Energy-optimized local exchange-correlation kernel for the electron gas: Application to van der Waals forces

We derive and parametrize a local, instantaneous exchange-correlation kernel fₗ₂ for the interacting electron gas. Our kernel is ``energy optimized: '' that is, it is chosen so that it leads, via the fluctuation-dissipation and adiabatic connection formulas, to an accurate correlation energy in the uniform electron gas. In this respect it differs from previous simplified kernels, which are typically optimized to provide accurate linear response at long wavelength. To the extent that it embodies relatively short-ranged correlation effects beyond the random phase approximation (RPA), we expect our kernel to be transferable to the calculation of beyond-RPA correlation effects in RPA-like codes for inhomogeneous systems. We apply it to calculate the van der Waals correlation energy between a pair of jellium slabs at all separations down to intimate contact.