Fourth-order gradient contributions in extended Thomas-Fermi theory for noninteracting fermions at finite temperature
Geldart, D. J. W.
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Nonlocal corrections to the free energy of a system of noninteracting fermions are considered within the framework of extended Thomas-Fermi theory. The density and temperature dependence of gradient corrections is given through fourth order in powers of the density gradient. The calculation is based on long-wavelength expansions of linear and nonlinear response functions of a nearly uniform system. Results are given in terms of Fermi-Dirac integrals and convenient forms are given which span the full density and temperature range from the degenerate limit to the classical limit
Geldart, D. J. W., and E. Sommer. 1985. "Fourth-order gradient contributions in extended Thomas-Fermi theory for noninteracting fermions at finite temperature." Physical Review B (Condensed Matter) 32(12): 7694-702. Copyright © 1985 American Physical Society.