In density functional theory of chemical reactivity the chemical potential (μ) and the hardness (η) are identified with the first and the second derivatives of the energy with respect to the number of electrons. In order to determine the values of these descriptors for isolated species, it is common to make use of a smooth quadratic interpolation between the N0-1, N0, and N0+1 electron systems ( N0 is an integer). This procedure, known as the one parabola model, leads, for the interpolation of the energy, to μ=-( I+A)/2 and η=I-A , where I and A are the vertical first ionization potential and electron affinity, respectively, of the isolated species. However, when two species are together, say A and B, it seems reasonable to assume that the values of the chemical potential and the chemical hardness of A and of B will change with respect to their values when the two species are isolated from each other. In this work, we will show that through a two parabolas interpolation between the N0-1, N0, and N0+1 electron systems, and introducing a parameter that is assumed to correct the curvature of the two parabolas of A and of B, because of the presence of both species, leads to slightly modified expressions for μ and η, with respect to the ones corresponding to the one parabola model. These new expressions are similar to those obtained by Miranda-Quintana and Ayers, from considering the presence of the interacting species as a perturbation in the grand canonical ensemble. The corresponding analysis for the Fukui function (f (r)) and the dual descriptor (△f (r)), which are defined as the first and second derivatives of the electronic density with respect to the number of electrons, will be also presented. Finally, we will discuss some examples to show the usefulness of the modified expressions.

Chemical potential, chemical hardness, Fukui function and dual descriptor for interacting systems

255th National Meeting (2018)

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