A Gradient Corrected Two-Point Weighted Density Approximation for Exchange Energies

A successful symmetric, two-point, nonlocal weighted density approximation for the exchange energy of atoms and molecules can be constructed using a power mean with constant power p when symmetrizing the exchange-correlation hole [Phys. Rev. A 85, 042519 (2012)]. In this work, we consider how this parameter depends on the system’s charge. Exchange energies for all ions with charge from \(-1\) to \(+12\) of the first eighteen atoms of the periodic table are computed and optimized. Appropriate gradient corrections to the current model, based on rational functions, are designed based on the optimal p values we observed for the ionic systems. All of the advantageous features (non-locality, uniform electron gas limit and no self-interaction error) of the original model are preserved.