Chemistry Reference
In-Depth Information
only two unoccupied orbitals, it cannot describe transitions to higher orbitals
accurately. In basis set calculations, the energies of the unbound orbitals that
have
converged
will vary wildly and give unreliable transition frequencies.
One class of XC functionals that should not have this problem are the
asymptotically corrected (AC) functionals.
217,218,227-229
LB94
230
is one of
these functionals, and its performance is shown in Table 8. AC XC potentials
tend to be too shallow in the core region, so the lower KS energy levels will be
too low while the AC piece forces the higher KS states to be bound and their
energies will cluster below zero. Thus, it can be expected that when using AC
functionals, the computed transition frequencies will be consistently underes-
timated.
The KS orbitals found using the OEP method are self-interaction free,
and they are usually better approximations to the true KS orbitals. OEP
also has the correct asymptotic behavior, and as we can see in Table 7, all
orbital energies are negative. In Table 8, the MAE for OEP is 0.34 eV , which
is much lower than that for LDA. Because OEP binds all orbitals, it allows
many more transitions to be calculated. A common OEP functional is exact
exchange (or an approximation
231
to it called KLI), which neglects correla-
tion effects, which are generally small contributions to the KS orbital
energies. Using exact exchange with the ALDA for
f
XC
(which does contain
correlation) leads to good transition frequencies as shown in Table 8.
Although LDA is sometimes closer to the experimental values for the lower
transitions, the value of OEP lies in its ability to describe both the higher as
well as the lower transitions.
Napthalene, a Small Molecule
Returning to our benchmark case of naphthalene: in Table 4 the LHF
(an OEP exact exchange method described above) method is used to find
the orbitals, which are then used with an LSDA or PBE kernel to find the tran-
sition frequencies. Also given are the results if the LSDA/PBE functional had
been used for both steps. We find that excitation energies from combining
LHF with a LDA/PBE kernel are in between the GGA and the hybrid results
(given in Table 4), except for the 1
1
A
u
Rydberg state, whose excitation energy
is significantly improved. The results do not change significantly whether the
LSDA kernel or the PBE GGA kernel is used together with an LHF potential.
The 1
1
B
1
g
and especially the 1
1
A
u
states of naphthalene are diffuse, so
it is not surprising that their excitation energies are considerably underesti-
mated in the LSDA and GGA treatment. Using the asymptotically correct
LHF potential corrects the excitation energy of the 1
1
A
u
state, which is a
pure one-particle excitation out of the 1
a
u
valence orbital into the 10
a
g
Rydberg orbital, the latter of which may be viewed as a 3
s
orbital of the
C
10
H
8
ion. In contrast, a strong mixture of valence and Rydberg excitations
occurs in the 1
1
B
1
g
state. The LHF potential improves the GGA results only
