Chemistry Reference
In-Depth Information
potentials is to use the optimized effective potential (OEP) method
159,174
and
include exact exchange or other self-interaction-free functionals.
219
OEP
produces a far more accurate KS potential, with the correct asymptotic
behavior. The major remaining error is simply the correlation contribution
to the position of the HOMO, i.e., a small shift. Unfortunately, we do not
yet have an accurate correlation energy functional to match with exact
exchange for energetics.
N
2
, a Very Small Molecule
To illustrate the influence of different ground-state potentials consider
the N
2
molecule. In all the cases discussed below, a SCF step was carried
out using the ground-state potential to find the KS levels, which are then
used as input to Eq. [47] with the ALDA XC kernel.
The KS energy levels and KS orbitals for the LDA functional are shown
in Table 7. The orbitals are calculated with two different numerical methods,
the first is fully numerical basis set free (i.e., solved on a real space grid) while
the other uses the Sadlej (52 orbitals) basis set
220
[the OEP results for the EXX
(KLI) approximation shown in Table 7 are also calculated basis set free]. Note
that the eigenvalues for the higher unoccupied states are positive. This is due to
the LDA potential being too shallow and not having the correct asymptotic
Table 7
Orbital Energies of the KS Energy Levels for N
2
at Separation
R
¼
2
:
0744 a.u.
Energies in (eV)
LDA
LDA
OEP
Basis Set Free
a
Sadlej
b
Basis Set Free
a
Orbital
Occupied Orbitals
1
s
g
380
:
05
380
:
82
391
:
11
1
s
u
380:02
380:78
391:07
2
s
g
28:24
28:52
35:54
2
s
u
13
:
44
13
:
40
20
:
29
1
p
u
11
:
89
11
:
86
18
:
53
3
s
g
10
:
41
10
:
38
17
:
15
Unoccupied Orbitals
1
p
g
2
:
21
2
:
23
8
:
44
4
s
g
0
:
04
0.66
5
:
05
2
p
u
>
0
1.93
4
:
04
3
s
u
>
0
1.35
3
:
54
1
d
g
>
0
—
2
:
76
5
s
g
>
0
3.20
2
:
49
6
s
g
>
0
—
2
:
33
2
p
g
>
0
3.89
2
:
17
3
p
u
>
0
—
2
:
04
a
From Ref. 221.
b
From Ref. 222.
