  We present calculations of the correlation energies of crystalline solids and
isolated systems within the adiabatic-connection fluctuation-dissipation
formulation of density-functional theory. We perform a quantitative comparison
of a set of model exchange-correlation kernels originally derived for the
homogeneous electron gas (HEG), including the recently-introduced renormalized
adiabatic local-density approximation (rALDA) and also kernels which (a)
satisfy known exact limits of the HEG, (b) carry a frequency dependence or (c)
display a 1/$k^2$ divergence for small wavevectors. After generalizing the
kernels to inhomogeneous systems through a reciprocal-space averaging
procedure, we calculate the lattice constants and bulk moduli of a test set of
10 solids consisting of tetrahedrally-bonded semiconductors (C, Si, SiC), ionic
compounds (MgO, LiCl, LiF) and metals (Al, Na, Cu, Pd). We also consider the
atomization energy of the H$_2$ molecule. We compare the results calculated
with different kernels to those obtained from the random-phase approximation
(RPA) and to experimental measurements. We demonstrate that the model kernels
correct the RPA's tendency to overestimate the magnitude of the correlation
energy whilst maintaining a high-accuracy description of structural properties.
