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affinity. In general, the [6, 6] addition becomes more favored as compared to the
[5, 6] one when the size of the metallic cluster increases and the deformation of
the fullerene cage is higher, and when the charge transfer to the cage is larger. This
is the first reported study that provides an extended guideline for experimental and
computational chemists to understand and predict the reactivity and regioselectivity
of the Diels-Alder cycloaddition on the
I
h
-C
80
based EMFs.
4.3
Dispersion Interactions
4.3.1
The Importance of the Dispersion Corrections for the Study
of Chemical Reactivity in Fullerenes
The DA cycloaddition between cyclopentadiene and C
60
for which experimental
results on energy barriers and reaction energies were known was studied by some
of us (Osuna et al.
2009b
). It was found that the two-layered ONIOM2(B3LYP/6-
31G(d):SVWN/STO-3G) method provides results very close to the full B3LYP/6-
31G(d) ones. Unfortunately, the exothermicity of the reaction and also the energy
barrier were clearly overestimated by these two methods compared to the experimen-
tal values (errors of ca. 12 kcal mol
−
1
, see Fig.
4.10
). Goerigk and Grimme (Goerigk
and Grimme
2010
) demonstrated that the B3LYP mean absolute deviation for an
extensive benchmark was reduced by about 2 kcal mol
−
1
when dispersion correc-
tions were taken into account (B3LYP-D). Similarly, Grimme and coworkers (Kruse
and Grimme
2009
; Korona et al. (
2009
; Hesselmann and Korona
2011
) pointed out
the importance of London dispersion corrections to obtain good estimates of the
interaction energy of C
60
and C
70
with encapsulated H
2
and a noble gas molecule.
In light of the Grimme and Korona observations, we decided to investigate the
effect of including dispersion interactions on the reaction and activation energies for
the DA cycloaddition between cyclopentadiene and C
60
. Our calculations includ-
ing dispersion corrections indicate that the inclusion of London dispersion effects is
mandatory to get an accurate description of the energy profile in the DA cycloaddition
studied (see Fig.
4.10
). B3LYP including Grimme dispersion corrections and also
the hybrid meta exchange-correlation DFT functional M06-2X, (Zhao and Truh-
lar
2008
) which includes medium-range correlation, yield reaction and activation
energies close to the experimental values. ONIOM2 (M06-2X:SVWN) gives also
accurate reaction energies (the reaction energy is overestimated by 2.2 kcal mol
−
1
,
see Fig.
4.10
), but somewhat less accurate activation barriers (5.2 kcal mol
−
1
higher
than the experimental value).
We finally performed calculations both with and without dispersion corrections
for the DA reaction of C
60
and several dienes and for the DA cycloaddition of a
(5,5) single walled carbon nanotube and 1,3-
cis
-butadiene. In all cases, large sta-
bilizations are found which range from 15 to 22 kcal mol
−
1
for the larger dienes
presenting aromatic rings, such as anthracene. The results obtained in this study
