Density Functional Theory and the Local Density Approximation
Density Functional Theory and the Local Density Approximation
Density Functional Theory and the Local Density Approximation
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<strong>Local</strong> <strong>Density</strong> <strong>Approximation</strong> (LDA)<br />
The idea: build E xc from <strong>the</strong> knowledge of <strong>the</strong> exchange-correlation<br />
energy per particle, ! xc , of <strong>the</strong> homogeneous electron gas<br />
Kohn & Sham, PRA 140, 1133 (1965)<br />
For <strong>the</strong> homogeneous electron gas <strong>the</strong> exact dependence of ! xc (n)<br />
can be computed by Quantum Monte Carlo.<br />
n<br />
! xc<br />
Ceperley & Alder, PRL 45, 566 (1980)<br />
LDA to E xc : How it is built<br />
E<br />
!<br />
( n(<br />
r)<br />
)<br />
= " n(<br />
r dr<br />
LDA<br />
xc xc<br />
)<br />
n<br />
n<br />
Picture courtesy of Andreas Savin Kohn & Sham, PRA 140, 1133 (1965)
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