Inhomogeneity Induced and Appropriately Parameterized Semilocal Exchange and Correlation Energy Functionals in Two-Dimensions

TL;DR

This paper develops and parameterizes new semilocal exchange and correlation energy functionals for two-dimensional systems using the density matrix expansion, improving the modeling of non-uniform electron densities in quantum dots.

Contribution

It introduces novel, parameterized semilocal exchange and correlation functionals based on DME tailored for 2D systems, incorporating non-uniform effects more accurately.

Findings

Functional performance is satisfactory for 2D quantum dots.

New functionals effectively model non-uniform electron densities.

Application results demonstrate suitability for 2D quantum systems.

Abstract

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.