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##### Density gradients for the exchange energy of electrons in two dimensions

**Authors**: S. Pittalis, E. Räsänen, J.G. Vilhena and M.A.L. Marques

**Ref.**: Phys. Rev. A **79**, 012503 (2009)

**Abstract**: We present a generalized gradient approximation to the exchange energy
to be used in density functional theory calculations of
two-dimensional systems. This class of approximations has a long and
successful history, but it has been not yet fully investigated for
electrons in two dimensions. We follow the approach originally
proposed by Becke for three-dimensional systems [Int. J. Quantum Chem. **23**, 1915 (1983),
J. Chem. Phys. **85**, 7184 (1986)]. The resulting functional depends on two parameters
that are adjusted to a test set of parabolically confined
quantum dots. Our exchange functional is then tested on a variety of
systems with promising results, reducing the error in the
exchange energy by a factor of four with respect to the simple local
density approximation.

**DOI**: 10.1103/PhysRevA.79.012503

**URL**: arxiv.org