Two-Electron Correlations in the Metallic Electron Gas

We present high-precision ab initio calculations of the four-point vertex function for the three-dimensional uniform electron gas using variational diagrammatic Monte Carlo. From these results, we extract Landau parameters that reveal a density-driven crossover from underscreening to over-screening, and obtain the full two-electron scattering amplitude on the Fermi surface with controlled accuracy. A residual analysis of the scattering amplitude against the charge-channel Kukkonen-Overhauser (KO⁺) interaction shows that only a minimal s-wave correction in the antiparallel-spin channel is needed, defining the sKO⁺ ansatz: KO⁺ within the local-density approximation plus this short-range correction. Using both our direct VDMC amplitudes and the sKO⁺ ansatz, we compute the electron-electron contribution to the thermal resistivity, obtaining quantitative agreement with experiments on simple metals (Al, Na, K, Rb). sKO⁺ thus provides a controlled UEG-based effective interaction for simple-metal transport and future first-principles extensions.