Chemistry Reference
In-Depth Information
0.5
ALDA
Hartree
KS
Exact
0.4
0.3
0.2
0.1
0.0
-0.15
-0.10
-0.05
0.00
Energy (a.u.)
Figure 11
Corrections due to using the Hartree and ALDA kernel on the exact KS
s
quantum defect of He. The Hartree kernel affects only the singlet defect, shifting them to
values that are too low. If a good XC kernel is then used, both the triplet and singlet
quantum defects should move from the Hartree kernel toward the exact QD values.
245
In this case, ALDA does a good job and is performing well.
value because the direct term includes no spin flipping. The Hartree approxi-
mation definitely improves the KS for the singlet. Finally, we include ALDA
XC corrections. Only if these latter corrections significantly improve the
results compared to the Hartree curves can we say TDDFT is really working
here. Clearly it does, reducing the Hartree error enormously.
The results of Figure 11 are also typical of He
p
transitions, and Be
s
and
p
transitions; however, for unknown reasons, the
s
!
d
transitions fail badly
for both of these systems.
244,246
Saving Standard Functionals
The incorrect long-range behavior of the potential from standard density
functionals is a problem only when Rydberg excitations are needed. It would
be unsatisfactory to perform a completely different type of calculation such as
OEP in order to include such excitations, especially if the cost of that calcula-
tion is untenable.
It is possible, with some thought and care, however, to extract the
Rydberg series from the short-ranged LDA potential by using quantum defect
