Accurate spin-dependent electron liquid correlation energies for local spin density calculations: a critical analysis

We assess various approximate forms for the correlation energy per particle of the spin-polarized homogeneous electron gas that have frequently been used in applications of the local spin density approximation to the exchange-correlation energy functional. By accurately recalculating the RPA correlation energy as a function of electron density and spin polarization we demonstrate the inadequacies of the usual approximation for interpolating between the para- and ferro-magnetic states and present an accurate new interpolation formula. A Padé approximant technique is used to accurately interpolate the recent Monte Carlo results (para and ferro) of Ceperley and Alder into the important range of densities for atoms, molecules, and metals. These results can be combined with the RPA spin-dependence so as to produce a correlation energy for a spin-polarized homogeneous electron gas with an estimated maximum error of 1 mRy and thus should reliably determine the magnitude of non-local corrections to the local spin density approximation in real systems.