E
C
I
The key problem in solving the manybody problem is that
the electrons form an interacting system with a
wavefunction of the form
Ψ
(
r
)
≡
Ψ
(
r
1
,
r
2
, . . . ,
r
N
)
.
I
In HF, all correlations except those required by the
Pauli
exclusion principle
are neglected. The exchange term in
the Hamiltonian (see eq. 32) has two roles; it introduces
the exclusion principle and an electronic selfinteraction
(which must be canceled in the correlation term).
I
The effect is always towards lower energy, which can be
interpreted as the interaction between the electron and a
positive
exchange hole
around it.
I
One way to interpret the
exchange energy
is that it gives
the lowering of the energy due to each electron
interacting with the corresponding exchange hole.
Notes
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
I
Taking the correlation effects between the electrons into
account involves introducing new degrees of freedom to
the wavefunction.
I
As a result, the energy of any state of the system always
decreases – this lowering is called the
correlation energy
E
This is the end of the preview.
Sign up
to
access the rest of the document.
 Winter '12
 Kotakoski
 DFT, Pauli exclusion principle, density functional theory, exclusion principle, ManyBody Systems

Click to edit the document details