Abstract
A simple-and-analytic form for total energy (or ground-state energy) in the uniform three-dimensional electron gas, expressed as a function of any Wigner-Seitz radius rs and relative spin polarization ζ is obtained with a very good accuracy of 0.036% from the Stoner model and our interpolation between high-and-low density limits with use of a two-point approach for the correlation energy and spin stiffness at rs = 1 and 70. This suggests a satisfactory desciption of some physical properties such as: paramagnetic-ferromagnetic phase transition and thermodynamic-and-optical phenomena.
Highlights
In the uniform three-dimensional electron gas (U3DEG) at zero temperature, it should be noted that the state of this system is entirely specified by the WignerSeitz radius rs being related to the total electron density
The aim of the present paper is to investigate a simpleand-analytic form for E(rs, ζ) in the U3DEG, obtained with a very good accuracy of 0.036% from the Stoner model, an interpolation between high-and-low density limits (HLDL), and a two-point approach for correlation energy Ec(rs, ζ) and spin stiffness αc(rs) at rs = 1 and 70, giving rise to a satisfactory description of some physical properties such as: PF-phase transition and thermodynamic-and-optical phenomena
Our numerical calculation indicates that it becomes negative for rs ≥ 5.2597 at ζ = 0, for rs ≥ 5.08 at ζ = 0.5, and for rs ≥ 4.55 at ζ =1, noting that this negative compressibility does not imply an instability of the system when a rigid background of compensating charge is assumed
Summary
In order to calculate the relative errors (RE) of E(rs, ζ) from the present result (1) and those from other approximate results evaluated from [4,8,9,11], neglecting the Stoner model, we will use the accurate results obtained from their diffusion Monte Carlo (DMC) method [4] by using backflow wave functions and twist averaged boundary conditions to obtain the accurate values of E(rs, ζ) at low densities with standard errors.
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