Conjugate-Gradient Optimization Method for Orbital-free Density Functional Calculations

TL;DR

This paper introduces a new conjugate-gradient method for solving spin-dependent extended Thomas-Fermi equations, improving accuracy and efficiency in orbital-free density functional calculations.

Contribution

A novel conjugate-gradient algorithm tailored for spin-dependent ETF equations, incorporating approximate line-search and collective spin density treatment.

Findings

Method achieves high accuracy in quantum dot and sodium cluster simulations.

Demonstrates improved computational efficiency over existing approaches.

Validates effectiveness for both 2D and 3D systems.

Abstract

Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient numerical numerical methodology. In this paper, we developed a new conjugate-gradient method for the numerical solution of spin-dependent extended Thomas-Fermi equation by incorporating techniques previously used in Kohn-Sham calculations. The key ingredient of the new method is an approximate line-search scheme and a collective treatment of two spin densities in the case of spin-dependent ETF problem. Test calculations for a quartic two-dimensional quantum dot system and a three-dimensional sodium cluster,$\mr{Na}_{216}$, with a local pseudopotential demonstrate that the method is accurate and efficient.