Kinetic contribution to the correlation energy density: benchmark to Tc[n] energy functionals

Since in density functional theory the classical form of the virial theorem does not hold due to the localization effect of exchange-correlation, it is important to investigate the kinetic contribution to correlation. Nearly exact tc([n]; r) kinetic contributions to the correlation energy densities are constructed for the two-electron He and H2 and for LiH and compared with various model tcmod([n]; r) energy densities. For comparative purpose the “global” Tc[n] energies are also given for several atomic and molecular systems. The model functionals are derived using the Levy-Perdew relation. Stollʹs correction is employed for those models, which are based on the electron gas model or capable of reproducing the uniform electron gas limit. This correction makes it possible to treat opposite- and parallel-spin correlation distinctly. The proper modelling of tc([n]; r) functionals provides the opportunity of a separate treatment of the potential part Wc[n] and the Tc[n] part of the correlation. The virial ratio −Tc/Ec is compared for several neutral and ionic systems and is found to be in the range 0.75–0.85 for neutral atomic systems, while for tightly bound atoms, like Be2+ a value of 0.96 is computed.