Homogeneous Electron Gas
Approximation for εxc 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 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 ρ⅓.
Read more about this topic: Local-density Approximation
Famous quotes containing the words homogeneous and/or gas:
“O my Brothers! love your Country. Our Country is our home, the home which God has given us, placing therein a numerous family which we love and are loved by, and with which we have a more intimate and quicker communion of feeling and thought than with others; a family which by its concentration upon a given spot, and by the homogeneous nature of its elements, is destined for a special kind of activity.”
—Giuseppe Mazzini (1805–1872)
“A new father quickly learns that his child invariably comes to the bathroom at precisely the times when he’s in there, as if he needed company. The only way for this father to be certain of bathroom privacy is to shave at the gas station.”
—Bill Cosby (20th century)