  We determine the correlation energy of BN, SiO$_2$ and ice polymorphs
employing a recently developed RPAx (random phase approximation with exchange)
approach. The RPAx provides larger and more accurate polarizabilities as
compared to the RPA, and captures effects of anisotropy. In turn, the
correlation energy, defined as an integral over the density-density response
function, gives improved binding energies without the need for error
cancellation. Here, we demonstrate that these features are crucial for
predicting the relative energies between low- and high-pressure polymorphs of
different coordination number as, e.g., between $\alpha$-quartz and stishovite
in SiO$_2$, or layered and cubic BN. Furthermore, a reliable (H$_2$O)$_2$
potential energy surface is obtained, necessary for describing the various
phases of ice. The RPAx gives results comparable to other high-level methods
such as coupled cluster and quantum Monte Carlo, also in cases where the RPA
breaks down. Although higher computational cost than RPA we observe a faster
convergence with respect to the number of eigenvalues in the response function.
