Spin-polarized electron liquid at arbitrary temperatures: Exchange-correlation energies, electron-distribution functions, and the static response functions

We use a recently introduced classical mapping of the Coulomb interactions in a quantum electron liquid [Phys. Rev. Lett. 84, 959 (2000)] to present a unified treatment of the thermodynamic properties and the static response of the finite-temperature electron Liquid, valid for arbitrary coupling and spin-polarization. The method is based on using a "quantum temperature" T- q such that the distribution functions of the classical electron liquid at T-q leads to the same correlation energy as the quantum electron liquid at T=0. The functional form of T-q(r(s)) is presented. The electron-electron p air-distribution functions (PDF's) calculated using T-q me in good quantita tive agreement with available (T=0) quantum Monte Carlo results. The method provides a means of treating strong-coupling regimes of n,T, and zeta curr ently unexplored by quantum Monte Carlo or Feenberg-functional methods. The exchange-correlation free energies, distribution functions g(11)(r), g(12) (r), g(22)(Y) and the local-field corrections to the static response functi ons as a function of density it, temperature T, and spin polarization zeta are presented and compared with any available finite-ir results. The exchan ge-correlation free energy f(xc)(n,T,zeta), is given in a parametrized form . It satisfies the expected analytic behavior in various limits of temperat ure, density, and spin polarization, and can be used for calculating other properties like the equation of state, the exchange-correlation potentials, compressibility, etc. The static local-field correction provides a static response function which is consistent with the PDF's and the relevant sum r ules. Finally, we use the finite-T re-potentials to examine the Kohn-Sham b ound- and continuum states at an Al13+ nucleus immersed in a hot electron g as to show the significance of the re-potentials.