Explicit estimation of ground-state kinetic energies from electron densities.

摘要: This paper discusses some initial steps toward the goal of finding explicit procedures for calculating, to a good approximation, minimum kinetic energy consistent with given particle density \ensuremath{\rho}(r) system fermions. The strategy proposed begins by separating desired into sum ${T}_{W}$+${T}_{\mathrm{theta}}$, where ${T}_{W}$\ensuremath{\ge}0 is Weizsaaumlcker F ${d}^{3}$r \ensuremath{\Vert}\ensuremath{\nabla}\ensuremath{\rho}${\ensuremath{\Vert}}^{2}$/8\ensuremath{\rho} , and ${T}_{\mathrm{theta}}$\ensuremath{\ge}0. Approximations are applied ${T}_{\mathrm{theta}}$ alone, sought in form interpolations that will be nearly correct two limits: small departures from uniform density, which exact results known linear-response theory, cases region containing no more than one spin becomes isolated rest distribution regions vanishing density. Only highly nonlocal functionals can behave properly either these limits. A few other conditions satisfactory approximations noted. Some interpolation formulas offered one-dimensional problems, tested on variety examples; such found give energies within percent all examined. More detailed tests possible comparing approximate potentials yielding or densities ground state potential; position dependence however, physically meaningless. remarks additional problems beset extension scheme three dimensions; foremost among computational tractability.