*3.4.2 Correlation between electrophilicity parameter (*E*) and global electrophilicity index (*w*)*

Based on the data listed in **Table 6**, the plot of electrophilicity parameters *E* for these series of benzofurazans **1a-c** against their global electrophilicity index *w,* determined in this work, was constructed. As can be seen in **Figure 13**, the relationship between *E* and *w* values is linear (r<sup>2</sup> > 0.9799) and results in the following equation:

$$E = -29.785 + 1.545 \, w \tag{6}$$

It is interesting to note that the relationships parameters *E* versus *w* have also been reported by many authors [51–56]. The data in **Table 7** are illustrative in this regard. Interestingly, the plot of Eq. (6) can be used to estimate the unknown electrophilicity parameter *E* values of other para-substituted benzofurazans. Using the *w* values calculated in the present work by DFT//B3LYP/6-31+ g(d,p), the *E* of **1d** (X = morpholine, *E* = �18.01), **1e** (X = piperidine, *E* = �18.52), and **1f** (X = pyrrolidine, *E* = -18.78) have been obtained (The structures of title compounds are given in **Figure 2**). The detailed results are already listed in **Table 6**.

**Figure 12.** *Electrophilicity parameters E of 7-X-4-nitrobenzofurazans 1a-c. [27, 29].*

**Benzofurazan 1a 1b 1c 1d 1e 1f** *Structure-Property Relationships in Benzofurazan Derivatives: A Combined Experimental… DOI: http://dx.doi.org/10.5772/intechopen.99246*


### **Table 6.**

*Electrophilicity parameter (E) and global electrophilicity index (w).*

#### **Figure 13.**

*Correlation between experimentally determined electrophilicities (E) and global electrophilicity index (ω) calculated at DFT//B3LYP/6-31+ g(d,p) in acetonitrile for the benzofurazans 1a-c.*


#### **Table 7.**

*Correlations of the electrophilicity parameters E of some representative electrophiles with their global electrophilicity w values.*

It should be noted that these predicted values of electrophilicity parameters *E* are smaller by 1.5 units than those reported values by Raissi and co-workers [27]. In all cases, the agreement between the *E* values of benzofurazans **1d-f** estimated using DFT//B3LYP/6-31+ g(d,p) and previously reported with the same method of calculation, but recorded in water medium [27] is remarkably good [57–61]. It is noteworthy to mention that the observed deviations between results give lower accuracy owing to their dependence on solvent polarity and to the added diffuse basis functions, that have also been observed in numerous systems. Chamorro and co-workers, have also observed a satisfactory correlations between the electrophilicity parameter E of various benzhydrylium cations and their global electrophilicity index ω calculated at B3LYP/6- 31 g(d) and HF/6-31 g(d) levels of theory Model I (E = �41.60+ 3.57 ω+), Model II (E = �40.42+ 2.08 ω+), Model III (E = �38.66 + 2.44 ω+) and Model IV (E = �47.2+ 20.0 ω+) [62].

#### **3.5 Effect of substituents X on electrophilicity:** *E* **vs.** *σ* **and** *w* **vs.** *σ* **correlations**

Examination of the data in **Tables 6** and **8** show that the electrophilicity parameter (*E*) or global electrophilicity index (*w*) of benzofurazans **1a-c** appears to be significantly dependent on the electronic nature of the substituents X, i.e. the *E* or *w* decrease regularly from X = Cl to X = OCH3 leading to a nice Hammett-type plots [63, 64] (**Figure 14**), which are defined by the following Equations

$$E = -16.475 + 2.878 \text{ } \sigma \left( \text{r}^2 = 0.9984 \right) \tag{7}$$

$$w = 8.614 + 1.810 \,\sigma \, \left( \mathbf{r}^2 = 0.9897 \right) \tag{8}$$

Correlations between *E* and *σ* parameters or *E* and *w* of various system have also been reported by many authors [65–72]. Zenz and Mayr, have established that the *E* parameters for a series of trans-β-nitrostyrenes correlate well with σ<sup>p</sup> values of their substituents (E = �13.95+ 2.08 <sup>σ</sup><sup>p</sup> (r<sup>2</sup> = 0.9847)) [69]. Recently, Rammah and


*a The <sup>σ</sup> values were taken from Ref. [63, 64]. <sup>b</sup>*

*The <sup>σ</sup> values calculated by using Eq. (7) with E from Table 6. <sup>c</sup>*

*Calculated by using Eq. (8) with w from Table 6. <sup>d</sup>*

*The dipole moment μ values calculated in this work.*

#### **Table 8.**

*Hammett constants (σ) values and dipole moment (μ, D) values.*

*Structure-Property Relationships in Benzofurazan Derivatives: A Combined Experimental… DOI: http://dx.doi.org/10.5772/intechopen.99246*

#### **Figure 14.**

*Correlations of the electrophilicity parameter E and global electrophilicity index w versus the Hammett's substituted σ<sup>p</sup> values. The values of E and w are given in Table 6. The σ<sup>p</sup> values were taken from Ref. [63, 64].*

co-workers, have also observed a linear correlation between the electrophilicity parameters *E* of a series of 2-N-(4<sup>0</sup> -X-pheny1)-4,6-dinitrobenzotriazole 1-oxides and the Hammett's substituent constants *<sup>σ</sup>* (*<sup>E</sup>* <sup>=</sup> �11.15+ 2.28 *<sup>σ</sup>* (r<sup>2</sup> = 0.9878)). [65]

In order to test the applicability of Eq. (7) for the prediction of the Hammett's constants σ<sup>p</sup> of other groups, we have calculated the global electrophilicity index (*w*) of benzofurazans **1 g-j (1 g**: X = HNOH, **1 h:** X = HNNH2, **1i:** X = HNH and **1j:** X = HNCH3). The results are listed in **Table 9** which also includes the σ<sup>p</sup> values


*a The w values calculated in this work.*

*b The dipole moment <sup>μ</sup> values calculated in this work. <sup>c</sup>*

*The σ<sup>p</sup> Cal values calculated by using Eq. (8) with w from Table 5. <sup>d</sup>*

*The σ<sup>p</sup> Exp values were taken from Ref. [63, 64].*

#### **Table 9.**

*Comparison between calculated and experimental reported Hammett's constants σ<sup>p</sup> for the HNOH, HNNH2, HNH and HNCH3 groups.*

previously published [63, 64]. As well be seen, **Table 2** clearly shows that the calculated σ<sup>p</sup> values are in good agreement with the experimental data.

Most importantly, the satisfactory correlations shown in **Figure 14** can be employed to obtain more information about the unknown Hammett's substituent constants (σ) of morpholine, piperidine and pyrrolidine groups.

Substitution of the *E* and *w* values for benzofurazans **1d-f** into the correlation Eqs. (7) and (8), the Hammett's σ<sup>p</sup> values are thus obtained for the three leavinggroups. As can be seen in **Table 8,** the σ<sup>p</sup> values estimated in the present work using work using Eqs. (7) or (8) are similar but relatively large compared with those previously reported (0.47 < σ<sup>p</sup> < 0.24) [27]. The major reason for the overestimation can, at least in part, be understood in terms of solvent polarity and also the used on the basis set with diffuse functions.
