Detection of Carbon, Sulfur, and Nitrogen Dioxide Pollutants with a 2D Ca12O12 Nanostructured Material

In recent times, nanomaterials have been applied for the detection and sensing of toxic gases in the environment owing to their large surface-to-volume ratio and efficiency. CO2 is a toxic gas that is associated with causing global warming, while SO2 and NO2 are also characterized as nonbenign gases in the sense that when inhaled, they increase the rate of respiratory infections. Therefore, there is an explicit reason to develop efficient nanosensors for monitoring and sensing of these gases in the environment. Herein, we performed quantum chemical simulation on a Ca12O12 nanocage as an efficient nanosensor for sensing and monitoring of these gases (CO2, SO2, NO2) by employing high-level density functional theory modeling at the B3LYP-GD3(BJ)/6-311+G(d,p) level of theory. The results obtained from our studies revealed that the adsorption of CO2 and SO2 on the Ca12O12 nanocage with adsorption energies of −2.01 and −5.85 eV, respectively, is chemisorption in nature, while that of NO2 possessing an adsorption energy of −0.69 eV is related to physisorption. Moreover, frontier molecular orbital (FMO), global reactivity descriptors, and noncovalent interaction (NCI) analysis revealed that the adsorption of CO2 and SO2 on the Ca12O12 nanocage is stable adsorption, while that of NO2 is unstable adsorption. Thus, we can infer that the Ca12O12 nanocage is more efficient as a nanosensor in sensing CO2 and SO2 gases than in sensing NO2 gas.


INTRODUCTION
Two-dimensional (2D) nanostructured materials are materials with sizes between 0.1 and 100 nm diameter and are used in the fabrication of nanodevices due to their high surface-tovolume ratio and good compatibility with the device architecture. 1,2 Nanostructured materials are composed of inplane bonds interwoven by weak van der Waals forces in a layered fashion. The uniqueness of these materials lies in the ability of modification through the rehybridization of orbitals and chemical bonds compared to their three-dimensional counterparts. 3,4 2D nanomaterials such as graphene hexagonal boron nitride 5,6 and metal dichalcogenides 7 have attracted lots of attention due to their satisfactory properties and widespread use in electronics, optoelectronics, catalysis, energy storage facilities, sensors, solar cells, lithium batteries, composites, etc. 2D nanomaterials can also be uniformly dispersed in waterbased lubricants with successful modification. 8−10 Due to their excellent properties, these materials find considerable applications. Several interesting properties have been reported for these materials. Recently, the magnetic homonuclear bonds in boron nitride nanosheets were reported in ref 11 using density functional theory (DFT) methods to examine the structural diversity of the considered nanostructured material. Their results demonstrated excellent stability and polarity, which was attributed to the magnetic moments of the homonuclear boron/nitrogen bond. The utilization of 2D boron nitride and its Ga-and Al-functionalized nanostructured composites as effective sensors of dichlorosilane was recently studied in ref 12. Their results revealed considerably stable adsorption of the studied gas onto the surface and show that functionalization with the metal atoms enhances the sensing attribute of the studied nanostructured materials. Also, the effectiveness of boron nitride nanostructured material has been investigated as a possible drug carrier for acetylsalicylic acid. The molecular electronic and structural properties of the complexes were considered by DFT methods. The surface was observed to bind effectively with the drug molecule via chemisorption and physisorption mechanisms and, as such, could deliver the considered drug molecule effectively. 13 DFT studies were equally employed for the investigation of monolayer MoS 2 and WSe 2 as well as few-layered transition-metal adsorptions of CO, NH 4 , NO, and NO 2 . Only minimal changes in adsorption characteristics were observed for the different studied gases regardless of significant changes in the electronic structure and properties orchestrated by band gap variations. Overall, the studied surfaces adsorbed NO 2 preferentially when compared to other counterparts. 14 NO 2 , SO 2 , and CO 2 are important ambient air pollutants and are highly intense in confined spaces, causing global challenges, which contribute to global warming, and they are toxic pollutant gases with pungent smell. Exposure to them might likely cause severe injury and perhaps result in death, depending on the degree of exposure. Nitrogen oxide (NO 2 ) and CO 2 constitute the main air pollutants, which result from combustion from power plants, vehicles, and several industrial processes. The presence of these gases in the atmosphere increases the risk of respiratory tract infections. 15 SO 2 is the main air pollutant released mostly as a result of the industrial operation as well as coal and oil burning. 16 However, it is an indirect greenhouse gas because it is coupled with elemental carbon to form aerosols. Eliminating these gases completely from the environment has been difficult for scientists and researchers for some decades, which is why an insight into the adsorption mechanism and potential of various efficient surfaces is still required; computational screening helps immensely in this regard. Recently, layered materials of different dimensions have attracted considerable attention due to their demonstrated potential as sensors, 17 supercapacitors, 18 catalyst, 19 and nanovehicles. 20 These materials continuously appear in scientific publications and conferences due to their high surface-to-volume ratio and high mechanical and chemical stability. Therefore, motivated by these reports, an attempt is put forward herein to investigate the efficacy of calcium oxide (Ca 12 O 12 ) nanostructured material as an efficient nanosensor of selected atmospheric gases (NO 2 , SO 2 , and CO 2 ). Appropriate quantum chemical calculations have been employed herein to arrive at various conclusions on the subject matter. The famous B3LYP with D3 dispersion of Grimme's has been utilized together with the split valence basis set 6-311++G(d,p) of John Popple. Molecular properties such as the frontier molecular orbital (FMO), which reveal molecular stability and electronic interactions with the external environment, are also considered; the adsorption behavior of the surface toward the studied gases has been considered appropriately. The susceptibility of intermolecular interactions of the adsorbate gases and the adsorbent surface is revealed by the natural bond orbital analysis, quantum theory of atoms in molecule (QTAIM), and noncovalent interaction based on the reduced density gradient model. These objectives have carefully been considered to address the formulated research questions, which are as follows: {1} Do Ca 12 O 12 nanocages possess the required surface-to-volume ratio to adsorb the studied gases? {2} If yes, what is the extent or affinity of Ca 12 O 12 toward the considered gases? {3} Which among the studied gases is preferentially (selectively) adsorbed by the studied surface? {4} What type of adsorption mechanism is exhibited by the adsorbent surface and how does the energy gap of the surface change upon the preferential adsorption of the considered gases? To address these questions, several adsorption configurations of Ca 12 O 12 nanocages with the respective gases have been investigated to evaluate the efficacy and potency of the surface to detect these pollutants.

COMPUTATIONAL DETAILS
Geometry optimization of all of the investigated gases and nanocages was conducted using the density functional theory (DFT) method at the B3LYP-GD3(BJ)/6-311+G(d,p) level of theory and was accomplished with the aid of the Gaussian 16 software program. 21 B3LYP-GD3(BJ), which is an exchange− correlation functional with the D3 version of Grimme's dispersion correction encompassing the famous Becke− Johnson damping was utilized for this study as it serves best for accurately predicting weak interactions and also mostly applied for adsorption studies as seen in reported works of several authors. 22, 23 We also ensured that the optimized structures attained local minima on the potential energy surface by taking into consideration frequency calculations at the same level of theory, and this was confirmed by the absence of imaginary frequencies. The Frontier molecular orbital (FMO) analysis was carried out to verify the stability of the isolated nanocage and gas-adsorbed nanocages. Natural bond orbital (NBO) analysis was also performed on the studied systems with the aid of the NBO 7.0 module 24 embedded in Gaussian 16 software code. The density of states (DOS) was established using Multiwfn 3.7 dev 25 and GaussSum 26 software. Molecular electrostatic potential (ESP) was performed using Multiwfn 3.7 dev, and the generated files were exported to VMD 1.9.3 27 software for visualization. Quantum theory of atoms in the molecule (QTAIM) topological analysis was also evaluated with the help of Multiwfn software package. Furthermore, the weak interaction involved during the adsorption studies was characterized by the noncovalent interaction (NCI) method using Multiwfn 3.7 dev and Gnuplot 28 software program.
Here, the relationship between electrical conductivity and E g can be seen in eq 1 29−31 where σ is electrical conductivity, k signifies the Boltzmann constant, and E g is the energy gap. Global reactivity descriptors were estimated based on Koopmans approximation using the following equations 32 where η, S, χ, and ω are chemical hardness, softness, electrophilicity, and nucleophilicity, respectively. Adsorption energies of the studied gases adsorbed on the respective nanocages were also computed using eq 8 35,36 E cage/gas is the total energies of the gas-adsorbed nanocage and E gas and E cage are the total energy of the adsorbed gas and isolated nanocage, respectively. The Basis set superposition error (BSSE) was evaluated by employing the counterpoise method suggested by Boys and Bernardi, and it is depicted in eq 9 37 cluster gas cluster (9) The transition between the recovery time of a sensor and adsorption energy is presented in eq 10 31,38−40 i k j j j y where τ is the recovery time, υ 0 is the attempt frequency and its value is taken as 10 −12 s −1 as reported by several authors, 40,41 E ads denotes adsorption energy, k and T represent Boltzmann's constant (8.62 × 10 −5 eV/K) and temperature (30 s 0 K), respectively. The optimized geometry of the studied gases is presented ( Figure 1). 42−44

Geometric and Structural
Analysis. Geometry optimization of Ca 12 O 12 nanocages was evaluated using the DFT/B3LYP-GD3(BJ)/6-311+G(d,p) method. The studied Ca 12 O 12 nanocage comprises eight hexagonal rings and six tetragonal rings, as shown in Figure 2. The Ca−O bond consists of two bonds, namely, a Ca−O bond between a hexagonal ring and a tetragonal ring, 64 and a Ca−O bond between two hexagonal rings. The Ca−O bond length existing between the two hexagonal rings was found to be 2.158 Å, while the Ca−O bond length exhibited between a hexagonal and a tetragonal was 2.197 Å. Initially, the adsorption of the studied gases (CO 2 , SO 2 , NO 2 ) on the Ca 12 O 12 nanocage was evaluated at different positions on the studied nanocage. The considered positions are as follows: on the center of the tetragon, on the center of the hexagon, on the and bonds, and on top of Ca and O atoms. However, after optimization of the adsorbed gases at different positions, the results show that the adsorbed gases preferred to be adsorbed on top of the Ca and O atoms as a result of the high electropositive and electronegative nature of the Ca and O atoms, respectively. Thus, the highly electronegative oxygen atoms present in the gases bind on top of the highly electropositive Ca atom, while the less electronegative atoms like sulfur and carbon atoms find its route on top of the O atom of the nanocage with the only exception of the nitrogen atom of the NO 2 gas, which preferred to bind to the Ca atom as a result of its high electronegativity close to that of the O atom present in the cage. Moreover, after adsorption of the gases (CO 2 , SO 2 , NO 2 ) on the Ca 12

Frontier Molecular Orbital.
Frontier molecular orbital (FMO) analysis was computed on the isolated nanocage and on the gas-adsorbed nanocage to characterize the reactivity, charge transfer, electrical conductivity, and stability occurring within each surface. 29,45−47 Basically, the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) are the primary orbitals that constitute the Frontier molecular orbitals. 48,49 In this arena, the orbital with electron-donating ability is termed the HOMO, while the orbital capable of accepting electrons is termed the LUMO. The discrepancy between the HOMO and LUMO is referred to as the energy gap. The energy gap is fully embodied for depicting the information on the reactivity, charge transfer, electrical conductivity, and stability of a particular structure. The higher the value of energy gap exhibited by a structure, the more stable and the lower the electrical conductivity, reactivity, and charge transfer that occurs within the compound, while the lower the energy gap, the lower the stability and greater will be reactivity, electrical conductivity, and charge transfer taking place within the structure. 50−53 The results obtained from the frontier molecular orbital analysis of the studied systems are presented in Table 2. From the result presented in the table, the isolated Ca 12 O 12 nanocage expressed an energy gap of 4.1176 eV at the Fermi level of −3.0526. However, after adsorption of the gases (CO 2 , SO 2 , NO 2 ) on the isolated Ca 12 O 12 nanocage, the energy gap of CO 2 @Ca 12 O 12 and SO 2 @Ca 12 O 12 nanocages was observed to increase with energy gap values of 4.1791 and 4.1808 eV at the Fermi level of −3.3005 and −3.3108 eV, respectively, while the NO 2 @Ca 12 O 12 nanocage demonstrated a decrease in the energy gap in comparison to the isolated Ca 12 O 12 nanocage possessing an energy gap of 2.0270 eV at the Fermi level of −4.5888 eV. At this end, the large energy gap of CO 2 @Ca 12 O 12 and SO 2 @Ca 12 O 12 nanocages compared to that of the isolated Ca 12 O 12 nanocage reflects the stable adsorption of CO 2 and SO 2 gas on the Ca 12 O 12 nanocage, while the low energy gap value of the NO 2 @Ca 12 O 12 nanocage compared to the isolated Ca 12 O 12 nanocage indicates unstable adsorption of the NO 2 on the Ca 12 O 12 nanocage with E g value less than 4 eV. From this line of reasoning and variations in the energy gap upon the preferential adsorption of the respective gases, we can infer that the Ca 12 O 12 nanocage is a better nanosensor for sensing CO 2 and SO 2 gases than NO 2 gas. This can be further confirmed based on the relationship of energy gap with electrical conductivity and the notion that potentiometric and voltammetric sensors are designed in line with either an increase or decrease in the energy gap upon adsorption. 54 The increase/decrease in the energy gap prior to adsorption could also suggest a possible transition of the Ca 12 O 12 nanocage from an insulator to a semiconductor and therefore could also facilitate the better sensing attributes exhibited in the case of CO 2 and SO 2 adsorption. However, NO 2 could also be sensed by the studied nanocage; nonetheless, the unfavorable nature of the adsorption by virtue of the dramatic decrease in energy gap, which is directly related to a decrease in conductivity, makes the adsorption process unfavorable and thus hinders the stability of the nanocage during the adsorption process. The exact reduction in energy gap was observed to be 2.1% for NO 2 @Ca 12 O 12 , which is dramatic in comparison with CO 2 (0.0615%) and SO 2 (0.0632%) adsorption and therefore further validates the unfavorable adsorption nature of this system. To confirm that charge was transferred from the adsorbed atmospheric pollutants (CO 2 , SO 2 , NO 2 ) to the Ca 12 O 12 nanocage, as reported in Section 3.1, we visualized their HOMO−LUMO plots, as seen in Figure 3. As evident from the plot, the HOMO of the isolated Ca 12 O 12 nanocage is concentrated only on the oxygen atoms of the nanocage, while the LUMO is evenly distributed on the oxygen and calcium atoms of the isolated Ca 12 O 12 nanocage. The HOMOs of the gas-adsorbed nanocages are localized only on the adsorbed gases (CO 2 , SO 2 , NO 2 ), while the LUMOs are majorly distributed on the Ca 12 O 12 nanocage. Thus, validating that charge was transferred from the adsorbed gases to the Ca 12 O 12 nanocage. Moreover, as reported previously, energy gap (E g ) determines the electrical conductivity of a system in the sense that as the energy gap decreases, the electrical conductivity of the system increases, while as the energy gap increases, its electrical conductivity decreases. The relationship between these two terms is summarized in eq 1.

Global Reactivity Descriptors.
Global reactivity descriptor was also considered in this study to confirm the chemical reactivity and natural stability of the studied isolated and gas-adsorbed nanocages. According to Koopmans'  theorem, global reactivity descriptor parameters such as ionization potential (IP), electron affinity (EA), global hardness (η), global softness (S), chemical potential (μ), electronegativity (χ), and electrophilicity (ω) are essential for characterizing the reactivity and stability of a compound. 32−34 Global reactivity descriptors of the studied systems estimated at the DFT/B3LYP-GD3(BJ)/6-311+G(d,p) level are presented in Table 3. Here, the ionization potential is related to the negative of the HOMO energy, while electron affinity is tagged to the negative of the LUMO energy. From the Chemical potential also gives important information on the reactivity of a particular compound with respect to polarizability. A high value of chemical potential for a compound indicates that the compound can easily be polarized in the presence of an external electric field or chemical reagent, while a low value in chemical potential suggests a lower effect of the external electric field or chemical reagent on polarizing the compound. In this lane, the NO 2 @Ca 12 O 12 nanocage also showed the highest value of chemical potential (−4.5888 eV) than all of the studied nanocages, indicating that it is the most reactive and unstable system compared to other studied   systems. This result also is in total agreement with the FMO and global softness and hardness results. Next, electronegativity and electrophilicity can also be utilized to characterize the reactivity of a compound. More specifically, electronegativity is the tendency of a particular compound to give out electrons.

NBO Analysis.
To validate the nature of the donor− acceptor orbital interaction persisting between the adsorbed gases on the selected nanocage, we employed the natural bond orbital (NBO) analysis to this effect. The NBO method serves as an approach for narrowing down the complex Schrodinger equation to a simple chemical bonding concept for its users to assimilate. 54 In addition, NBO analysis also gives a good highlight on the intermolecular charge transfer and electron delocalization taking place between the adsorbed gases and the studied nanocage. 55−57 In this study, NBO analysis was established using the DFT/B3LYP-GD3 (BJ)/6-311+G(d,p) method. The strength of interaction occurring between the donor and acceptor orbital is characterized by stabilization energy (E 2 ). The more intense the donor−acceptor orbital interaction, the higher the value of stabilization energy. The stabilization energy experienced by the donor−acceptor orbitals of the studied systems was calculated in line with our previous work. 58 The stabilization energy constituting the most interacting donor−acceptor orbitals of the studied systems is shown in Table 4. From the result, the isolated Ca 12 O 12 nanocage was found to exhibit the bonding donor− acceptor interaction of σ → σ* and the nonbonding interaction of LP → σ*. Systematically, the σ → σ* bonding interaction was observed between the donor and acceptor orbitals of However, for the CO 2 @Ca 12 O 12 nanocage, the most persisting interactions were obvious from the donor−acceptor orbitals of LP → LP*, π* → LP, π* → σ*, and π* → LP*. The LP → LP* nonbonding interaction was visible in LP (3)

Density of States (DOS).
The density of states plots have been utilized to further give insight into the charge density transfer arising from intermolecular interactions of the gases with the nanostructured surface. 59−61 Partial density of states (PDOS) explicates the contributions of individual atomic and molecular orbitals to distinct quantum states in the studied nanostructured materials. 62 The conductivities of the surfaces are also revealed from the DOS plots more explicitly. The PDOS of the surface along with the adsorbed gases is shown in Figure 4, while the energy gap and total DOS are shown in Figure 5. The s, p, and d orbitals are observed to contribute the maximum to the HOMO energies in the PDOS plots of the nanosurface, while the LUMO has its maximum contributions from the s-and p-hybridized orbitals. In the three different adsorption configurations of the adsorbed gases on the nanosurfaces, the electronic hybridization from the atomic orbitals was observed to change considerably with major contributions from the d and s atomic orbitals to the LUMO, while the HOMO was observed to be dominant in the adsorbed gases and to be absent in the surface of the adsorbed cases, signifying significant charge density delocalization from the surface to the gas fragments and vice versa. Prior to adsorption of the gases (CO 2 , NO 2 , SO 2 ) on the Ca 12 O 12 nanocage, negative LUMO density was observed to be dominant in the ring cage, whereas after the adsorption of the gases, the LUMO density was observed to change considerably, and the LUMO at the nanocage centers changed to positive density, thus confirming the electron density transfer from the surface to the gases. The HOMO in all cases for the adsorbed nanocages is localized majorly in the CO 2 , NO 2 , and SO 2 fragments. This result clearly shows that the delocalization of charge density occurs upon the adsorption of CO 2 , NO 2 , and SO 2 , and considerable changes in energy gap, as shown in Figure 4b, were observed in both the PDOS and total DOS plots, thus affirming the sensitivity of the surface to the adsorbed gases.
3.6. Molecular Electrostatic Potential Analysis. The visualization of molecular electrostatic potential surfaces is highly essential for the wholistic comprehension of electron density localization, biointeraction, hydrogen bonding interactions, and the detection of potential reactive sites in molecules. Regions of high electron densities are explicated by low values of electrostatic potential, and high ESP values often express the relative absence of electron density. 63,64 To understand and predict the most susceptible regions of both nucleophilic and electrophilic adsorption sites, the ESP isosurface plot was obtained from the B3LYP/6-311+G(d,p) optimized geometry. The molecular electrostatic potential (MEP) isosurface is shown in Figure 6. It clearly shows that the negative electrostatic density regions are localized on the oxygen atoms of the clusters, sulfate, carbonate, and nitrate anions adsorbed on the nanocages, while the electropositive zones are located on the metal centers of the nanoclusters, in accordance with the Mulliken population distribution. The regions of low electrostatic potential density are marked in blue, while the negative ESP regions are marked in red. The ESP isosurface clearly shows that regions of high electron density, which could act as potential adsorption sites, are localized on the oxygen atoms of the nanoclusters, whereas the region with the strongest attraction potential is the red-colored surface on the nanocluster and exhibits a high propensity for electrophilic adsorption. Positive ESP regions marked in white are minimally dispersed in between the metal centers and oxygen atoms of the adsorbed gases.  3.7. Adsorption of CO 2 , SO 2 , and NO 2 on the Ca 12 O 12 Nanocage. Adsorption energy (E ads ) and thermodynamic parameters were also evaluated to confirm the type of adsorption and the feasibility of adsorption of the studied gases on the Ca 12 O 12 nanocage during the adsorption process. In this present study, adsorption energy and thermodynamics parameters of the investigated gas-adsorbed nanocages were evaluated using the DFT/B3LYP-GD3(BJ)/6-311+G(d,p) theory level. As obvious from our result presented in Table  5, it is clearly observed that all of the gas-adsorbed nanocages exhibited negative values of adsorption energy, signifying a favorable adsorption process. Also, taking into consideration the calculated thermodynamics parameters such as enthalpy of adsorption (ΔH), Gibb's free energy of adsorption (ΔG), and entropy of adsorption (ΔS) of the gas-adsorbed nanocages, the adsorption of all of the studied gases presented negative values of ΔH and ΔG, while the ΔS value was positive. This result revealed that the adsorption process of the studied gases on the Ca 12 O 12 nanocage is favorable and spontaneous. Here, the E ads of CO 2 @Ca 12  .82 kcal/mol, and 465.14 cal/mol K −1 , respectively. To sum up, we can infer that the high adsorption energy of CO 2 @ Ca 12 O 12 and SO 2 @Ca 12 O 12 can be related to chemisorption, while low adsorption energy of NO 2 @Ca 12 O 12 corresponds to physisorption; this is consistent with other studies. 65,66 Thus, this result is also in tandem that the adsorption of CO 2 and SO 2 on the Ca 12 O 12 nanocage is stable adsorption, while that of NO 2 adsorption is unstable adsorption.

Quantum Theory of Atoms in Molecule (QTAIM).
Quantum theory of atoms in molecule is a paramount quantum mechanics tool used for analyzing the type of chemical interaction and strength of the interaction occurring between two bonded atoms. 35−37,67 QTAIM provides adequate information on the type of inter-and intramolecular interactions such as covalent (shared) interaction and noncovalent (closed shell) interactions, e.g., electrostatic interaction, van der Waals interaction, and hydrogen bond interaction that is evident between two bonded atoms. 68 Also, QTAIM depends fully on the electron density or charge distribution present in the chemical bond interaction in the sense that a decrease in in the electron density corresponds to a closed-shell interaction, while an increase in electron density is in relation to a covalent (shared) interaction. 69 Herein, Bader's topological analysis 70 was utilized for characterization of the nature and strength of chemical bond interaction and electron density distribution between the sensed gases and the Ca 12 O 12 nanocage at the DFT/B3LYP-GD3(BJ)/6-311+G-(d,p) level of theory using the Multiwfn software package. The B3LYP-GD3(BJ) hybrid exchange−correlation functional with D3 version of Grimme's dispersion correction incorporated with Becke−Johnson damping correction was employed for the characterization of these interactions due to the fact that it can accurately predict weak interactions. As proposed by Bader, two or more atoms involved in an intra-and intermolecular interaction are linked by a bond path. In the same line, a saddle point along the bond path, which indicates an area of maximum distribution of electron density, is associated with the bond critical point (BCP). Several parameters can be obtained from a bond critical point between two or more interacting atoms, which is crucial for characterizing the nature and strength of a chemical bond interaction. A few among those parameters are electron density ρ(r), Laplacian of electron density ∇ 2 ρ(r), Lagrangian kinetic energy G(r), potential energy density V(r), total energy density H(r), electron localization function (ELF), localized orbital locator (LOL), bond ellipticity (ε), and eigenvalues of the diagonalized Hessian matrix (λ 1 , λ 2 , λ 3 ). More importantly, from the abovementioned parameters, when ∇ 2 ρ(r) < 0 and H(r) < 0, it indicates covalent (shared) interaction, while a noncovalent (closed shell) interaction originating from weak hydrogen bond, van der Waals interaction, and electrostatic interaction exist when ∇ 2 ρ(r) > 0 and H(r) > 0. However, a partially covalent interaction is prompt to occur when ∇ 2 ρ(r) > 0 and H(r) < 0. In addition, G(r)/|V|(r) > 1 confirms that  the type of chemical bond interaction is noncovalent (closed shell) in nature, while covalent (shared) interaction is prominent when G(r)/|V|(r) < 0.5. Similarly, partially covalent interaction is prevalent when G(r)/|V|(r) is between 0.5 and 1. Specifically, ELF occurs as a result of local excess kinetic energy density, which is attributed to Pauli repulsion. The ELF value is always observed in the range of 0−1, and when its value is between 0.5 and 1, it symbolizes the delocalization of electron density. ELF < 0.5 indicates the presence of noncovalent (closed shell) interactions, while ELF > 0.5 signifies that the type of chemical bond interaction is that of a covalent (shared) interaction. In the same light, when LOL > 0.5, it indicates that electron density is localized, while the delocalization of electron density appears when LOL < 0.5. Furthermore, the strength of the bond formed during the intermolecular interaction between the adsorbed gas and the Ca 12 O 12 nanocage can be characterized by the eigenvalues of the diagonalized Hessian matrix (λ 1 and λ 3 ). In characterizing the strength of the bond formed, a high value of |λ 1 /λ 3 | obtained from the resulting bond formed indicates that the bond is strong. Another significant topological parameter is the bond ellipticity (ε), which measures the extent of accumulation of charge based on the orbital of the electronic structure. Bond ellipticity also conveys useful information on the stability of a bond. A high bond ellipticity value (ε > 1) demonstrates that the bond formed during the chemical interaction is unstable. The results obtained from the topological analysis of the studied gas-adsorbed nanocages are presented in Table 6 and More interestingly, bond ellipticity (ε) values of the studied gas-adsorbed nanocages are less than 1, indicating that bonds formed during the interaction are stable. However, the ε value of the N 27 −O 7 interaction that arises from the adsorption of NO 2 gas on the Ca 12 O 12 nanocage was found to be higher than that of other interactions, which implies that the bond formed during the interaction is less stable compared to those visualized on the adsorption of CO 2 and SO 2 on the Ca 12 O 12 nanocage. This result also supports the unstable adsorption of NO 2 gas on the Ca 12 O 12 nanocage. Moreover, Ca−O interactions exhibited higher |λ 1 /λ 3 | values, indicating that the strength of their bonds is very strong.
3.9. Noncovalent Interaction (NCI) Analysis. Even though QTAIM analysis can characterize noncovalent interactions, it lacks accuracy in predicting noncovalent interactions associated with weak interactions such as van der Waals interactions, hydrogen bond interactions, and πstacking interactions, which are essential in the formation of chemical bonds. 71−73 To tackle this bottleneck between our adsorbed gases and the Ca 12 O 12 nanocage, we employed a real space method known as noncovalent interaction (NCI) analysis. The strength and type of noncovalent interaction present can be characterized using the product sign of the second eigenvalue of diagonalized Hessian matrix sign (λ 2 ) and electron density ρ(r). Hence, the isosurface plot constituting the sign (λ 2 )ρ(r) real space function as the x-axis and reduced density gradient (RDG) on the vertical axis can brilliantly exhibit the strength and type of interaction that is consistent during adsorption of the studied gases and the Ca 12 O 12 nanocage. In characterizing the weak interaction based on the RDG isosurface plot, the RDG isosurface value was set at 0.5 a.u. From the RDG isosurface plot as elucidated in Figure  8, when sign(λ 2 )ρ(r) < 0 reflects strong attraction (blue

ACS Omega
http://pubs.acs.org/journal/acsodf Article region), while van der Waals interaction is visible when sign(λ 2 )ρ(r) ≈0 (green region). However, a strong repulsive interaction is obvious when sign (λ 2 )ρ(r) > 0 (red region). As evident from our RDG isosurface plots, it can be seen that for the gas-adsorbed nanocages, spike indicates strong attraction, and strong repulsion was prominent while it was absent for the isolated Ca 12 O 12 nanocage. Also, from the NCI plots, strong repulsive interaction was present in the gas-adsorbed nanocages. Interestingly, strong attraction and van der Waals interaction was found to exist in all of the gas-adsorbed nanocages, but the density of the spike characterizing the region of these interactions was seen to be higher in the CO 2 @ Ca 12 O 12 gas-adsorbed nanocage and the SO 2 @Ca 12 O 12 gasadsorbed nanocage than that in the NO 2 @Ca 12 O 12 gasadsorbed nanocage. This clear observation also confirms the classification of adsorption of CO 2 and SO 2 on the Ca 12 O 12 nanocage as stable adsorption, while the adsorption of NO 2 on the Ca 12 O 12 nanocage is unstable.

Recovery Time.
The recovery time of a sensor is very essential in the sensing mechanism. A sensor exhibiting long recovery time indicates strong adsorption, and thus the desorption of the adsorbate utilized would be difficult. 38 The recovery time of a sensor is always determined experimentally by heating the sensor at a higher temperature or with the aid of vacuum ultraviolet (UV) light. 39,40 In addition, during the adsorption of an adsorbate on a sensor, high adsorption energy will lead to a long recovery time of the sensor. Here, we considered the recovery time of our nanosensor after the adsorption of CO 2 , SO 2 , and NO 2 gases using the relationship between the recovery time and the adsorption energy as used by several authors, and it is presented in eq 10 in Section 2. The computed result for the recovery time is presented in Table 7. As evident from the table, it is observed that the recovery of NO 2 from the surface of Ca 12 O 12 is shorter (0.46 s) compared to the recovery of CO 2 (9.607 s) and SO 2 (8.028 s), and this correlates perfectly with the computed adsorption energies. This further validates the unfavorable adsorption nature of NO 2 , and thus, this gas will easily be desorbed from the surface. In fact, the sensitivity of the surface toward the NO 2 gas is very small from this standpoint, and the gas relatively spends only limited time on the adsorbent surface before being desorbed. Moreover, among the sensed gases, the desorption of SO 2 gas from the surface of the Ca 12 O 12 nanosensor is much more difficult due to its high adsorption energy (−5.85 eV) and thus corresponds to a long recovery time of the simulated nanosensor.

CONCLUSIONS
Conclusively, we have meticulously executed quantum mechanical calculations on the Ca 12 O 12 nanocage as a trustworthy nanosensor for sensing CO 2 , SO 2 , and NO 2 with the aid of high-level density functional theory at the B3LYP-GD3(BJ)/6-311+G(d,p) level of theory. Electronic properties such as frontier molecular orbital (FMO), natural bond order (NBO), density of states (DOS), and molecular electrostatic potential (MESP) were determined in this work. Similarly, interaction properties like adsorption energy, quantum theory of atoms in molecule (QTAIM), and noncovalent interaction (NCI) were explicitly evaluated. In addition, the recovery time of the Ca 12 O 12 nanosensor was also estimated on desorption of the titled gases. The results from the adsorption energy of the studied systems revealed that CO 2 @Ca 12 O 12 , SO 2 @Ca 12 O 12 , and NO 2 @Ca 12 O 12 gas-adsorbed nanocages exhibited remarkable adsorption energy values of −2.01, −5.85, and −0.69 eV, respectively. The high adsorption energy of CO 2 @Ca 12 O 12 and SO 2 @Ca 12 O 12 gas-adsorbed nanocages is associated with chemisorption (stable adsorption), while the low adsorption energy of NO 2 @Ca 12 O 12 gas-adsorbed nanocage can be related to physisorption (unstable adsorption). Frontier molecular orbital (FMO) and global reactivity descriptor also confirmed the stable adsorption nature of CO 2 and SO 2 on the Ca 12 O 12 nanocage and the unstable adsorption of NO 2 on the Ca 12 O 12 nanocage. This conclusion was further affirmed by carefully observing the variations in energy gap. Thus, the resultant increase in the energy gap of the Ca 12 O 12 nanocage upon the preferential adsorption of CO 2 and SO 2 , making the conductivity of the nanocage to tend toward that of semiconductors, was used to validate this observation. Several reports show that the increase or decrease in the energy gap of nanosensor materials affects the sensing attributes of the systems and is often used as a broader mark to assess the efficacy of sensor materials toward a specific adsorbent. The exact change in the energy gap for NO 2 adsorption was computed to be 2.1%, which shows a dramatic reduction in stability and conductivity in comparison with other studied gases and hence affirms the inability of the Ca 12 O 12 nanosensor material to sense this gas effectively. In addition, the results from the topological analysis (QTAIM) were also in agreement with the abovementioned result in the sense that the bond ellipticity values originating from the adsorption of CO 2 and SO 2 on the Ca 12 O 12 nanocage were greater than that of NO 2 adsorption. Also, noncovalent interaction analysis revealed that the adsorption of CO 2 and SO 2 on the Ca 12 O 12 nanocage is strong and stable adsorption by revealing denser colored spikes at the strong attraction region (blue region), while the adsorption of NO 2 was also verified to be weak and unstable with the appearance of less-dense colored spikes at the strong attraction region (blue region). The results obtained from the computations of desorption time revealed a shorter recovery time for the Ca 12 O 12 nanosensor after the adsorption of NO 2 gas due to the weak and unstable adsorption nature and therefore suggest that NO 2 can easily desorb from the surface of the studied nanocage than being adsorbed. At this point, we can strongly infer that our simulated Ca 12 O 12 nanocage is more efficient and sensitive in sensing CO 2 and SO 2 gas than NO 2 .