Kinetic energy of an electron gas

1985 ◽  
Vol 32 (4) ◽  
pp. 2670-2670 ◽  
Author(s):  
Ronald Bass
Keyword(s):  
1998 ◽  
Vol 58 (20) ◽  
pp. 13465-13471 ◽  
Author(s):  
Yan Alexander Wang ◽  
Niranjan Govind ◽  
Emily A. Carter

2004 ◽  
Vol 70 (20) ◽  
Author(s):  
John F. Dobson ◽  
Hung M. Le ◽  
Giovanni Vignale

1972 ◽  
Vol 50 (15) ◽  
pp. 1756-1763 ◽  
Author(s):  
B. B. J. Hede ◽  
J. P. Carbotte

Correlations in an electron gas are particularly important at metallic densities because the potential energy cannot be ignored in comparison with the kinetic energy; in particular, interactions are not weak as r → 0, so that a simple Born approximation does not hold in this limit. Short-range correlations between oppositely-spinned electrons can be accounted for by an infinite series of particle–particle ladder diagrams. It leads to a Bethe–Goldstone type of equation which can be solved by an angle-averaged approximation. The resultant spin-up-down p.d.f. is positive over a wide range of metallic densities. A further correction by including particle–hole scattering effects changes the previous results only slightly.


A variational principle is constructed which leads directly to the March-Murray perturbation series relating the particle density ρ (r) with the one-body potential V (r) in an electron gas. An explicit, though perturbative, form for the Hohenberg-Kohn universal functional, which is essentially the kinetic energy density, is thereby obtained. When the spatial variations of density and potential are slow, the usual Thomas-Fermi ρ 5/3 relation between kinetic energy density and particle density is regained. The present approach also leads to a systematic formulation of the gradient expansion of the kinetic energy density.


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