12.3 Baird’s 4n Rule
Hückel’s rule has shown the importance of molecular topology in order to determine the aromaticity of molecular systems. In this section, we will show that the
electronic state also plays an important role and actually gives rise to a different
counting rule. The number of studies devoted to the aromaticity of excited states is
scarce when compared with the ground-state literature, but the importance of
excited-state aromaticity is very well highlighted in the excellent recent review of
Ottosson and coworkers [37], which puts forward how this property can be used to
rationalize a number of photophysical and photochemical reactions. For instance,
the design of appropriate antiaromatic olefins could lead to excited triplet-state
species suitable for adiabatic Z/E photoisomerization [38] and triplet-state aromaticity was used to explain the stability of substituted fulvenes [39] and the dipole
moments of fulvenes, fulvalenes, and azulene [40]. One of the first evidences of
excited-states aromaticity is due to Baird [15], who used perturbation molecular
orbital theory and Dewar resonance energy arguments to show that aromatic singlet
annulenes were antiaromatic in the lowest-energy excited triplet state (T 1 ), and vice
versa. Baird’s rule states that 4nπ monocycles are aromatic in the T 1 but it is also
generally accepted that these compounds are also aromatic in the lowest-lying
excited singlet states (S 1 ). In 2008, Soncini and Fowler generalized Baird’s rule
stating that open-shell 4n + 2 (4n) annulenes with even (odd) total spin are aromatic, whereas odd (even) total spin monocyclic compounds are antiaromatic [41].
The same year, Mandado and coworkers concluded that all these rules are particular
cases of a more general rule applying separately to α and β electrons [42].
In the following we will focus on analyzing the changing patterns of electron
delocalization and the aromaticity of different vertical excited states of benzene,
cyclobutadiene (CBD) and planar cyclooctatetraene (COT).
1 To this aim, we will
use electron sharing indices (ESI) and multicenter (MCI) aromaticity indices (see
Table 12.2). Interestingly, the ESIs reveal the true symmetry of the excited state
without the need of optimizing the geometry, as they do not depend on the symmetry of the ground state. For instance, benzene’s S 1 keeps the D 6h electronic
distribution but there is small reduction of the ESIs of the peripheral CC bond that
goes with the corresponding decrease of aromaticity. On the contrary, the next two
lowest-energy singlet states, S 2 and S 3 , show the symmetry break to D 2h and a
substantial reduction of aromaticity as compared to S 1 . T 1 exhibits a more evident
symmetry break (ESIs that differ by 0.33 e) and a significant reduction of aromaticity, thus confirming Baird’s rule. According to Soncini and Fowler’s extension of the latter, the lowest-lying quintet state (Q 1 ) should be also aromatic. This
rule cannot be fully confirmed by our calculations as B3LYP assigns a clear
1
The ground-state minimal energy structure of COT is a non-aromatic and non-planar species that
is not so interesting from Baird's rule perspective. For this reason, we have chosen the planar D 4h
COT, which is not an energy minimum but is a stationary point of the potential energy surface with
bond-length alternation and well-known antiaromatic character.
326
F. Feixas et al.
Hückel’s rule has shown the importance of molecular topology in order to determine the aromaticity of molecular systems. In this section, we will show that the
electronic state also plays an important role and actually gives rise to a different
counting rule. The number of studies devoted to the aromaticity of excited states is
scarce when compared with the ground-state literature, but the importance of
excited-state aromaticity is very well highlighted in the excellent recent review of
Ottosson and coworkers [37], which puts forward how this property can be used to
rationalize a number of photophysical and photochemical reactions. For instance,
the design of appropriate antiaromatic olefins could lead to excited triplet-state
species suitable for adiabatic Z/E photoisomerization [38] and triplet-state aromaticity was used to explain the stability of substituted fulvenes [39] and the dipole
moments of fulvenes, fulvalenes, and azulene [40]. One of the first evidences of
excited-states aromaticity is due to Baird [15], who used perturbation molecular
orbital theory and Dewar resonance energy arguments to show that aromatic singlet
annulenes were antiaromatic in the lowest-energy excited triplet state (T 1 ), and vice
versa. Baird’s rule states that 4nπ monocycles are aromatic in the T 1 but it is also
generally accepted that these compounds are also aromatic in the lowest-lying
excited singlet states (S 1 ). In 2008, Soncini and Fowler generalized Baird’s rule
stating that open-shell 4n + 2 (4n) annulenes with even (odd) total spin are aromatic, whereas odd (even) total spin monocyclic compounds are antiaromatic [41].
The same year, Mandado and coworkers concluded that all these rules are particular
cases of a more general rule applying separately to α and β electrons [42].
In the following we will focus on analyzing the changing patterns of electron
delocalization and the aromaticity of different vertical excited states of benzene,
cyclobutadiene (CBD) and planar cyclooctatetraene (COT).
1 To this aim, we will
use electron sharing indices (ESI) and multicenter (MCI) aromaticity indices (see
Table 12.2). Interestingly, the ESIs reveal the true symmetry of the excited state
without the need of optimizing the geometry, as they do not depend on the symmetry of the ground state. For instance, benzene’s S 1 keeps the D 6h electronic
distribution but there is small reduction of the ESIs of the peripheral CC bond that
goes with the corresponding decrease of aromaticity. On the contrary, the next two
lowest-energy singlet states, S 2 and S 3 , show the symmetry break to D 2h and a
substantial reduction of aromaticity as compared to S 1 . T 1 exhibits a more evident
symmetry break (ESIs that differ by 0.33 e) and a significant reduction of aromaticity, thus confirming Baird’s rule. According to Soncini and Fowler’s extension of the latter, the lowest-lying quintet state (Q 1 ) should be also aromatic. This
rule cannot be fully confirmed by our calculations as B3LYP assigns a clear
1
The ground-state minimal energy structure of COT is a non-aromatic and non-planar species that
is not so interesting from Baird's rule perspective. For this reason, we have chosen the planar D 4h
COT, which is not an energy minimum but is a stationary point of the potential energy surface with
bond-length alternation and well-known antiaromatic character.
326
F. Feixas et al.