Towards nonlocal density functionals by explicit modelling of the exchange-correlation hole in inhomogeneous systems

We put forward an approach for the development of a nonlocal density functional by a direct modeling of the shape of exchange-correlation (xc) hole in inhomogeneous systems. The functional is aimed at giving an accurate xc energy and an accurate corresponding xc potential even in difficult near-degeneracy situations such as molecular bond breaking. In particular we demand that: (1) the xc hole properly contains −1 electron, (2) the xc potential has the asymptotic −1/r behavior outside finite systems, and (3) the xc potential has the correct step structure related to the derivative discontinuities of the xc energy functional. None of the currently existing functionals satisfies all these requirements. These demands are achieved by screening the exchange hole in such a way that the pair-correlation function is symmetric and satisfies the sum rule. These two features immediately imply (1) and (2) while the explicit dependence of the exchange hole on the Kohn-Sham orbitals implies (3). Preliminary calculations show an improved physical description of the dissociating hydrogen molecule. Though the total energy is still far from perfect, the binding curve from our nonlocal density functional provides a significant improvement over the local density approximation.