Laplacian‐based models for the exchange energy

Recent Quantum Monte Carlo data for the exchange‐correlation energy density of pseudopotential systems strongly suggest the value of using the Laplacian of the density as a variable for constructing first‐order corrections to the local density approximation of density functional theory. We report on an exchange functional built on these observations and extended to the all‐electron case. The model keeps the typical properties of constraint‐based generalized gradient approximations (GGAs) and also has a finite‐valued potential at the nucleus, unlike the GGA. Problems with oscillatory behavior in the potential due to higher order derivatives are controlled by a curvature minimization constraint. The results are tested against exact potentials for the He and Ne atom. A combination of gradient and Laplacian as suggested by a gradient expansion of the exchange hole gives the best overall results.