  We present an embedding approach to treat local electron correlation effects
in periodic environments. In a single, consistent framework, our plane-wave
based scheme embeds a local high-level correlation calculation (here Coupled
Cluster Theory, CC), employing localized orbitals, into a low-level correlation
calculation (here the direct Random Phase Approximation, RPA). This choice
allows for an accurate and effcient treatment of long-range dispersion effects.
Accelerated convergence with respect to the local fragment size can be observed
if the low-level and high-level long-range dispersion are quantitatively
similar, as is the case for CC in RPA. To demonstrate the capabilities of the
introduced embedding approach, we calculate adsorption energies of molecules on
a surface and in a chabazite crystal cage, as well as the formation energy of a
lattice impurity in a solid at the level of highly accurate many-electron
perturbation theories. The absorption energy of a methane molecule in a zeolite
chabazite, for instance, is converged with an error well below 20 meV at the CC
level. As our largest periodic benchmark system, we apply our scheme to the
adsorption of a water molecule on titania in a supercell containing more than
1000 electrons.
