value of 0.17 Å seems to confirm the aromatic character of this closo borane.
Resonance energies per face calculated by Aihara [48] indicate that [B 7 H 7 ]
2− is the
most aromatic closo borane [B n H n ]
2− (n = 5–12) after [B 6 H 6 ]
2− . Similar links are
found for C 4 H 4
2− , C 5 H 5
− and C 7 H 7
+ with [B 5 H 5 ]
2− , [B 6 H 6 ]
2− , and [B 8 H 8 ]
2− ,
respectively [63]. As a summary, the ECSA method links highly stable monocyclic
hydrocarbon reference compounds fulfilling (4n + 2)π Hückel’s electron rule with
the corresponding monodeltahedral closo borane clusters that obey the 4n + 2
Wade-Mingos rule. Noticeably the value of n has not the same meaning in one
equation and the other. In (4n + 2)π Hückel’s rule n can be any integer and has no
direct relationship with the structure; conversely in 4n + 2 Wade-Mingos’ rule n is
structure dependent and refers to the number of vertexes occupied by boron atoms.
12.6 Conclusions
One of the main difficulties faced by researchers interested in aromaticity characterization is the lack of a physical basis for this property, which makes its quantification difficult. The existence of rules of aromaticity that provide the magical
numbers of electrons that are required to reach this property helps to characterize
C
C
H
H
H
H
cS
eT
sA
C C
B B
H
B B
H
H
H
H
H
H
C B
H
H
H
H
B B
H
H
H
H
H
H
H
H
H
H
H
H
1.329
1.085
1.457
1.094
1.221
1.640
1.235
1.623
1.217
1.380
1.764
1.186
1.316
C
C
H
H
H
H
B
B
H
H
H
H
B
B
H
H
H
H
H
sA
B
B
H
H
H
H
H
H
(a)
(b)
Scheme 12.3 a Link established by ECSA between ethene and diborane. The total number of
valence electrons in the confined space in blue remains constant and equal to 12. b A number of
species derived from the application of ECSA to ethene (bond lengths in Å)
eT
sA
sR
2H
H
H
H
H
H
B
B
B
B
B
B
H
H
H
H
H
H
B
B
B
B
B
B
B
H
H
H
H
H
H
H
2B
B
B
B
B
B
H
H
H
H
H
H
HB
Scheme 12.4 Link established by ECSA between benzene and [B 7 H 7 ]
2−
. The total number of
valence electrons in the confined space remains constant and equal to 30
12 Rules of Aromaticity
331
Resonance energies per face calculated by Aihara [48] indicate that [B 7 H 7 ]
2− is the
most aromatic closo borane [B n H n ]
2− (n = 5–12) after [B 6 H 6 ]
2− . Similar links are
found for C 4 H 4
2− , C 5 H 5
− and C 7 H 7
+ with [B 5 H 5 ]
2− , [B 6 H 6 ]
2− , and [B 8 H 8 ]
2− ,
respectively [63]. As a summary, the ECSA method links highly stable monocyclic
hydrocarbon reference compounds fulfilling (4n + 2)π Hückel’s electron rule with
the corresponding monodeltahedral closo borane clusters that obey the 4n + 2
Wade-Mingos rule. Noticeably the value of n has not the same meaning in one
equation and the other. In (4n + 2)π Hückel’s rule n can be any integer and has no
direct relationship with the structure; conversely in 4n + 2 Wade-Mingos’ rule n is
structure dependent and refers to the number of vertexes occupied by boron atoms.
12.6 Conclusions
One of the main difficulties faced by researchers interested in aromaticity characterization is the lack of a physical basis for this property, which makes its quantification difficult. The existence of rules of aromaticity that provide the magical
numbers of electrons that are required to reach this property helps to characterize
C
C
H
H
H
H
cS
eT
sA
C C
B B
H
B B
H
H
H
H
H
H
C B
H
H
H
H
B B
H
H
H
H
H
H
H
H
H
H
H
H
1.329
1.085
1.457
1.094
1.221
1.640
1.235
1.623
1.217
1.380
1.764
1.186
1.316
C
C
H
H
H
H
B
B
H
H
H
H
B
B
H
H
H
H
H
sA
B
B
H
H
H
H
H
H
(a)
(b)
Scheme 12.3 a Link established by ECSA between ethene and diborane. The total number of
valence electrons in the confined space in blue remains constant and equal to 12. b A number of
species derived from the application of ECSA to ethene (bond lengths in Å)
eT
sA
sR
2H
H
H
H
H
H
B
B
B
B
B
B
H
H
H
H
H
H
B
B
B
B
B
B
B
H
H
H
H
H
H
H
2B
B
B
B
B
B
H
H
H
H
H
H
HB
Scheme 12.4 Link established by ECSA between benzene and [B 7 H 7 ]
2−
. The total number of
valence electrons in the confined space remains constant and equal to 30
12 Rules of Aromaticity
331