Geldart, D. J. W.Sommer, E.2013-06-192013-06-191985-12/15Geldart, 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.0163-1829http://dx.doi.org/10.1103/PhysRevB.32.7694http://hdl.handle.net/10222/25119Nonlocal 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 limitFermion systemsFree energyThomas-Fermi modelarticle32127694