Generalized Shannon’s entropy as generator of local density functionals

Abstract

In this letter, we present a relationship among Shannon’s generalized entropy and kinetic energy, exchange energy, and Coulomb energy density functionals, also we showed that the electron density gradient of Fisher’s entropy may be simplified to density powers, such that it is possible to write a general expression of the local electron energy as a linear combination of generalized entropies. The functional proposed was tested in the first ten neutral atoms and on a set of 1864 molecules. The proposed local density functional overestimates the energy in cases highly correlated electronic systems.