Inhomogeneity induced and appropriately parameterized semilocal exchange and correlation energy functionals in...

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Semilocal exchange energy functionals are crucial for density functional theory (DFT) in describing electron interactions.
• The density matrix expansion (DME) provides a robust framework for constructing accurate exchange functionals.
• Two-dimensional (2D) quantum systems, like quantum dots, present unique challenges for electronic structure calculations.

Purpose of the Study:

• To develop and propose novel semilocal exchange energy functionals using the density matrix expansion (DME) within a two-dimensional (2D) formalism.
• To construct a complementary correlation functional that incorporates non-local effects.
• To evaluate the performance of the newly developed functionals for 2D quantum systems.

Main Methods:

• Construction of parameterized semilocal exchange energy functionals based on the DME, incorporating flexible parameters and momentum forms to capture density non-uniformities.
• Development of a correlation functional by adapting a local correlation functional for 2D homogeneous electron gas and inducing non-local effects via a parametric exchange functional.
• Application of the proposed exchange-correlation functionals to model parabolic quantum dots with varying electron numbers and confinement strengths.

Main Results:

• The proposed DME-based exchange functionals exhibit unique and superior modeling of exchange holes.
• The constructed correlation functional effectively incorporates non-local effects.
• Calculations for parabolic quantum dots using the new functionals yielded satisfactory results, demonstrating their efficacy for 2D systems.

Conclusions:

• The developed meta generalized gradient approximations based on DME are accurate for semilocal exchange energy functionals in 2D.
• The proposed functionals provide a reliable tool for studying electronic properties of two-dimensional quantum systems.
• These functionals show significant promise for advancing theoretical investigations in condensed matter physics and quantum chemistry.