Local-density approximation: Difference between revisions

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== Homogeneous electron gas ==

Approximation for ''ε''_xc depending only upon the density can be developed in numerous ways. The most successful approach is based on the homogeneous electron gas. This is constructed by placing ''N'' interacting electrons in to a volume, ''V'', with a positive background charge keeping the system neutral. ''N'' and ''V'' are then taken to infinity in the manner that keeps the density (''ρ'' = ''N'' / ''V'') finite. This is a useful approximation as the total energy consists of contributions only from the kinetic energy, electrostatic interaction energy and exchange-correlation energy, and that the wavefunction is expressible in terms of planewaves. In particular, for a constant density ''ρ'', the exchange energy density is proportional to ''ρ''^⅓.

== Exchange functional ==