.© 2023 The Author(s).Published by the Royal Society of Chemistry RSC Adv., 2023, 13, 28885-28903 | 28889 Paper RSC Advances

Table 3
The calculated energy values of the highest occupied molecular orbital (E HOMO ) and lowest unoccupied molecular orbital (E LUMO ), energy gap (E g ), Fermi level energy (E f ), and work function (F) of the nanocluster and complexes a a All factors are in electron volt (eV).

Table 4
The calculated global reactivity parameters of the studied system a

Table 5
The highest second order perturbation energy (E 2 ) of the studied system calculated by DFT at the B3LYP-D3/6-31G(d,p) level of theory

Table 7
The calculated excitation energy (DE), maximum absorbance (l max ) along with oscillator strength (f), and dipole moment (D m ) of the studied system and the net charge on phosgene gas (Q T ) after adsorption

Table 8
The electrical conductivity, recovery time, and sensing response of the system under study calculated by DFT at the B3LYP-D3/6-31G(d,p) level of theory a a Here, E g = energy gap, E INT = counterpoise corrected interaction energy in kcal mol −1 , s = recovery time in second, s = complexes electrical conductivity, S = sensitivity.