The Born-Oppenheimer
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Transcript The Born-Oppenheimer
Born-Oppenheimer approximation
H Tn Te Vnn Vee Vne
H( R, r ) E( R, r )
Nuclear coordinates
Electronic coordinates
B
A
He
[Te Vne Vee ]e (r; R) Ee ( R)e (r; R)
( R, r ) n ( R)e (r; R)
Parameter
Born-Oppenheimer approximation (continued)
*
*
*
dr
T
dr
V
dr
e n e nn e [Te Vne Vee ]
E dr
*
e
dr dr
*
e
dr V
*
e nn
2
e
2
Vnn n dr e Vnn n
dr H dr H
*
e
e
n n
n
*
e
e
e
Ee n
*
*
dr
T
dr
e n e Tn (n e )
Tn n dr e Tn n
2
Born-Oppenheimer approximation (continued)
[Te Vne Vee ]e (r; R) Ee ( R)e (r; R)
*E ] ( R) E* ( R)
[
T
V
dr T n drnne Vnne n dre [Tne Vne Vee ]
*
e n
( R*,
r ) n ( R)e (r; R)
E dr
e
BO-approximation
• a particular form of the
wavefunction
• neglect the nuclear
derivatives of the electronic
wavefunction
• neglect the kinetic energy
of the nuclei
QC method
• make a guess for the initial
structure
• determine the electronic
wavefunction
• add the nucleur repulsion
• minimize the total energy
• add nucleur kinetic energy