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>Density</strong> <strong>Functional</strong> <strong>Theory</strong>:<br />
The History<br />
Thomas-Fermi-Dirac Model (1929):<br />
First model where <strong>the</strong> energy is expressed in<br />
terms of <strong>the</strong> electron density<br />
E. Fermi, Nobel laureate 1938<br />
Kohn-Hohenberg-Sham (1964):<br />
Exact univoque relationship between ground<br />
state energy <strong>and</strong> electron density<br />
W. Kohn, Nobel laureate 1998<br />
E xc [n] - Properties<br />
E<br />
xc<br />
=<br />
s<br />
e!<br />
e<br />
!<br />
[ n]<br />
( T [ n]<br />
! T [ n])<br />
+ ( V [ n]<br />
V [ n])<br />
H<br />
– Does not depend on V ext (<strong>the</strong> specific system): it is a<br />
‘universal’ functional.<br />
– The exact dependence on n(r) is unknown<br />
E xc must be approximated in applications
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