  Semi-local density functionals for the exchange-correlation energy of
electrons are extensively used as it produce realistic and accurate results for
finite and extended systems. The choice of techniques play crucial role in
constructing such functionals of improved accuracy and efficiency. An accurate
and efficient semi-local exchange energy functional in two dimensions is
constructed by making use of the corresponding hole based on the density matrix
expansion. The exchange hole involved is localized under the generalized
coordinate transformation and satisfies all the relevant constraints.
Comprehensive testing and excellent performance of the functional is
demonstrated versus exact exchange results. The functional also achieves
remarkable accuracy by substantially reducing the errors present in the local
and non-empirical density functionals proposed so far for two dimensional
systems. The underlying principles involved in the functional construction are
physically appealing and practically useful for developing range separated and
non-local functionals in two dimensions.
