  We use continuum mechanics [Tao \emph{et al}, PRL{\bf 103},086401] to
approximate the dynamic density response of interacting many-electron systems.
Thence we develop a numerically efficient exchange-correlation energy
functional based on the Random Phase Approximation (dRPA). The resulting
binding energy curve $E(D)$ for thin parallel metal slabs at separation $D$
better agrees with full dRPA calculations than does the Local Density
Approximation. We also reproduce the correct non-retarded van der Waals (vdW)
power law $E(D)\aeq -C_{5/2}D^{-5/2}$ as $D\to\infty$, unlike most vdW
functionals.

Mesoscale and Nanoscale Physics;Atomic Physics