  The Random Phase Approximation (RPA) is a widely employed post Hartree-Fock
or DFT method, capable of capturing van der Waal interactions and other dynamic
correlation effects at relatively low costs of $\mathcal O(N^3)$ in time and
$\mathcal O(N^2)$ in memory, if calculated from imaginary time propagators.
However, since it neglects anti-symmetrization RPA is biased, overestimating
the correlation energy and bond lengths in general. The Second Order Screened
Exchange offers amelioration by anti-symmetrizing one Coulomb interaction but
it comes at considerable costs of $\mathcal O(N^5)$ in time and $\mathcal
O(N^4)$ in memory, since it has to be calculated from the direct ring Coupled
Cluster Doubles (drCCD) amplitudes. We propose a diagrammatic method,
exchanging adjacent pairs in the RPA diagrams - hence its name - offering
similar accuracy but with memory requirement of only $\mathcal O(N^2)$. The
correction is calculated from imaginary time propagators similar to efficient
RPA implementations. It can be calculated in $\mathcal O(N^5)$ steps in
momentum space or $\mathcal O(N^4)$ steps in real space. It improves on SOSEX
in the uniform electron gas for low densities, where correlation effects are
stronger, and first calculations of lattice constants in solids are in
excellent agreement with experiment.
