Gradient correction to the statistical electronic free energy at nonzero temperatures: Application to equation-of-state calculations

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Abstract
The gradient correction to statistical kinetic free energy, well known at zero temperature, is generalized to finite temperatures, following the prescriptions of the density-functional formalism. The coefficient of the gradient term, a function of electron density, is explicitly determined, and an accurate approximation, suitable for numerical computation, is given. The corrected kinetic free energy, with a phenomenological extrapolation to all temperatures of the exchange and correlation contribution, is applied to equation-of-state calculations. Results are presented in the case of Be, Al, and Cu, for temperatures up to 50 eV and compressions 0.1, 1, and 10, and the influence of the gradient correction is discussed.