  The construction of meta generalized gradient approximations based on the
density matrix expansion (DME) is considered as one of the most accurate
technique to design semilocal exchange energy functionals in two-dimensional
density functional formalism. The exchange holes modeled using DME possess
unique features that make it a superior entity. Parameterized semilocal
exchange energy functionals based on the DME are proposed. The use of different
forms of the momentum and flexible parameters is to subsume the non-uniform
effects of the density in the newly constructed semilocal functionals. In
addition to the exchange functionals, a suitable correlation functional is also
constructed by working upon the local correlation functional developed for 2D
homogeneous electron gas (2D-HEG). The non-local effects are induced into the
correlation functional by a parametric form of one of the newly constructed
exchange energy functionals. The proposed functionals are applied to the
parabolic quantum dots with a varying number of confined electrons and the
confinement strength. The results obtained with the aforementioned functionals
are quite satisfactory which indicates why these are suitable for
two-dimensional quantum systems.
