Knox synthesized cycloheptatrienyl cation (C 7 H 7
+
), a molecule with six π-electrons
which represents the first experimental support to Hückel’s rule [27]. Although the
original formulation of the 4n + 2 rule was limited to monocycles, Clar and later on
Glidewell and Lloyd generalized the concept to characterize the aromaticity of
polycyclic aromatic hydrocarbons (PAH) [20, 22]. In addition, the 4n + 2 rule has
been used to rationalize multifold aromaticity in all-metal clusters [3]. More
recently, Mayer derived the 4n + 2 rule analytically to determine the energetic effects
of the ring closure [28]. As mentioned above, important advances in the field of
aromaticity has led to the definition of a number of versatile descriptors based on the
measurement of structural, magnetic, energetic or electronic properties. Before
applying these indicators to complex molecular systems, the performance of such
descriptors is usually assessed for a set of annulenes and PAH that obey 4n + 2 and
4n aromaticity rules. One of the first aromaticity criteria was suggested by Breslow
who proposed to estimate the aromatic character of a ring by comparing the π-energy
of a cyclic π-conjugated system with respect to the corresponding iso-π-electronic
linear compound [29]. A decrease of energy upon cyclization is related to aromaticity while an increase points out antiaromaticity. In 1972, Hobey demonstrated
that Breslow’s proposal is connected to the 4n + 2 Hückel’s rule [30]. The 4n + 2 rule
has also been assessed by means of other energetic and magnetic indicators,
including aromatic stabilization energy (ASE) calculations, nucleus independent
chemical shifts (NICS) [31] and ring currents [32] among many others.
The concept of aromaticity is strongly related to molecular topology and cyclic πelectron delocalization. The aim of this section is to explore the nature of π-electron
delocalization patterns in simple aromatic and antiaromatic compounds that are in
agreement with the 4n + 2 and 4n rules respectively. To this end, we selected a set of
neutral annulenes and their respective dianions and dications. Electronic delocalization is usually studied by computing the so-called electron sharing indices
(ESI) or through the calculation of the electron localization function (ELF) [33]. In
this work we made use of ESI calculated in the framework of the quantum theory of
atoms in molecules (QTAIM) [34]. The sum of all ESI gives the total delocalization
of the system, δ TOT . Interestingly, for planar systems the total electronic delocalization can be exactly split into σ and π contributions, δ TOT = δ σ + δ π . To analyze the
differences on electronic delocalization between aromatic and antiaromatic systems,
we studied how δ π changes when two π-electrons are either added or removed from a
set of 4n + 2 aromatic and 4n antiaromatic systems [35]. Let us consider an aromatic
4n + 2 system such as benzene (see Scheme 12.1). If we add two electrons to
benzene (N electrons), we obtain a 4n system (C 6 H 6
2− with N + 2 electrons), which
should be antiaromatic according to Hückel’s rule. Therefore, we expect these two
added electrons will be mainly localized and the value of δ π will be barely affected
with respect to C 6 H 6 . As Table 12.1 shows, δ π is 3.369 e for C 6 H 6 whereas the total
electronic delocalization in C 6 H 6
2− is 3.482 e. We added a pair of π-electrons but
only an increment of 0.113 e is observed. Thus, a net change on electronic delocalization close to zero is expected when going from N to N + 2 species if N is an
aromatic 4n + 2 system. On the other hand, if we subtract two π-electrons from C 6 H 6
to obtain the antiaromatic C 6 H 6
2+ (with N − 2 electrons) one expects a significant
12 Rules of Aromaticity
323
+
), a molecule with six π-electrons
which represents the first experimental support to Hückel’s rule [27]. Although the
original formulation of the 4n + 2 rule was limited to monocycles, Clar and later on
Glidewell and Lloyd generalized the concept to characterize the aromaticity of
polycyclic aromatic hydrocarbons (PAH) [20, 22]. In addition, the 4n + 2 rule has
been used to rationalize multifold aromaticity in all-metal clusters [3]. More
recently, Mayer derived the 4n + 2 rule analytically to determine the energetic effects
of the ring closure [28]. As mentioned above, important advances in the field of
aromaticity has led to the definition of a number of versatile descriptors based on the
measurement of structural, magnetic, energetic or electronic properties. Before
applying these indicators to complex molecular systems, the performance of such
descriptors is usually assessed for a set of annulenes and PAH that obey 4n + 2 and
4n aromaticity rules. One of the first aromaticity criteria was suggested by Breslow
who proposed to estimate the aromatic character of a ring by comparing the π-energy
of a cyclic π-conjugated system with respect to the corresponding iso-π-electronic
linear compound [29]. A decrease of energy upon cyclization is related to aromaticity while an increase points out antiaromaticity. In 1972, Hobey demonstrated
that Breslow’s proposal is connected to the 4n + 2 Hückel’s rule [30]. The 4n + 2 rule
has also been assessed by means of other energetic and magnetic indicators,
including aromatic stabilization energy (ASE) calculations, nucleus independent
chemical shifts (NICS) [31] and ring currents [32] among many others.
The concept of aromaticity is strongly related to molecular topology and cyclic πelectron delocalization. The aim of this section is to explore the nature of π-electron
delocalization patterns in simple aromatic and antiaromatic compounds that are in
agreement with the 4n + 2 and 4n rules respectively. To this end, we selected a set of
neutral annulenes and their respective dianions and dications. Electronic delocalization is usually studied by computing the so-called electron sharing indices
(ESI) or through the calculation of the electron localization function (ELF) [33]. In
this work we made use of ESI calculated in the framework of the quantum theory of
atoms in molecules (QTAIM) [34]. The sum of all ESI gives the total delocalization
of the system, δ TOT . Interestingly, for planar systems the total electronic delocalization can be exactly split into σ and π contributions, δ TOT = δ σ + δ π . To analyze the
differences on electronic delocalization between aromatic and antiaromatic systems,
we studied how δ π changes when two π-electrons are either added or removed from a
set of 4n + 2 aromatic and 4n antiaromatic systems [35]. Let us consider an aromatic
4n + 2 system such as benzene (see Scheme 12.1). If we add two electrons to
benzene (N electrons), we obtain a 4n system (C 6 H 6
2− with N + 2 electrons), which
should be antiaromatic according to Hückel’s rule. Therefore, we expect these two
added electrons will be mainly localized and the value of δ π will be barely affected
with respect to C 6 H 6 . As Table 12.1 shows, δ π is 3.369 e for C 6 H 6 whereas the total
electronic delocalization in C 6 H 6
2− is 3.482 e. We added a pair of π-electrons but
only an increment of 0.113 e is observed. Thus, a net change on electronic delocalization close to zero is expected when going from N to N + 2 species if N is an
aromatic 4n + 2 system. On the other hand, if we subtract two π-electrons from C 6 H 6
to obtain the antiaromatic C 6 H 6
2+ (with N − 2 electrons) one expects a significant
12 Rules of Aromaticity
323