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 [115,116], 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

$$\delta \mu =\int f({\bf r}) \delta V^{ext}({\bf r}) d^3r = -\sum_I \phi_I \delta {\bf R}_I$$ (24)

where $\phi _I =(\partial {\bf F}_I/\partial N)_{V^{ext}}= -(\partial \mu /\partial R_I)_N$, $N$ is the number of electrons, $f({\bf r})$ the electronic Fukui function [116,117], $V^{ext}({\bf r})$ the external potential at r, ${\bf R}_I$ the cartesian coordinate of the $I^{th}$ nucleus and ${\bf F}_I$ the force on the $I^{th}$ nucleus.