Shannon Entropy in Atoms: A Test for the Assessment of Density Functionals in Kohn-Sham Theory

Electron density is used to compute Shannon entropy. The deviation from the Hartree-Fock (HF) of this quantity has been observed to be related to correlation energy. Thus, Shannon entropy is here proposed as a valid quantity to assess the quality of an energy density functional developed within Kohn-Sham theory. To this purpose, results from eight different functionals, representative of Jacob's ladder, are compared with accurate results obtained from diffusion quantum Monte Carlo (DMC) computations. For three series of atomic ions, our results show that the revTPSS and the PBE0 functionals are the best, whereas those based on local density approximation give the largest discrepancy from DMC Shannon entropy.