  We derive 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 not yet
been 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 4 with respect to the simple local density approximation.
