Adjacent Pairs Exchange correction to the Random Phase Approximation

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.