In Silico Designing of Mg12O12 Nanoclusters with a Late Transition Metal for NO2 Adsorption: An Efficient Approach toward the Development of NO2 Sensing Materials.

Gas sensors are widely used for detection of environmental pollution caused by various environmental factors such as road traffic and combustion of fossil fuels. Nitrogen dioxide (NO2) is one of the leading pollutants of the present age, which causes a number of serious health issues including acute bronchitis, cough, and phlegm, particularly in children. Nowadays, researchers are focused on designing new sensor materials for detection and removal of NO2 from the environment. In this line, we have made an attempt to design NO2 sensing materials by using theoretical techniques. Here, we have reported decoration of Mg12O12 nanoclusters with a late transition metal (Cu) by employing density functional theory at the B3LYP/6-31G(d,p) basis set. The decoration of metal on Mg12O12 gives two geometries (M1 and M2) with adsorption energies of -363.81 and -384.09 kJ/mol, respectively. Adsorption of NO2 on pristine Mg12O12 expressed an adsorption energy value of -62.36 kJ/mol. Adsorption of NO2 on Cu-decorated Mg12O12 nanocages delivered two geometries (N1 and N2) with adsorption energies of -442.56 and -447.64 kJ/mol. Metal-decorated Mg12O12 nanoclusters offer better adsorption of NO2 as compared to pristine Mg12O12 . Adsorption of NO2 on Cu-Mg12O12 nanoclusters also causes narrowing of band gap of magnesium oxide nanoclusters. Large dipole moment, high Q NBO with large electrophilic index in NO2-Cu-Mg12O12 nanoclusters suggested that metal-decorated Mg12O12 nanoclusters are efficient candidates for NO2 adsorption. Different geometric parameters and results of global reactivity descriptors show that NO2-Cu-Mg12O12 nanoclusters are quite stable in nature with least reactivity. Thus, conceptualized systems are potential candidates for applications in NO2 sensing materials.

Introduction

Magnesium oxide is a large band gap material that is a potential candidate for numerous applications like sensors,[1] spintronic,[2] catalysis,[3] energy storage,[4] and ceramics.[5] In the literature, various investigations (experimental[6,7] as well as theoretical[8−10]) are present, which explore the cluster formation of magnesium oxide. Saunders spectroscopic investigation of (MgO) revealed that small clusters of MgO (n = 6, 9, 12, and 15) are quite stable in nature.[11] Similarly, theoretical studies also unveil that a MgO cage form is quite stable in nature.[8]

Moreover, the literature is quite rich regarding adsorption of various analytes on the surface of Mg nanoclusters. Nicholas and his co-workers conducted a comprehensive density functional theory (DFT) study in which they adsorbed acetylene on the surface of Mg clusters.[12] Noei and Peyghan also investigated NO adsorption on Mg by using DFT calculations.[13] Some cations and anions are also adsorbed on the external surface of Mg nanoclusters by Solimannejad and his co-workers.[14]

Metal decoration on the external surface of nanoclusters is an efficient technique for boosting the optoelectronic, nonlinear, and electronic properties of nanoclusters.[15−17] The literature is quite extensive regarding the doping and decoration of nanostructures with metal atoms. By doping here, we mean that an atom of the nanostructure is replaced with a metal, whereas decoration means that the metal atom is just adsorbed on the surface. For doping when an external atom is added, a defect may be created, which imparts certain interesting properties but also renders the system unstable in terms of binding energies. The binding energies of such systems are generally low. On the other hand, decoration does not disturb the intrinsic stability of the systems. Moreover, the metal atoms can easily be detached from the nanostructure as and when required. These characteristics motivated us to study decoration rather than doping with metal atom. Shakerzdeh et al. performed a detailed study for enhancing electronic, nonlinear, and magnetic properties of Mg and Be12O12 nanoclusters by alkali metal doping.[18] C- and Si-decorated Mg nanoclusters were also investigated in the literature by Kakemam and his co-authors for exploring the change in electronic, structural, and nonlinear properties of Mg nanoclusters.[19] Further, adsorption of transition metals (Fe, Ni, Co, and Mn) on Mg nanoclusters was studied by Javan et al. for expressing the change in electronic and magnetic properties.[20] Shamlouei et al. discussed the doping of transition metals on the surface of Mg nanocages for investigating the change in structure–property relationship and nonlinear optical properties of resultant nanocages.[21] A main criterion for selecting the metal for the decoration is the stability of the resultant complex. Early transition metals bind too tightly to detach the metal from the surface at the end. On the other hand, late transition metals bind with these surfaces with reasonable affinity. A number of reports are already available for nickel decoration in the literature, whereas copper-decorated surfaces are not well explored. Moreover, copper is generally not poisoned by the analytes, whereas nickel is poisoned. Copper also has good tendency to adsorb various oxygen-containing analytes.

Nitrogen dioxide (NO2) is one of the leading pollutants of the present age, which causes a number of serious health issues including acute bronchitis, cough, and phlegm, particularly in children. Further, various reports are present in which NO2 was adsorbed on X12Y12 nanocages. Beheshtian et al. studied the NO2 adsorption on B12N12 nanoclusters.[22] Similarly, NO and CO adsorption on Al12N12 nanoclusters was studied in the past by Peyghan and his co-workers.[23] In another report, Peyghan and his co-authors worked on Al12N12 nanoclusters for selective NO2 adsorption.[24] Further, SiC-doped nanotubes were also successfully used for NO2 adsorption.[25] Ga- and Mg-doped Al12N12 nanoclusters were also used by Soltani and his co-workers for NO2 and SO2 adsorption.[26] The literature is quite extensive with respect to decoration of a metal on X12Y12 nanoclusters followed by adsorption of analytes.[15,27−32]

Keeping in view all previous reports, we become interested to study the copper-decorated Mg nanoclusters for NO2 adsorption. In the literature, a number of reports illustrated that copper binds to X12Y12 nanoclusters effectively. Also, copper also has good tendency to adsorb various oxygen-containing analytes. To our best knowledge, there is no such report in the literature at present in which Cu decoration is done on Mg for NO2 adsorption. We explore the change in electronic and adsorption behavior of Cu-decorated Mg upon NO2 adsorption. Frontier molecular orbital analysis, density of states, adsorption energy, QNBO, dipole moment, and bond lengths of copper-decorated Mg, NO, and NO nanoclusters have been calculated by employing density functional theory. At last, global reactivity descriptors are also calculated for describing the stability and reactivity of nanoclusters. Results of all analyses suggested that our Cu-decorated Mg nanoclusters are good candidates for NO2 adsorption.

Results and Discussion

Bond Length and Interaction Energy

Mg contains an equal number of electropositive and electronegative atoms, which is why it is a neutral cluster with zero dipole moment due to centrosymmetry. There are two types of bond that is noted in Mg, one is b66 and the other is b64. The bond shared between one hexagonal and tetragonal ring is described as b64, and the bond shared between two hexagonal rings is considered as b66. The optimized geometry of Mg at the B3LYP/6-31G(d,p) basis set is expressed in Figure . DFT-based b66 and b64 calculated bond lengths are 1.77 and 1.80 Å, respectively.

Figure 1

Optimized geometry of Mg nanoclusters at B3LYP/6-31G(d,p).

Initially, six different positions for the decoration of a metal were tested. These positions are named as follows: r (top of the hexagonal ring), r (top of the tetragonal ring), b (top of the bond shared between two hexagonal rings), b (top of the bond shared between hexagonal and tetragonal rings), O (top of the oxygen atom), and Mg (top of the magnesium metal). Initially, inputs for the decoration of late transition metal “Cu” on the abovementioned were done. But unfortunately, all abovementioned inputs changed into two kinds of geometries, which were O and r. Among them, the most stable geometries were selected for further investigation and for analyte adsorption.

Decoration of Cu on Mg nanoclusters provides two geometries (as we mentioned earlier) named as M1 (when Cu adsorbed on the top of the oxygen atom) and M2 (when Cu adsorbed on the top of the hexagonal ring). The optimized geometries of both systems at the B3LYP/6-31G(d,p) basis set of DFT are shown in Figure . The distance and adsorption energy play a vital role for measuring the stability and performance of the resultant designed geometries for analyte adsorption. The DFT-based calculated bond distances of Cu metal from Mg in M1 and M2 geometries are 1.82 and 1.78 Å, respectively. The interaction of Cu metal is at a small distance from the nanocage in M2 geometry. The adsorption energies of Cu-Mg systems are −363.81 and −384.09 kJ/mol for M1 and M2 geometries, respectively. M1 disclosed a low value of adsorption energy, which might be due to a large distance of the metal from the nanocage, and similarly, M2 disclosed a high adsorption energy value due to a small distance of Cu from the nanocage. Further, the adsorption energy of metal on the top of the hexagonal ring is strong, which is due to the interaction of metal with many atoms (6 atoms in rings), which is not possible for M1. Overall, both geometries show fine values of adsorption energy and could be used for good analyte adsorption.

Figure 2

Optimized geometries of M1 and M2 at the B3LYP/6-31G(d,p) basis set of DFT.

Next, adsorption of analytes, i.e., NO2 on pristine and metal-decorated Mg nanoclusters, is extensively studied, and results are presented in Table . Adsorption of NO2 on metal-decorated Mg provided two geometries named as N1 (NO2 adsorption on M1) and N2 (NO2 adsorption on M2). The optimized geometries of NO and N1, N2 (at the B3LYP/6-31G(d,p) basis set) are shown in Figure . Adsorption of NO2 on pristine Mg shows a small value of adsorption energy (Ead = −62.36 kJ/mol). The large distance and small adsorption energy of NO suggested that the adsorption of NO2 on nanoclusters is not favorable in nature. However, decoration of Cu metal on Mg enhances the adsorption of NO2 on nanoclusters. The DFT-based calculated adsorption energies of NO2 on Cu-Mg nanoclusters (N1 and N2) are −442.56 and −447.64 kJ/mol, respectively. These adsorption energy values are quite high as compared to the NO system, which is due to the decoration of Cu metal on nanoclusters. The distance of NO2 from metal-adsorbed nanoclusters in N1 and N2 is 1.84 Å, which is quite small as compared to 2.11 Å (noted in NO). Thus, small distances and large adsorption energy values in N1 and N2 geometries suggested that the decoration of Cu metal creates a favorable environment for adsorption of NO2, which is not seen in pure Mg nanoclusters. From the above discussion, it is evidently concluded that Cu-decorated Mg nanocages are good aspirants for NO2 adsorption, particularly N2, due to large adsorption energy values.

Table 1

Bond Distances, QNBO, and Adsorption Energies of All Studied Systems at the B3LYP/6-31G(d,p) Level of DFT

system	dM-Cagea	dNO2-Metalb	QNBO on metal	QNBO on NO2	Eadc
Mg12O12
NO2-Mg12O12		2.11		0.009	–62.36
Cu-Mg12O12 (M1)	1.82		1.009		–363.81
NO2-Cu-Mg12O12 (N1)	1.80	1.84		1.042	–442.56
Cu-Mg12O12 (M2)	1.72		1.012		–384.09
NO2-Cu-Mg12O12 (N2)	1.81	1.84		1.039	–447.64

Distance of metal from Mg cluster in Å.

Distance of NO2 from metal in Å.

Adsorption energy in kJ/mol.

Figure 3

B3LYP/6-31G(d,p) basis set-based optimized geometries of NO, N1, and N2.

Natural Bonding Orbital (QNBO) Analysis

Natural bonding orbital (QNBO) analysis unveils the charge shifting within a system.[33−39] It also explores the change in electronic behavior of an under investigation system by installing different metals and analytes. Mg being a neutral system have an equal number of electropositive and electronegative atoms and a specific electronic behavior. However, its electronic behavior is disturbed by decoration of a late transition metal (Cu). The QNBO values on Cu in M1 and M2 geometries are 1.009 and 0.012 e, respectively. M2 disclosed a higher value of QNBO on metal as compared to the M1 geometry, which might be due to a small distance of metal from the nanocluster.

The DFT-based calculated QNBO values on NO2 gas in NO, N1, and N2 geometries are 0.009, 1.042, and 1.039 e, respectively. NO expressed the lowest value of QNBO, which might be due to the lowest charge transfer from the nanocage to NO2 (due to a large distance). Meanwhile, N1 and N2 show high QNBO charges as compared to NO2-adsorbed Mg, which might be due to the better decoration of copper metal and also due to the small size of NO2 from NO nanoclusters. Overall, the decreasing trend of QNBO of all studied systems is N1 > N2 > M1 > M2 > NO. From the above discussion, it is evidently concluded that fine charge transfer occurs from metal-decorated Mg to NO2 gas, which is not seen in NO. Thus, Cu decoration on Mg is a good approach for maximum QNBO transfer to an analyte (NO2) as shown in Table .

Dipole Moment

Dipole moment analysis is useful to highlight the transfer of charges within a system.[40−46] Generally, dipole moment and QNBO charges are both calculated for a system having a potential for charge transfer. Due to these reasons, we also considered dipole moment analysis for our studied systems along with QNBO analysis.

Mg being centrosymmetric shows a zero dipole moment value because the number of electropositive and electronegative sites in studied systems are the same (Figure ). However, the adsorption of Cu on Mg nanocages causes a change in dipole moment value, which is due to the interaction of electron-rich metal with neutral nanoclusters. The calculated dipole moment for M1 and M2 are 1.27 and 2.54 D, respectively. The M2 geometry disclosed a higher value of dipole moment as compared to M1, which is due to high QNBO values and large distances, which is a key factor that operates here. Similarly, the adsorption of NO2 on Mg expressed a dipole moment value of 3.03 D. Meanwhile, the adsorption of NO2 on metal-adsorbed Mg nanoclusters, i.e., N1 and N2, expressed dipole moment values of 7.49 and 7.05 D, respectively. Higher values of dipole moment are seen in N1 as compared to the N2 and NO geometry. This is probably due to a higher QNBO charge in the case of N1 geometry and a large distance of NO2 from metal-decorated Mg. The change in dipole moment value of the N1 and NO geometry is very high, which suggested that the decoration of Cu on Mg enhances the dipole moment of the resultant geometry. The trend of dipole moment is similar to the trend of QNBO charges, which suggested that our systems are quite interesting for NO2 adsorption. The decreasing order of dipole moment of NO2 adsorbed systems is N1 > N2 > NO. This trend clearly indicated that Cu decoration on Mg nanocages enhances the charge separation. Thus, our systems are fine candidates for the development of better NO2 sensing materials.

Figure 4

Dipole moment of all studied systems in Debye.

Frontier Molecular Orbital Analysis

Frontier molecular orbitals, i.e., highest occupied molecular orbital and lowest unoccupied molecular orbital, determine the charge transfer and performance of a material for sensing and adsorption of a specific analyte gas. The difference of energies of both orbitals determine the value of band gap (HOMO–LUMO energy gap[43,46]). Generally, a narrow band gap allows the maximum charge transfer from HOMO to LUMO. Therefore, frontier molecular orbital analysis is performed for valuable insights into the energies of HOMO, LUMO, Fermi level, and HOMO–LUMO energy gap of studied systems. The band gap of semiconductors like nanocages is determined by using the following equation:[47−49]Here, Eg represents the band gap, EHOMO and ELUMO are the energies of HOMO and LUMO orbitals, and EFL is the Fermi level. Fermi level is actually the mid-point of both frontier molecular orbitals, or it is the mid-point of the HOMO–LUMO energy gap.[34]

Mg12O12 is a centrosymmetric semiconductor with a large band gap. The DFT-based calculated energy values of HOMO and LUMO of Mg are −6.56 and −1.69 eV, respectively, with a band gap of 4.87 eV (Table ). The Fermi level of Mg is located at −4.13 eV. The values of HOMO and LUMO of metal-adsorbed Mg nanocages (M1 and M2) are −4.23, −3.55 eV and −1.71, −1.62 eV, respectively. Both M1 and M2 have destabilized HOMO and stable LUMO as compared to Mg nanocages. The adsorption of copper metal on Mg disturbs the electronic behaviors and also changes the position of frontier molecular orbitals. The newly formed HOMO is formed at the higher level as compared to the previous positioned HOMO level, which causes narrowing of band gap and high charge transfer between two molecular orbitals. The calculated band gap in M1 and M2 geometries are 2.51 and 1.94 eV. These values of band gap clearly indicated that the adsorption of copper metal effectively causes narrowing of band gap, which causes high charge shifting between two molecular orbitals. The Fermi level of M1 and M2 is located at −2.14 and −1.80 eV.

Table 2

Energy of HOMO, LUMO, and Fermi Level along with Band Gaps of All Studied Systems at the B3LYP/6-31G(d,p) Basis Set of DFT

systems	EHOMO (eV)	ELUMO (eV)	EFL (eV)	Eg (eV)
Mg12O12	–6.56	–1.69	–4.13	4.87
NO2-Mg12O12	–6.58	–2.28	–3.33	4.30
Cu-Mg12O12 (M1)	–4.23	–1.72	–2.14	2.51
NO2-Cu-Mg12O12 (N1)	–6.04	–2.08	–3.06	3.95
Cu-Mg12O12 (M2)	–3.55	–1.61	–1.80	1.94
NO2-Cu-Mg12O12 (N2)	–6.35	–2.05	–3.21	4.30

The adsorption of NO2 on pure Mg reported a band gap value of 4.30 eV, with HOMO and LUMO energies of −6.58 and −2.28 eV. Adsorption of NO2 on Mg causes narrowing of band gap as compared to pristine Mg, which causes high shifting of charge between molecular orbitals. When NO2 was adsorbed on M1 and M2 geometries (N1 and N2), then significant narrowing of band gap is noted as compared to pure Mg nanocages. The band gap value of N1 and N2 is noted as 3.95 and 4.30 eV with Fermi levels of −3.06 and −3.21 eV, respectively. These values are quite smaller as compared to the band gap value of Mg. The narrow band gap helps to enhance the sensing ability of resultant nanoclusters. From the above discussion, it is clearly indicated that the decoration of Cu and adsorption of NO2 on a metal-decorated geometry efficiently narrow the band gap and enhance the adsorption ability for NO2. Thus, reported systems are fine candidates for NO2 sensing materials. Distribution of HOMO and LUMO is expressed in Figure . The distribution of HOMO and LUMO is correlated with density of states. So, next we have performed density of states analysis in order to explore the presence of both orbitals on whole systems.

Figure 5

Distribution pattern of HOMO and LUMO on all studied systems at the B3LYP/6-31G(d,p) basis set.

Density of States Analysis

Density of states (DOS) analysis has been performed at the B3LYP/6-31G(d,p) level of DFT, and DOS plots are shown in Figure . Density of states analysis is performed in order to gain specific understanding related to the distribution of molecular orbitals on studied systems. It shows a correlation between frontier molecular orbitals and distribution of HOMO and LUMO. From Figure , it is indicated that HOMO and LUMO density is equally distributed in the nanocage. When the metal (Cu) is positioned on Mg nanocages (M1 and M2), then HOMO density is present on HOMO and LUMO is majorly distributed on the metal and cage, indicating that the metal has an excess of electron, which transfer to nanocages. When NO2 was adsorbed on pristine Mg nanocages, then HOMO is distributed on Mg nanocages while LUMO is positioned near NO2, indicating that the charge is going to transfer toward the gas. At last, the adsorption of NO2 on metal-decorated Mg causes shifting of HOMO and LUMO more toward the NO2 gas and Cu metal. So, from Figure and the above discussion, it is evidently concluded that the decoration of Cu on Mg significantly enhances the NO2 adsorption also causes major shifting of HOMO and LUMO densities.

Figure 6

Density of states plots of all studied systems at the B3LYP/6-31G(d,p) level of DFT.

Global Descriptors of Reactivity

Various global descriptors of reactivity like electronegativity (X), global hardness (η), global softness (S), chemical potential (μ), electron affinity (EA), ionization potential (I), and electrophilic index (ω) are considered as key parameters for determining the chemical reactivity, stability in nature, reaction nature, and electronegative potential of studied systems. All descriptors of reactivity are calculated at the B3LYP/6-31G(d,p) level of DFT. The results of abovementioned descriptor are mentioned in Table . The ionization potential and electron affinity of a molecule are directly related to HOMO and LUMO values, respectively. The ionization potentials of Mg, NO, M1, M2, N1, and N2 are 6.560, 6.580, 4.230, 6.040, 3.550, and 6.350 eV, respectively. Mg nanocages have the highest value of ionization potential, whereas the second highest value of ionization potential is seen in NO nanoclusters, which might be due to a high energy of HOMO. However, decoration of Cu on Mg (M1 and M2) described ionization potential values of 4.230 and 3.550 eV, respectively. Both values indicated that adsorption of Cu on nanocages significantly causes stabilization of HOMO due to a low energy. Adsorption of NO2 on metal-decorated Mg (N1 and N2) expressed a low ionization potential than pure Mg nanoclusters, which indicated that NO2 adsorption causes stabilization of HOMO and also stabilizes the resultant system. The electron affinity values of Mg, NO, M1, M2, N1, and N2 are 1.690, 2.280, 1.720, 1.610, 2.080, and 2.050 eV, respectively. Electron affinity values show that adsorption of Cu and NO2 on Mg significantly enhances the electron affinity aptitude. The values of chemical hardness and softness for Mg, NO, M1, M2, N1, and N2 are 2.345, 2.150, 1.255, 0.970, 1.980, 2.150 eV and 0.205, 0.233, 0.398, 0.515, 0.253, and 0.233 eV–1, respectively. All designed systems expressed are stable in nature with large values of chemical hardness and small values of global softness. The small values of global softness suggested that the systems are least reactive and more stable in nature, which is also confirmed from chemical potential values. Electrophilic index plays a key role in deciding the efficiency of metal-decorated nanoclusters for gas sensing ability. Generally, large values of electrophilic index favor more sensing of a gas analyte by enhancing the adsorption character of resultant systems. The electrophilic index of Mg nanocages is 3.494 eV, where the adsorption of NO2 enhances the electrophilic index to 4.564 eV. The adsorption of NO2 on Cu-decorated Mg (N1 and N2) disclosed electrophilic index values of 4.163 and 4.102 eV, respectively. These values of electrophilic index are quite high as compared to Mg nanocages, which suggested that our metal decoration on nanoclusters is a fine approach for enhancing the NO2 adsorption.

Table 3

IP (Ionization Potential in eV), EA (Electron Affinity in eV), X (Electronegativity), μ (Chemical Potential in eV), η (Global Hardness in eV), S (Global Softness in eV–1), and ω (Global Electrophilic Index in eV) of Studied Systems

systems	IP	EA	X	μ	η	S	ω
Mg12O12	6.560	1.690	4.125	–4.125	2.435	0.205	3.494
NO2-Mg12O12	6.580	2.280	4.430	–4.430	2.150	0.233	4.564
Cu-Mg12O12 (M1)	4.230	1.720	2.975	–2.975	1.255	0.398	3.526
NO2-Cu-Mg12O12 (N1)	6.040	2.080	4.060	–4.060	1.980	0.253	4.163
Cu-Mg12O12 (M2)	3.550	1.610	2.580	–2.580	0.970	0.515	3.431
NO2-Cu-Mg12O12 (N2)	6.350	2.050	4.200	–4.200	2.150	0.233	4.102

Conclusions

In summary, advance quantum chemical techniques have been used for exploring the electronic and adsorption behavior of Mg nanoclusters. Decoration of a late transition metal (Cu) on Mg nanoclusters provides two geometries named as M1 and M2 with adsorption energy values of −363.81 and −384.09 kJ/mol, respectively. Adsorption of NO2 on pristine Mg nanocages takes place with an adsorption energy of −62.36 kJ/mol, where adsorption of NO2 on metal-decorated geometries (N1 and N2) expressed adsorption energy values of −442.57 and −447.64 kJ/mol, respectively. Adsorption energy values suggested that decoration of Cu on Mg offers favorable NO2 adsorption. The HOMO–LUMO energy values of NO are low as compared to pristine Mg nanoclusters, which indicated that NO2 adsorption on metal-decorated nanoclusters causes narrowing of band gap and maximizes the charge transfer between molecular orbitals. Values of QNBO and dipole moment also enhance upon adsorption of NO2 on Cu-Mg nanoclusters, which also demonstrated that designed systems have large charge separations and fine natural bond charge shifting aptitude. Further, density of states analysis is also performed in order to explore the distribution pattern of HOMO and LUMO on studied systems. At last, global descriptors of reactivity are also measured for describing the chemical stability and reactivity of studied systems, which suggested that NO2 adsorption on metal-decorated Mg nanoclusters enhances the electrophilic index and ionization potential. In addition, small values of chemical softness suggested that metal-decorated NO nanoclusters are chemically stable with least chemical reactivates. Results of all analyses suggested that our designed systems are good candidates for high-performance NO2 sensing materials.

Computational Methodology

All calculations in the present study have been performed by using density functional theory at the B3LYP/6-31G(d,p) level. The B3LYP method along the 6-31G(d,p) basis set of DFT is frequently used and very famous for such kind of systems (nanoclusters).[50−54] Gaussian 09[55] was used for all calculations, and visualization was done through GaussView 5.0.[56] Initially, different orientations of Cu metal on the surface of Mg were investigated and the most stable metal decorated nanocluster was selected for further analysis. Adsorption of NO2 on Cu-decorated Mg nanoclusters provides two geometries named as N1 and N2.

The interaction energies of metal-decorated Mg (M1 and M2) were calculated by utilizing eq . Similarly, interaction/adsorption energies of NO2-adsorbed Mg nanocluster and NO2-adsorbed Cu-Mg nanoclusters (N1 and N2) were calculated by using eqs and 4, respectively.

Different equations were utilized for calculating different global reactivity indices such as electrophilic index (ω in eV), global softness (S in eV–1), electronegativity (X in eV), global hardness (η in eV), and chemical potential (μ in eV), which are given below:

Avogadro software was used for drawing the HOMO and LUMO distribution, and pymolyze 1.0 was used for plotting the DOS spectra.