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 a within the DFT formalism. We find a = 2 [r3]/Z, in atomic units where Z is the atomic number and [r3] is the expectation of r3. This formula predicts qualitatively good values and tendencies for atoms with 4 less-than-or-equal-to Z less-than-or-equal-to 36. Furthermore, the associated radial induced dipole-moment density behaves as expected.