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We use a recently introduced classical mapping of the Coulomb interactions in a quantum electron liquid ͓Phys. Rev. Lett. 84, 959 ͑2000͒] 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 Tϭ0. The functional form of T q (r s ) is presented. The electron-electron pair-distribution functions ͑PDF's͒ calculated using T q are in good quantitative agreement with available (Tϭ0) quantum Monte Carlo results. The method provides a means of treating strong-coupling regimes of n,T, and currently unexplored by quantum Monte Carlo or Feenberg-functional methods. The exchange-correlation free energies, distribution functions g 11 (r), g 12 (r), g 22 (r) and the local-field corrections to the static response functions as a function of density n, temperature T, and spin polarization are presented and compared with any available finite-T results. The exchange-correlation free energy f xc (n,T,), is given in a parametrized form. It satisfies the expected analytic behavior in various limits of temperature, 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 localfield correction provides a static response function which is consistent with the PDF's and the relevant sum rules. Finally, we use the finite-T xc-potentials to examine the Kohn-Sham bound-and continuum states at an Al 13ϩ nucleus immersed in a hot electron gas to show the significance of the xc-potentials. PHYSICAL REVIEW B15 DECEMBER 2000-II VOLUME 62, NUMBER 24 PRB 62

We use the now well known spin unpolarized exchange-correlation energy E(xc) of the uniform electron gas as the basic "many-body" input to determine the temperature T(q) of a classical Coulomb fluid having the same correlation energy as the quantum system. It is shown that the spin-polarized pair distribution functions (SPDFs) of the classical fluid at T(q), obtained using the hypernetted chain equation, are in excellent agreement with those of the T = 0 quantum fluid obtained by quantum Monte Carlo (QMC) simulations. These methods are computationally simple and easily applied to problems which are currently beyond QMC simulations. Results are presented for the SPDFs and the local-field corrections to the response functions of the electron fluid at T = 0 and finite T.

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