  Semilocal exchange-correlation functionals are the most accurate, realistic
and widely used ones to describe the complex many-electron effects of
two-dimensional quantum systems. Beyond local density approximation, the
generalized gradient approximations(GGAs) are designed using reduced density
gradient as main ingredient. An enhancement factor is constructed using the
inhomogeneity parameter of GGAs by taking care of the low and high density
behaviors of it. Thus, the exchange energy functional proposed by making use of
the aforementioned enhancement factor, significantly reduces the error compare
to the previously proposed gradient approximations. Another enhancement factor
and corresponding energy functional is also constructed using the inhomogeneity
parameter originally introduced by Becke [J. Chem. Phys. 109, 2092 (1998)].
Comprehensive testing and performance of both the functionals are demonstrated
with respect to the exact exchange formalism by considering two-dimensional
parabolically confined quantum dots with varying particle number and
confinement strength as a test case.
