Exchange-correlation potentials and local energies per particle along non-linear adiabatic connections

We study non-linear adiabatic connection paths in density-functional theory using modified electron-electron interactions that perform a long-range/short-range separation of the Coulomb interaction. These adiabatic connections allows to define short-range exchange-correlation potentials and short-range local exchange-correlation energies per particle that we have calculated accurately for the He and Be atoms and compared to the corresponding quantities in the local density approximation (LDA). The results confirm that the LDA better describes exchange-correlation potentials and local exchange-correlation energies per particle when the range of the interaction is reduced.