  The random phase approximation to the correlation energy often yields highly
accurate results for condensed matter systems. However, ways how to improve its
accuracy are being sought and here we explore the relevance of singles
contributions for prototypical solid state systems. We set out with a
derivation of the random phase approximation using the adiabatic connection and
fluctuation dissipation theorem, but contrary to the most commonly used
derivation, the density is allowed to vary along the coupling constant
integral. This yields results closely paralleling standard perturbation theory.
We re-derive the standard singles of G\"orling-Levy perturbation theory
[G\"orling and Levy, Phys. Rev. A {\bf 50}, 196 (1994)], highlight the analogy
of our expression to the renormalized singles introduced by Ren and coworkers
[Ren, Tkatchenko, Rinke, and Scheffler, Phys. Rev. Lett. {\bf 106}, 153003
(2011)], and introduce a new approximation for the singles using the density
matrix in the random phase approximation. We discuss the physical relevance and
importance of singles alongside illustrative examples of simple weakly bonded
systems, including rare gas solids (Ne, Ar, Xe), ice, adsorption of water on
NaCl, and solid benzene. The effect of singles on covalently and metallically
bonded systems is also discussed.
