**2. Computational method**

The stable structures of the studied systems (CX[4] and CX[4]-gas) have been calculated with the DFT method by using the B3LYP [16, 19–21] coupled to the D3BJ (empirical Becke and Johnson damping dispersion corrections) in combination with the 6-31 + G(d) basis set, as implemented in GAUSSIAN 09 package [22] and the Gauss View [23] as a visual program. We have been calculated the binding energies of the CX[4]-gas take into account the Basis Set Superposition Error (BSSE) counterpoise (CP) correction energy of Boys and Bernardi [24].

The binding energies are given by the following formula:

$$\mathbf{\bar{A}}E\_{\text{CX}[4]-gas} = E\_{\text{CX}[4]-gas} - E\_{\text{CX}[4]} - E\_{\text{gas}} + B\text{SSE} \tag{1}$$

where ECX[4]-gas, ECX[4] and Egas are the total energies of host-guest and host or guest molecules. The electronic parameters of the studied complexes are very effective to show the sensibility of the specific gas inside or outside the cavity. We analyzed then the infrared spectrum of these complexes using the DFT/B3LYP-D3 method. The nature of the interaction between the CX[4] molecule and the pollutant gases is better explained using the Non covalent interaction via RDG analysis [25].

### **3. Results and discussions**

#### **3.1 Geometry optimizations**

The CX[4]-gas complexes have been optimized at the DFT/B3LYP-D3 (**Figure 1**). In this study, we have placed the NO3, NO2, CO2 and N2 gas in the exo or endo-cavity positions. **Table 1** presents the Binding energy Eb (in (kcal/mol)) of CX[4]-gas complexes. The binding energy value of the CX[4]-CO2 is equal to 21.33 kcal/mol (see **Figure 1**). We show that, the CX[4]-CO2(endo) complex is more stable than that of CX[4]-CO2(exo). In addition, from the CX[4]-NO3 complex, the NO3 gas has placed in the endo or the exo-cavity position. In this situation, we have obtained a divergence in the case of the interaction of CX[4] with NO3 outside the cavity that is why, we have tested the case where the NO3 gas perpendicular to the 4-fold axis of CX[4] and a parallel position of the NO3 (NO3 parallel to the 4-fold axis). We have been noted a very weak energy of the CX[4]-NO3(perp.) complex in comparison with the CX[4]- NO3(paral.) complex. Moreover, we have noted that the interaction between the CX[4] molecule and the NO3(paral.) is stabilized by a low dipole moment. We have calculated

**303**

**Table 1.**

**Figure 1.**

*Possibility of Complexation of the Calix[4]Arene Molecule with the Polluting Gases…*

two positions for the guest N2: the N2 gas located on the outside of cavity and this gas located perpendicular to the 4-fold axis of CX[4] molecule. We have shown that the CX[4]-N2(endo) has a very strongest energy, which explain that this geometry is more stable than CX[4]-N2(exo) (see **Table 1**). The binding energy (Eb) of the stable complex is equal to 18.90 kcal/mol. Finally, from the CX[4]-NO2(exo) complex, we note that the NO2 gas is located in the outside of the H-link network of the phenolic hydroxyl groups. The binding energy of the CX[4]-NO2(endo) complex is equal to 20.54 kcal/mol (see **Table 1**). As we see, The binding energy of the CX[4]-NO2(endo)

*Optimized geometries of the CX[4]-CO2(endo) (a), CX[4]-CO2(exo) (b), CX[4]-NO3(paral.) (c), CX[4]-NO3(perp.) (d), CX[4]-NO2(endo) (e), CX[4]-NO2(exo) (f\*), CX[4]-NO2(exo) (g\*), CX[4]-N2(endo) (h) and CX[4]-N2(exo)*

**Complexes Eb BSSE Eb (with BSSE)**

CX[4]-NO3(perp.) 16.51 6.05 22.56 CX[4]-N2(exo) 16.89 1.70 18.59 CX[4]-N2(endo) 16.90 1.80 18.70 CX[4]-NO2(exo)f\* 18.17 1.82 19.99 CX[4]-NO2(exo)g\* 18.11 1.80 19.91 CX[4]-NO2(endo) 17.83 2.71 20.54 CX[4]-CO2(endo) 18.62 2.71 21.33 CX[4]-CO2(exo) 18.10 2.71 20.81

*(i) complexes using B3LYP-D3BJ/6-31 + G(d) method (top view).*

*Binding energy Eb (in (kcal/mol)) of CX[4]-gas complexes.*

CX[4]-NO3 (paral.) 24.62 6.17

*DOI: http://dx.doi.org/10.5772/intechopen.93838*

*Possibility of Complexation of the Calix[4]Arene Molecule with the Polluting Gases… DOI: http://dx.doi.org/10.5772/intechopen.93838*

#### **Figure 1.**

*Environmental Issues and Sustainable Development*

molecule.

**2. Computational method**

**3. Results and discussions**

**3.1 Geometry optimizations**

possibility of the encapsulation of these gases by the CX[4] molecule to show the sensibility of this molecule to the polluting gases outside or inside the cavity. We have chosen the NO3, NO2, CO2 and N2 gas as guest's because they can be formed a dipole-dipole interactions and a CH…π hydrogen-bonding with the CX[4] molecule. By using the density functional theory (DFT) calculations, we have described the dynamic stabilities of the endo-vs. exo-cavity of the CX[4]-gas complexes. The vibrational properties of the CX[4]-gas complexes have been studied. The Molecular electrostatic potential studies of these host-guests complexes have been performed. The Non-covalent interaction via RDG function are very important to know the nature of the interactions between the specific guests and the CX[4]

The stable structures of the studied systems (CX[4] and CX[4]-gas) have been calculated with the DFT method by using the B3LYP [16, 19–21] coupled to the D3BJ (empirical Becke and Johnson damping dispersion corrections) in combination with the 6-31 + G(d) basis set, as implemented in GAUSSIAN 09 package [22] and the Gauss View [23] as a visual program. We have been calculated the binding energies of the CX[4]-gas take into account the Basis Set Superposition Error (BSSE) counterpoise (CP) correction energy of Boys and Bernardi [24].

where ECX[4]-gas, ECX[4] and Egas are the total energies of host-guest and host or guest molecules. The electronic parameters of the studied complexes are very effective to show the sensibility of the specific gas inside or outside the cavity. We analyzed then the infrared spectrum of these complexes using the DFT/B3LYP-D3 method. The nature of the interaction between the CX[4] molecule and the pollutant gases is better explained using the Non covalent interaction via RDG analysis [25].

The CX[4]-gas complexes have been optimized at the DFT/B3LYP-D3 (**Figure 1**). In this study, we have placed the NO3, NO2, CO2 and N2 gas in the exo or endo-cavity positions. **Table 1** presents the Binding energy Eb (in (kcal/mol)) of CX[4]-gas complexes. The binding energy value of the CX[4]-CO2 is equal to 21.33 kcal/mol (see **Figure 1**). We show that, the CX[4]-CO2(endo) complex is more stable than that of CX[4]-CO2(exo). In addition, from the CX[4]-NO3 complex, the NO3 gas has placed in the endo or the exo-cavity position. In this situation, we have obtained a divergence in the case of the interaction of CX[4] with NO3 outside the cavity that is why, we have tested the case where the NO3 gas perpendicular to the 4-fold axis of CX[4] and a parallel position of the NO3 (NO3 parallel to the 4-fold axis). We have been noted a very weak energy of the CX[4]-NO3(perp.) complex in comparison with the CX[4]- NO3(paral.) complex. Moreover, we have noted that the interaction between the CX[4] molecule and the NO3(paral.) is stabilized by a low dipole moment. We have calculated

[ ]− − [ ] [ ] = − −+ Ä*E E E E BSSE CX gas CX gas CX* 4 44 *gas* (1)

The binding energies are given by the following formula:

**302**

*Optimized geometries of the CX[4]-CO2(endo) (a), CX[4]-CO2(exo) (b), CX[4]-NO3(paral.) (c), CX[4]-NO3(perp.) (d), CX[4]-NO2(endo) (e), CX[4]-NO2(exo) (f\*), CX[4]-NO2(exo) (g\*), CX[4]-N2(endo) (h) and CX[4]-N2(exo) (i) complexes using B3LYP-D3BJ/6-31 + G(d) method (top view).*


#### **Table 1.**

*Binding energy Eb (in (kcal/mol)) of CX[4]-gas complexes.*

two positions for the guest N2: the N2 gas located on the outside of cavity and this gas located perpendicular to the 4-fold axis of CX[4] molecule. We have shown that the CX[4]-N2(endo) has a very strongest energy, which explain that this geometry is more stable than CX[4]-N2(exo) (see **Table 1**). The binding energy (Eb) of the stable complex is equal to 18.90 kcal/mol. Finally, from the CX[4]-NO2(exo) complex, we note that the NO2 gas is located in the outside of the H-link network of the phenolic hydroxyl groups. The binding energy of the CX[4]-NO2(endo) complex is equal to 20.54 kcal/mol (see **Table 1**). As we see, The binding energy of the CX[4]-NO2(endo)

complex is higher than that of CX[4]-CO2(exo/endo). Therefore, The CX[4]-NO2(endo) complex is more stable than others, which is explained by the lowest dipole moment.
