Electrodonating and Electroaccepting Powers

By introducing an electron bath that represents the chemical environment in which a chemical species is immersed, and by making use of the second-order Taylor series expansions of the energy as a function of the number of electrons in the intervals between N − 1 and N, and N and N + 1, we show that the electrodonating (ω-) and the electroaccepting (ω+) powers may be defined as ω∓ = (μ∓)2/2η∓, where μ∓ are the chemical potentials and η∓ are the chemical hardnesses, in their corresponding intervals. Approximate expressions for ω- and ω+ in terms of the ionization potential I and the electron affinity A are established by assuming that η- = η+ = η = μ+ − μ-. The functions ω∓(r) = ω∓ f ∓(r), where f ∓(r) are the directional Fukui functions, derived from a functional Taylor series for the energy functional truncated at second order, represent the local electrodonating and electroaccepting powers.