Chemistry Reference
In-Depth Information
25
Continuum
5
6S
24
4S
3
3P
23
22
2P
21
2S
20
Exact KS
ALDAx
EXX
19
Figure 6
Spectrum of helium calculated using the ALDAx kernel and the exact exchange
kernel
232
with the exact KS orbitals. The importance of nonlocality for the XC kernel
can be seen, as the exchange part of ALDA gives a noticeable error compared to the
exchange part of the true functional (the AEXX kernel for He).
Errors in Potential vs. Kernel
It has long been asserted that fixing the defects in the potential, especially
its asymptotic behavior, is the major challenge to improving TDDFT
results.
227-229
We argue here that this assertion is overly simplistic, and base
this upon tests carried out on atoms and small molecules. In large molecules,
where the scientific interest is in the many low-lying transitions, the potential
can be sufficiently accurate, while the kernel may play a larger role.
The analysis done for naphthalene above can shed some light of the gen-
eral failure of TDDFT in underestimation of the
1
L
a
transitions in PAHs.
Using the self-interaction free LHF potential does not obviate this problem,
as is illustrated in Table 9. To the best of our knowledge, the cause of this
shortcoming of TDDFT is not well understood. We note, however, that the
same incorrect ordering of
1
L
a
and
1
L
b
occurs in the CIS approximation,
which is also self-interaction free. The analysis here shows that this is a failure
of approximations for the XC kernel rather than to the ground-state potential.
Table 9
Naphthalene: Effect of Ground-State Potential on the Excitations of Table 4
Method
1
1
B
3
u
1
1
B
2
u
2
1
A
g
1
1
B
1
g
2
1
B
3
u
1
1
A
u
LSDA
4.191
4.026
5.751
4.940
5.623
5.332
LHF/LSDA
4.317
4.143
5.898
5.097
5.752
5.686
PBE
4.193
4.031
5.753
4.957
5.622
5.141
LHF/PBE
4.295
4.121
5.876
5.091
5.741
5.693
''best''
4.0
4.5
5.5
5.5
5.5
5.7
