  We investigate the adiabatic approximation to the exact-exchange kernel for
calculating correlation energies within the adiabatic-connection
fluctuation-dissipation framework of time-dependent density functional theory.
A numerical study is performed on a set of systems having bonds of different
character (H$_2$ and N$_2$ molecules, H-chain, H$_2$-dimer, solid-Ar and the
H$_2$O-dimer). We find that the adiabatic kernel can be sufficient in strongly
bound covalent systems, yielding similar bond lengths and binding energies.
However, for non-covalent systems the adiabatic kernel introduces significant
errors around equilibrium geometry, systematically overestimating the
interaction energy. The origin of this behaviour is investigated by studying a
model dimer composed of one-dimensional closed-shell atoms interacting via
soft-Coulomb potentials. The kernel is shown to exhibit a strong frequency
dependence at small to intermediate atomic separation that affects both the
low-energy spectrum and the exchange-correlation hole obtained from the
corresponding diagonal of the two-particle density matrix.
