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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Born-Oppenheimer approximation III<br />
Adiabatic approximation: Ions move on the potential-energy surface of the<br />
electronic ground state only.<br />
Te<br />
©Vee<br />
T N©V NN<br />
r ©VeN<br />
<br />
r<br />
<br />
R ©ε<br />
R<br />
R<br />
Ψ0<br />
χ <br />
<br />
<br />
R<br />
x<br />
<br />
t<br />
R<br />
¦ε0<br />
<br />
R<br />
¦i¯h ∂ ∂t χ<br />
Neglect quantum effects in ionic dynamics replace time-dependent<br />
ionic Schrödinger equation by classical Newtonian equation of motion<br />
<br />
R<br />
Ψ0<br />
x<br />
<br />
t<br />
R<br />
(5)<br />
∂ 2 P I<br />
E 0<br />
t<br />
∂t 2<br />
<br />
R<br />
<br />
¦ε0<br />
∇I E0<br />
<br />
<br />
R<br />
R ©VNN<br />
<br />
R<br />
(6)<br />
Force ∇I E0 R contains contributions from the direct ion-ion interaction<br />
and a term from the gradient of the electronic total energy<br />
<br />
J. HAFNER, <strong>AB</strong>-<strong><strong>IN</strong>ITIO</strong> <strong>MATERIALS</strong> <strong>SIMULATIONS</strong> Page 7
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