Analytical approximation to the local softness and hypersoftness and to their applications as reactivity indicators

Local density functional theory derivatives of the electron density have been calculated analytically for the set of canonical hydrogenic orbitals; original solutions have been obtained using the novel density gradient theorem. Results for the first and second derivatives of electron density over N (number of electrons) and over μ (chemical potential) have been demonstrated. Calculations of the state functions ΔN, ΔE, and Δμ disturbed by an external potential Δv(r) have been obtained via the concept of alchemical derivatives. The local softness s(r) and local hypersoftness [ds(r)/dN]v have been proved to provide crucial chemical information on the sensitivity of orbital density to the disturbance of the external potential Δv(r), leading to electron exchange ΔN and the corresponding changes of the state functions ΔE, Δμ. The results are fully compatible with the well-understood character of atomic orbitals in chemistry and open a perspective to applications to atoms, free or bonded.