Symmetric two-point weighted density approximation for exchange energies

We describe a symmetric, two-point, nonlocal weighted density approximation for the exchange energy of atoms and compare it to conventional density functionals and the conventional weighted density approximation. Even the simplest two-point weighted density approximation gives results comparable to the best generalized gradient approximations. Unlike those functionals, however, the two-point weighted density approximation is fully nonlocal, has no self-interaction error, approximately fulfills the Pauli principle, and preserves the uniform electron gas limit.