Density-functional-theory softness kernel

A model for the density-functional-theory (DFT) softness kernel is proposed. The model satisfies a number of known physical conditions such as translational invariance, the Hellmann-Feynman theorem, and the correct normalization of the linear-response function for a system with a constant number of electrons. Henceforth, explicit formulas are obtained for a number of DFT reactivity parameters. Our procedure is applied to derive a rather simple and compact formula to compute atomic static dipole polarizabilities α within the DFT formalism. We find α=2〈${\mathit{r}}^3$〉/Z, in atomic units where Z is the atomic number and 〈${\mathit{r}}^3$〉 is the expectation of ${\mathit{r}}^3$. This formula predicts qualitatively good values and tendencies for atoms with 4≤Z≤36. Furthermore, the associated radial induced dipole-moment density behaves as expected.