AB-INITIO SIMULATIONS IN MATERIALS SCIENCE - VASP
AB-INITIO SIMULATIONS IN MATERIALS SCIENCE - VASP
AB-INITIO SIMULATIONS IN MATERIALS SCIENCE - VASP
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2<br />
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©Exc<br />
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43<br />
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r(<br />
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Density-functional theory IV<br />
E n<br />
¦T<br />
n<br />
©<br />
E H<br />
with the exchange-correlation energy<br />
n<br />
n ©V<br />
r<br />
r<br />
n d3r (16)<br />
<br />
<br />
E xc<br />
n<br />
r<br />
<br />
¦n<br />
r<br />
ε xc<br />
n<br />
r d 3 r<br />
(17)<br />
where ε xc n r is the exchange-correlation energy of a homogeneous<br />
electron gas with the local density n r<br />
<br />
Kohn-Sham equations:<br />
¯h 2<br />
V<br />
2m ∇2©<br />
r<br />
©<br />
e 2<br />
r <br />
n r<br />
d 3 r©µ xc n r<br />
φ i<br />
r<br />
<br />
¦εi φi <br />
r<br />
(18)<br />
V e f f<br />
¨<br />
r<br />
with the exchange-correlation potential<br />
µ xc<br />
n<br />
r<br />
¦<br />
δE xc<br />
n r<br />
δn r<br />
δ n r<br />
δn<br />
ε xc<br />
n<br />
r<br />
r<br />
(19)<br />
J. HAFNER, <strong>AB</strong>-<strong><strong>IN</strong>ITIO</strong> <strong>MATERIALS</strong> <strong>SIMULATIONS</strong> Page 15
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