  The "ACFD-RPA" correlation energy functional has been widely applied to a
variety of systems to successfully predict energy differences, and less
successfully predict absolute correlation energies. Here we present a
parameter-free exchange-correlation kernel that systematically improves
absolute correlation energies, while maintaining most of the good numerical
properties that make the ACFD-RPA numerically tractable. The "RXH" kernel is
constructed to approximate the true exchange kernel via a carefully weighted,
easily computable radial averaging. Correlation energy errors of atoms with two
to eighteen electrons show a thirteenfold improvement over the RPA and a
threefold improvement over the related "PGG" kernel, for a mean absolute error
of 13mHa or 5%. The average error is small compared to all but the most
difficult to evaluate kernels. van der Waals $C_6$ coefficients are less well
predicted, but still show improvements on the RPA, especially for highly
polarisable Li and Na.
