Chemistry Reference
In-Depth Information
kcal mol
−
1
,
E
‡
17.1 kcal mol
−
1
), type B [6, 6] bond
6
(
E
R
=−
=
11.0 kcal
mol
−
1
,
E
‡
18.3 kcal mol
−
1
), and type D [5, 6] bond
e
(
E
R
=−
4.1 kcal mol
−
1
,
=
E
‡
17.2 kcal mol
−
1
), situated all of them in the down region. Finally, the titanium
carbide
D
3h
-C
78
based EMF (Ti
2
C
2
@
D
3h
-C
78
) most favored additions correspond to
the cycloaddition over type D [5, 6]
c
bond (
E
R
=−
=
18.1 kcal mol
−
1
,
E
‡
=
17.4
kcal mol
−
1
), type B [6, 6]
3
bond (
E
R
=−
14.1 kcal mol
−
1
,
E
‡
=
18.2 kcal
mol
−
1
) and type D [5, 6]
f
bond (
E
R
=−
14.6 kcal mol
−
1
,
E
‡
19.3 kcal
mol
−
1
). In Fig.
4.4
the different reactivity for all nonequivalent bonds is compared.
In Table
4.1
we report the C-C bond distances and pyramidalization angles for
each studied system. As can be seen there, for the empty fullerene and Sc
3
N@
D
3h
-
C
78
EMF (the least strained cage as discussed before), the most favorable addition
sites present the shortest C-C bond distances (
1
,
7
, and
b
for
D
3h
-C
78
, and
4
,
6
and
c
for Sc
3
N@
D
3h
-C
78
). But there are some bonds that although they present
similar bond distances, their reaction energies are clearly different (for instance,
bonds
6
and
7
in Sc
3
N@
D
3h
-C
78
). As it happens with bond distances, the predic-
tion of the fullerene reactivity analyzing the pyramidalization angles is not clear.
These observations indicate that in the case of endohedral compounds, there is not
an overall correlation between C-C bond distances, pyramidalization angles and
reaction energies.
It is usually said that in DA reactions it is very important to have good overlaps
between the HOMO orbital of the diene and the LUMO orbital of the dienophile.
In the present case,
s-cis-
1,3-butadiene acts as the diene while fullerenes and EMF
compounds act as the dienophiles. In Fig.
4.5
we report the 3 lowest-energy un-
occupied molecular orbitals (LUMOs) of
D
3h
-C
78
and the related Ti
2
C
2
@
D
3h
-C
78
EMF. As can be seen there, because of the largely delocalized molecular orbitals,
there are many bonds that present the correct shape to interact with the HOMO of
the diene. For example, for the titanium EMF the bonds that present similar suit-
able antibonding character to interact correctly with the diene are:
a, c, f, 1, 2, 3,
4, 5,
and
7
. However, three of these bonds (
4
,
5
, and
7
) present endothermic re-
action energies. Hence, predictions of the fullerene and EMF reactivities based on
the LUMO orbitals analysis are also too imprecise, as one finds too many bonds
suitable to interact, although some of them are not very reactive. Therefore bond
distances, pyramidalization angles or LUMOs shape cannot be used as a predictor
of fullerene compounds reactivity, and as a consequence, all the possible additions
should be investigated in order to give the correct picture of the reactivity of the con-
sidered compound. Even so, these tools are shown to be very useful for analyzing
the different reactivity trends.
We have seen that the most reactive bonds in Sc
3
N@
D
3h
-C
78
exhibit short C-C
bond distances with relatively high pyramidalization angles and situated far from
the scandium atoms' influence. When the reaction takes place on Y
3
N@
D
3h
-C
78
the
addition is basically favored over bond
d
having one of the yttrium atoms in close
contact and one of the longest C-C bonds. The same situation is found for the
f
bond
in the Ti
2
C
2
system. This preference for these bonds closer to the metal cluster is
due to the fact that an addition there reduces the strain energy of the cage. We have
to keep in mind that fullerene deformation energies for Y
3
N and Ti
2
C
2
EMFs are
much larger than the one found for the Sc
3
N EMF. Thus, changes on the carbon cage
=
