Modified Fourth-Order Kinetic Energy Gradient Expansion with Hartree Potential-Dependent Coefficients

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Density Functional Theory

Background:

• Accurate kinetic energy (KE) functionals are crucial for electronic structure calculations.
• Existing semilocal functionals often struggle with accuracy for both atomic and extended systems.
• The development of improved gradient expansion (GE) functionals is an ongoing challenge.

Purpose of the Study:

• To develop a modified fourth-order kinetic energy gradient expansion (GE4m) functional.
• To enhance the GE4m functional's accuracy for light atoms by incorporating the reduced Hartree potential.
• To introduce and test the novel u-meta-generalized-gradient-approximation (uMGGA) functional, named uGE4m.

Main Methods:

• Developed a modified fourth-order kinetic energy gradient expansion (GE4m) based on semiclassical neutral atom theory.
• Modified GE4m coefficients using the reduced Hartree potential, creating the uGE4m functional.
• Established a benchmark dataset including total KE and KE differences for atoms, molecules, and jellium clusters in a slowly varying density regime.

Main Results:

• The initial GE4m functional showed significant improvement over known semilocal functionals for large atoms and jellium surfaces.
• The modified uGE4m functional demonstrated consistently good performance for all tested properties, unlike most GGA and meta-GGA KE functionals.
• The study confirmed the importance of the reduced Hartree potential for constructing accurate KE functionals.

Conclusions:

• The uGE4m functional represents a qualitative advancement in kinetic energy functional development.
• The reduced Hartree potential is a key ingredient for next-generation kinetic energy functionals.
• uGE4m offers a robust and accurate approach for describing kinetic energy in systems with slowly varying electron densities.