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metal cluster increases (a more pyramidalized bond), the more reactive the considered
bond should be. Moreover, in EMFs, the electronic transfer from the metal clusters
to the carbon cage implies a reduction of the reactivity of the fullerene because of
the destabilization of the EMF LUMOs disfavoring their interaction with the HOMO
of the diene (in Diels-Alder reaction fullerene compounds act as a dienophile). It
is usually found in fullerenes and EMFs that cycloadditions occur preferentially on
short C-C bonds with lobes of opposite sign on each C atom in some of the accessible
LUMOs of the fullerene cage. The double bond character and appropriate shape of
the LUMO of these C-C bonds facilitate the interaction with the HOMO of the diene.
Thus, bonds with high pyramidalized angles, short C-C distances and correct LUMO
shape should be those more reactive in cycloaddition reactions involving EMFs.
Based on these observations, we present here a study on the Diels-Alder [4
2]
reaction at the BP86/TZP//BP86/DZP level of theory over the 13 non-equivalent
bonds of the
D
3h
-C
78
pristine cage, and its Sc
3
N, Y
3
N, and Ti
2
C
2
EMFs. In
D
3h
-C
78
related EMFs, as opposite to the C
80
systems described in previous sections where the
metal clusters can freely rotate, the rotation of TNTs and carbide unit encapsulated is
highly impeded. Thus, we can directly investigate the changes in the reactivity of the
different non-equivalent bonds (13 in total, see Fig.
4.3
) due to the presence of the
different metal clusters: different orientation, shape, and strain on the fullerene cage
(see Fig.
4.3
). The fullerene deformation energies found at BP86/TZP//BP86/DZP
level are 32.2, 67.5, and 39.9 kcal mol
−
1
for Sc
3
N, Y
3
N, and Ti
2
C
2
, respectively,
indicating that the Y
3
N cluster (the largest one) induces the larger strain on
D
3h
-C
78
cage, followed by Ti
2
C
2
and Sc
3
N in this order.
In Fig.
4.4
we report the activation barriers and reaction energies for each addition
site for
D
3h
-C
78
,Sc
3
N@
D
3h
-C
78
,Y
3
N@
D
3h
-C
78
, and Ti
2
C
2@
D
3h
-C
78
.
D
3h
-C
78
,
Sc
3
N@
D
3h
-C
78
and Ti
2
C
2@
D
3h
-C
78
have 7 different [6, 6] type bonds: (i) Type
A (pyracylenic) bonds 1 and 7; (ii) Type B bonds 2, 4, 5, and 6; and (iii) Type C
(pyrenic) bond 2. Furthermore, there are 6 [5, 6] type bonds, all of them correspond-
ing to the Type D (corannulene), bonds a-f (see Figs.
4.1
and
4.3
for bond types and
nomenclature used here). The large yttrium based TNT cluster occupies the same
position as the Sc
3
N one, but it is forced to adopt a pyramidal configuration inside the
D
3h
-C
78
cage. Therefore, two clearly differentiated areas are present: the so-called
up
region, which is more influenced by the nitrogen atom, and the
down
region which
has the yttrium atoms in close contact. In each area, the 13 non-equivalent bonds
might be considered to take into account all the different addition sites.
Our results indicate that, as a general trend, reaction energies became less exother-
mic (less favorable) and reaction barrier heights increase when a metallic cluster is
encapsulated (see Fig.
4.4
). For the three EMFs, the formal charge transferred from
the metal cluster to the fullerene cage is six electrons, inducing a reduction of the
electron affinity of the carbon cage. Moreover, it is worth to mention here that there
exists a good correspondence between the products obtained under thermodynamic
conditions (those more stable) and those that exhibit lower reaction activation bar-
riers, i.e., the kinetic control products (Garcia-Borràs et al.
2012b
). But the most
important observation is the largely different regioselectivities found for all four
systems.
+
