The generalised relativistic Lindhard functions

We present here analytic expressions for the generalised Lindhard function, also referred to as Fermi Gas polarisation propagator, in a relativistic kinematic framework and in the presence of various resonances and vertices. Particular attention is payed to its real part, since it gives rise to substantial difficulties in the definition of the currents entering the dynamics.Comment: 48 pages, 2 figures, to be published in EPJ

Correct dissociation limit for the exchange-correlation energy and potential

Local and semilocal functional like the local density (LDA) and generalized gradient approximations (GGA) fail to provide correct behavior during the dissociation of electron pair bonds: the asympinterdependencetotic potential energy curve is wrong, the dissociation in the heteronuclear case leads to partially ionic instead of neutral atoms, and the time-dependent density functional theory (TD-DFT) excitation energies behave incorrectly upon bond stretching. We demonstrate that such errors can be avoided by the use of an orbital-dependent exchange-correlation (xc) functional. Such a functional needs to incorporate, in contrast to the popular exact exchange functional, the electron correlation effects. The demonstration is given for the electron pair bond of a diatomic molecule AB with just one orbital on A and one on B. This simple two-orbital model affords an analytical inversion of the density response function, which is used to show that the orbitaldependent xc functional described previously, possesses the correct dissociation limit for the xc energy and potential. The correct potential (xc hole potential in the symmetric case A=B, for example, for the dissociating