Density-functional-theory softness kernel.

Abstract

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 \ensuremath{\alpha} within the DFT formalism. We find \ensuremath{\alpha}=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\ensuremath{\le}Z\ensuremath{\le}36. Furthermore, the associated radial induced dipole-moment density behaves as expected.