Fukui functional analysis
The Fukui function is one of the most important concepts in Density Functional Theory (DFT). It is widely used to predict active sites and provides information about local site reactivity within the molecule. The Fukui function can be defined as,
\(f=\left(\frac{\partial\rho(r)}{\partial N}\right)_{v}\) (1)
Where N is the number of atoms within the molecule, ρ(r) is electron density in the partial derivatives, v represents the external potential. Due to discontinuity, this equation cannot be evaluated directly[29,30]. Hence, the following modified equation is used for calculating Fukui function[31]
\(\text{\ f}_{k}^{+}=\left[q\left(n+1\right)-q\left(N\right)\right]\)For nucleophilic attack (2)
\(\text{\ f}_{k}^{-}=\left[q\left(N\right)-q\left(n-1\right)\right]\)For electrophilic attack (3)
\(\text{\ f}_{k}^{0}=\frac{1}{2}\left[q\left(n+1\right)-q\left(n-1\right)\right]\)For radical attack (4)
Where +, -, and 0 signs denote the nucleophilic, electrophilic and radical attack.