Uniform electron gases. II. The generalized local density approximation in one dimension

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• The Local Density Approximation (LDA) is a fundamental tool in density functional theory.
• LDA's accuracy is limited for systems with rapidly varying electron densities.
• There is a need for improved approximations beyond LDA.

Purpose of the Study:

• Introduce a generalized Local Density Approximation (gLDA).
• Enhance the accuracy of density functional theory calculations.
• Develop a more robust functional for electron correlation energy.

Main Methods:

• Incorporated the one-electron Seitz radius (rs) and a two-electron hole curvature parameter (η).
• Developed an explicit gLDA functional for one-dimensional systems.
• Compared gLDA performance against LDA, Møller-Plesset perturbation theory, and exact calculations.

Main Results:

• gLDA reduces to LDA for the infinite homogeneous electron gas.
• gLDA is exact for finite uniform electron gases on spheres.
• gLDA shows improved accuracy for inhomogeneous electron systems.

Conclusions:

• The gLDA functional offers a significant improvement over traditional LDA.
• This generalization provides a more accurate description of electron correlation.
• gLDA holds promise for various applications in quantum chemistry and condensed matter physics.