Nonlocal Exchange from a Two-Point Weighted Density Approximation with Flexible p-Mean Coupling 

We present a symmetric, fully nonlocal two-point weighted-density approximation (WDA) for electronic exchange that follows the spirit of Cuevas-Saavedra et al. while introducing some physically-motivated departures. First, we enforce density-weighted symmetry of the exchange hole, ensuring the full density weighted limit rather than simply adhering to the pointwise symmetry of the uniform electron gas limit. Second, we introduce a flexible, density-dependent p-mean that adapts the coupling between points to the inhomogeneity of the density. This flexibility leads to faster numerical convergence and enhanced accuracy. Third, we explore two-point coupling beyond the p-mean formalism. Across open- and closed-shell atoms and small molecules, these methods yield exchange energies competitive with leading GGAs while improving self-interaction behavior. Here, we outline the construction and constraints of our approach, and the results for various chemical environments.