Gradient approximated exchange energy functionals with improved performances for two-dimensional quantum dot systems

Semilocal exchange-correlation functionals are frequently used to accurately describe the complex many-electron effects of two-dimensional quantum systems. Most of these functionals are designed using the reduced density gradient as the main ingredient. A semilocal functional for the exchange and the corresponding enhancement factor is constructed using the inhomogeneity parameter of the generalized gradient approximations by analyzing the small and large-density gradient expansion of the exchange hole. This exchange functional significantly reduces the error compared to the existing gradient approximations. Performance of the proposed semilocal functional is demonstrated by considering parabolic and Gaussian quantum dots with varying particle number and confinement strength. The results are also compared with that of the exact exchange formalism by considering it as the standard.