Tallberg, DFT17 Poster A20: Shannon entropy and correlation energy for electrons in atoms

In this work, we compute the Shannon entropy defined in terms of the one particle electron density ρ for some neutral and charged atomic systems. As shown recently by Nagy [1], the knowledge of Shannon entropy density, namely −ρ log ρ, is sufficient to know any physical observable for a Coulomb system. This definition of quantum entropy is here used to measure the entanglement of electrons due to Coulomb correlation. In particular, we compare different calculations performed with highly correlated methods (quantum Monte Carlo) with the Hartree-Fock independent particle model. All systems are considered in the ground state so we use the basic result of density functional theory that the electronic density brings all information about the N-particle wavefunction. We limit our test examples to a set of atoms in a spherically symmetric ground state including also fractional nuclear charges. We analyze the behaviour of Shannon entropy up to the limit of extremely weak binding where the ionization potential goes to zero