We present first-principles calculations for the fcc noble gas solids Ne, Ar, and Kr applying the adiabatic connection fluctuation-dissipation theorem (ACFDT) to evaluate the correlation energy. The ACFDT allows us to describe long-range correlation effects including London dispersion or van der Waals interaction on top of conventional density functional theory calculations. Even within the random phase approximation, the typical 1∕V² volume dependence for the cohesive energy of the noble gas solids is reproduced, and equilibrium cohesive energies and lattice constants are improved compared to density functional theory calculations. Furthermore, we present atomization energies for H₂, N₂, and O₂ within the same post-density-functional-theory framework, finding an excellent agreement with previously published data.