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!<br />
<br />
¢<br />
<br />
r<br />
¢<br />
On site Coulomb repulsion<br />
L(S)DA fails to describe systems with localized (strongly correlated) d and f<br />
<strong>electrons</strong> ¡wrong one-electron energies<br />
Strong <strong>in</strong>tra-atomic <strong>in</strong>teraction is <strong>in</strong>troduced <strong>in</strong> a (screened) Hartree-Fock like<br />
manner ¡replac<strong>in</strong>g L(S)DA on site<br />
E HF¤<br />
1<br />
2 ∑<br />
γ<br />
" <br />
Uγ1 γ3 γ2γ4<br />
Uγ1γ3 γ4 γ2<br />
ˆn γ1 γ 2 ˆn γ3 γ 4<br />
determ<strong>in</strong>ed by the PAW on site occupancies<br />
ˆn γ1 γ 2¤<br />
Ψs2 m2 <br />
¢<br />
£m1<br />
and the (unscreened) on site electron-electron <strong>in</strong>teraction<br />
U γ1 γ 3 γ 2 γ 4¤<br />
m1 m3<br />
r<br />
1<br />
¢ ¢<br />
m2m4 £<br />
¢ Ψs1 £<br />
δ s1 s 2<br />
δ s3 s 4<br />
(<br />
¢ m £<br />
are the spherical harmonics)<br />
M. MARSMAN, <strong>VASP</strong> WORKSHOP, VIENNA 10-15 FEBRUARY 2003. Page 10
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