**3.6 Correlation between dipole moment (μ) and Hammett's substituent constants (σ)**

As shown in **Table 8** and **Figure 15**, the dipole moments (μ) calculated at DFT// B3LYP/6-31+g(d,p) for these series of benzofurazans **1a-f** are highly sensitive to the electronic nature of the substituent X, e.g., it decreases from μ = 17.08 D to μ = 7.23 D as the substituent X changes from a strong electron-withdrawing group (X = Cl) to a strong electron-donating group (X = morpholine). The linear relationship as expressed by Eq. (9) relates the dipole moment μ for **1a-f** directly to the Hammett's substituent constant σ.

#### **Figure 15.**

*Correlation between calculated dipole moment (μ) for the benzofurazans 1a-f and Hammett's substituent constant σ calculated at DFT//B3LYP/6-31+ g(d,p) in acetonitrile.*

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

$$
\mu = 9.135 \text{--} 9.839 \text{ } \sigma \left( \text{r}^2 = 0.9908 \right) \tag{9}
$$

On the other hand, comparing the electrophilicity parameter *E* and global electrophilicity index *w* with the dipole moment (μ), we found that the *E* and values *w* correlate well with the μ as shown in **Figure 16**. In addition, the high dipole moment values being related to the strong effect exerted by the electron-donating group X clearly indicate that our benzofurazans **1b-j** can offer certain potential for nonlinear optical (NLO) applications.

**Figure 16.** *Correlation E vs. μ and w vs. μ for the benzofurazans 1a-fcalculated at DFT//B3LYP/6-31+ g(d,p) in acetonitrile.*

#### **Figure 17.**

*Correlations of the global electrophilicity index wVC of the benzofurazans 1a-f versus the Hammett's substituted σ<sup>p</sup> values. The values of wCV are given in Table 1. The σ<sup>p</sup> values were taken from Ref. [63, 64].*
