An electronic temperature definition for the reactive electronic species: Conciliating practical approaches in...

By working under the framework of the Helmholtz potential as a functional of the equilibrium density matrix, in this contribution, we provide theoretical evidence about a particular thermodynamic situation, where electronic species display their highest susceptibility to exchange electrons to or from surroundings. This situation is denominated as the electronic temperature condition. Neutral chemical species display their lowest possible hardness value at the electronic temperature condition, and remarkably, under this circumstance, the exchange of any amount of electronic charge will necessarily be translated into a net increase in the corresponding chemical hardness. Chemical response functions defined as partial derivatives of the Helmholtz potential with respect to the (average) number of electrons and evaluated at the electronic temperature condition provide comparable results than those obtained from the coarse quadratic approximation to the exact dependence of the electronic energy vs the number of electrons, including composite quantities as the electrophilicity index. In this context, we show that the exact Helmholtz potential dependence with respect to the number of electrons can accurately be approximated by "temperature dependent" polynomial fits (up to fourth order), evaluated at the electronic temperature condition.