12.5 Equivalence Between Wade-Mingos’
and Hückel’s Rules
Closo boron hydride clusters are anions with the general formula [B n H n ]
2− that
have the structure of a polyhedron with triangular faces [59]. They are very stable
and unreactive and because of that they are considered aromatic. They obey the
2n + 2 Wade rule [17, 60], in which n are the vertexes of the polyhedron, or
Mingos’ 4n + 2 rule [16, 61]. Both rules are equivalent: Wade’s rule refers to the
cage electron pairs whereas Mingos’ rule incorporates also the exo electron pairs
corresponding to the B–H bonds, thus referring to the total number of valence
electrons.
In a recent work [62], some of us have established a link between the hydrocarbon and boron hydride chemistries by showing that hydrocarbons and boron
hydrides have a common root regulated by the number of valence electrons in a
confined space. Application of the so-called electronic confined space analogy
(ECSA) method to archetypal hydrocarbons leads to well-known boron hydrides
and, even more importantly, it allows the design of new interesting molecules that
can be a source of inspiration for synthetic chemists. In addition, application of
ECSA also allows to reach the conclusion that the 4n + 2 Wade-Mingos rule for
three-dimensional closo boranes is equivalent to the (4n + 2)π Hückel rule for
bidimensional PAHs [63].
The steps followed to apply the ECSA method are the following: (1) first we
state the model organic compound; (2) next we define its confined space (cS) as the
molecular space occupied by the molecule; (3) we transmute each C atom into a B
atom and one electron (eT); (4) these extra electrons are replaced by sacrificial
atoms (sA); (5) and finally (if necessary) we generate the new boronhydride
compound by structural relaxation (sR). During the whole process, the number of
valence electrons in the corresponding confined space remains unaltered. As sacrificial atoms we use H
+
, B
3+ or [BH]
4+ among others. These cations have empty
valence orbitals perfectly suited to form multicenter bonds. As an example of the
procedure, in Scheme 12.3 we apply the ECSA method in the case of ethene. ECSA
links ethene with diborane (Scheme 12.3a). However, it also links ethene with
known dianionic diboranes (B 2 R 4
2−
) [64–69] and yet to be discovered R 2 CBR 2
2− ,
B 2 HR 4
− or R 2 CHBR 2
2− species (Scheme 12.3b).
When the ECSA method is applied to aromatic molecules, a connection between
the aromatic closo boranes following the Wade-Mingos rule and the classical
organic molecules that obey Hückel’s rule emerges [63]. As an example, let us
consider benzene that is the archetype of the aromatic molecules (see Scheme 12.4).
In this case 36 electrons is the total number of valence electrons in the confined
space. The electronic transmutation with B
− drives us to [B 6 H 6 ]
6− with chair-like
structure. The sacrificial group we add is [BH]
4+ leading to hexagonal pyramid
[B 7 H 7 ]
2− that is not a minimum, but relaxes to a pentagonal bipyramid [B 7 H 7 ]
2− , as
experimentally found [70]. The NICS(0) of −22.8 ppm points out that [B 7 H 7 ]
2− is
at least as aromatic as benzene [63]. The relatively low bond length alternation
330
F. Feixas et al.
and Hückel’s Rules
Closo boron hydride clusters are anions with the general formula [B n H n ]
2− that
have the structure of a polyhedron with triangular faces [59]. They are very stable
and unreactive and because of that they are considered aromatic. They obey the
2n + 2 Wade rule [17, 60], in which n are the vertexes of the polyhedron, or
Mingos’ 4n + 2 rule [16, 61]. Both rules are equivalent: Wade’s rule refers to the
cage electron pairs whereas Mingos’ rule incorporates also the exo electron pairs
corresponding to the B–H bonds, thus referring to the total number of valence
electrons.
In a recent work [62], some of us have established a link between the hydrocarbon and boron hydride chemistries by showing that hydrocarbons and boron
hydrides have a common root regulated by the number of valence electrons in a
confined space. Application of the so-called electronic confined space analogy
(ECSA) method to archetypal hydrocarbons leads to well-known boron hydrides
and, even more importantly, it allows the design of new interesting molecules that
can be a source of inspiration for synthetic chemists. In addition, application of
ECSA also allows to reach the conclusion that the 4n + 2 Wade-Mingos rule for
three-dimensional closo boranes is equivalent to the (4n + 2)π Hückel rule for
bidimensional PAHs [63].
The steps followed to apply the ECSA method are the following: (1) first we
state the model organic compound; (2) next we define its confined space (cS) as the
molecular space occupied by the molecule; (3) we transmute each C atom into a B
atom and one electron (eT); (4) these extra electrons are replaced by sacrificial
atoms (sA); (5) and finally (if necessary) we generate the new boronhydride
compound by structural relaxation (sR). During the whole process, the number of
valence electrons in the corresponding confined space remains unaltered. As sacrificial atoms we use H
+
, B
3+ or [BH]
4+ among others. These cations have empty
valence orbitals perfectly suited to form multicenter bonds. As an example of the
procedure, in Scheme 12.3 we apply the ECSA method in the case of ethene. ECSA
links ethene with diborane (Scheme 12.3a). However, it also links ethene with
known dianionic diboranes (B 2 R 4
2−
) [64–69] and yet to be discovered R 2 CBR 2
2− ,
B 2 HR 4
− or R 2 CHBR 2
2− species (Scheme 12.3b).
When the ECSA method is applied to aromatic molecules, a connection between
the aromatic closo boranes following the Wade-Mingos rule and the classical
organic molecules that obey Hückel’s rule emerges [63]. As an example, let us
consider benzene that is the archetype of the aromatic molecules (see Scheme 12.4).
In this case 36 electrons is the total number of valence electrons in the confined
space. The electronic transmutation with B
− drives us to [B 6 H 6 ]
6− with chair-like
structure. The sacrificial group we add is [BH]
4+ leading to hexagonal pyramid
[B 7 H 7 ]
2− that is not a minimum, but relaxes to a pentagonal bipyramid [B 7 H 7 ]
2− , as
experimentally found [70]. The NICS(0) of −22.8 ppm points out that [B 7 H 7 ]
2− is
at least as aromatic as benzene [63]. The relatively low bond length alternation
330
F. Feixas et al.