FUKUI

Compute, within the linear response perturbation theory, the nuclear Fukui function $\phi _I$ formally identified as a reactivity index of the density functional theory [108,109], according to the postulated criterion for $\delta \mu$ . The quantity $\delta \mu$ is the change in the electronic chemical potential $\mu$ and is given by

$$\delta \mu =\int f(\mathbf{r}) \delta V^{ext}(\mathbf{r}) d^3r = -\sum_I \phi_I \delta \mathbf{R}_I$$ (262)

where $\phi _I =(\partial \mathbf{F}_I/\partial N)_{V^{ext}}= -(\partial \mu /\partial R_I)_N$ , $N$ is the number of electrons, $f(\mathbf{r})$ the electronic Fukui function [109,110], $V^{ext}(\mathbf{r})$ the external potential at r, $\mathbf{R}_I$ the cartesian coordinate of the $I^{th}$ nucleus and $\mathbf{F}_I$ the force on the $I^{th}$ nucleus.