Accurate electron correlation energy functional: Expansion in the interaction renormalized by the random-phase approximation

We present an accurate local density functional for electronic-structure calculations within the density functional theory (DFT). The functional is derived by analyzing the structure of the standard perturbative expansion of the correlation energy of the interacting uniform electron gas. Then, the expansion is partially resummed and reorganized as a self-consistent series in powers of a renormalized electron-electron interaction vertex based on the screened frequency-momentum-dependent dielectric matrix given by the well-known random-phase approximation. First, we demonstrate that the range of ${r}_{s}$, where this reorganized and renormalized series converges, contains and is significantly larger than the average range realized in real crystalline materials. Using a combination of analytical, numerical, and stochastic integration techniques we are able to calculate all the diagrams which have contribution up to the same leading order. We benchmarked the functional using the quantum espresso implementation of the DFT applied to the same list of materials, selected previously by other authors, in its entirety without any modification of the list. We find that for ground-state properties in general, such as equilibrium atomic distances and bulk moduli, the functional presented here is more accurate than the currently available most popular one.