In eq. ( ) I, A, µ, and F are the ionization potential, electron affinity, chemical potential and the universal DFT functional, respectively. Δρ C and Δρ K represent changes in electron density when losing or gaining an electron, respectively. Higher order terms in eq. ( ), and following equations in this section, are not relevant for the discussion and will be omitted. Note that eq. ( ) expresses χ I as a function of the chemical potential. CDFT hardness also has a well-known approximation (the Parr-Pearson hardness, η T ), obtainable by finite-differences: