More than 30 years ago, Bader et al. [20] and Cremer et al. [21] published two
seminal papers about the use of electron distributions and bcp properties for
describing conjugation, hyperconjugation and homoaromaticity features. Those
papers opened the way to the study of the various facets related to electron delocalization through electron-based descriptors. One main conclusion was that the
electronic effects predicted by orbital models could be mirrored into observable
properties of the electron density distribution, along with the important additional
pro that being based on an observable, the analysis may be equally applied to non
planar systems, where the σ-π separation of the molecular orbital models does no
longer apply. In those two studies, descriptors like the electron-density-based bond
orders, the bond ellipticity and the degree of the alignment of axes uniquely
defining the plane of the π-electron distribution for each CC bond had for the first
time been introduced to quantify the extent of electron delocalization (and aromaticity). Successful applications of the method had then concerned several
interesting cases, like the assessment of potential homoaromatic conjugation in a
series of non planar cations, including the debated case of the homotropylium
cation [21, 22] or the characterization of competing electron conjugation pathways
in some 11,11-disubstituted 1,6-methane[10]annulenes [23, 24].
Though it had been unequivocally shown that the electron density bears recognizable signatures (of the effects) of electron delocalization, it later on became
progressively evident that its very mechanism is immediately related only to the
quantum-mechanical correlation among electron pairs. Such correlation had long
time before already been discussed, among others, by Mc Weeney [25] and Bader
and Stephens [26]. The so called exchange-correlation density, ρ 2,xc (r 1 , r 2 ), is an
useful tool to study such correlation. It measures the deviation between the true pair
density of a system and that given by the purely classical description of a product of
two independent electron densities, not subject to any Coulomb and Fermi correlation of electron motions. Use of the exchange-correlation density has led through
years to the definition of several electron delocalization descriptors, like the so
called delocalization indices (DI’s) [27], that provide an estimate of the number of
electrons pairs delocalized (shared) between two atoms Ω and Ω′, no matter
whether they are or they are not directly linked by a bond path. DI’s have been
largely employed to highlight delocalization effects and to quantify aromaticity, for
example through the so-called para-delocalization index PDI [28] or the Fermi Hole
Delocalization Density index, FHDD [29], which both represent global measures of
electron delocalization non homogeneity. The performance of such global aromaticity indicators has also been extensively compared with that of several other
aromaticity measures, less fundamental in nature and based instead on given,
indirect consequences of electron delocalization. The HOMA (Harmonic Oscillator
Model of Aromaticity) [30, 31] and NICS (Nucleus-Independent Chemical Shift)
[32, 33] indices, represent just two popular examples. HOMA exploits the increase
of the CC bond length equalization with increasing electron delocalization homogeneity, while NICS the supposedly different magnetic shielding of a magnetic test
dipole at the center of a conjugated ring in the presence of a diatropic (aromatic
system) or paratropic (antiaromatic system) ring current. Both indices have been
5 Exploring Chemistry Through the Source Function …
105
seminal papers about the use of electron distributions and bcp properties for
describing conjugation, hyperconjugation and homoaromaticity features. Those
papers opened the way to the study of the various facets related to electron delocalization through electron-based descriptors. One main conclusion was that the
electronic effects predicted by orbital models could be mirrored into observable
properties of the electron density distribution, along with the important additional
pro that being based on an observable, the analysis may be equally applied to non
planar systems, where the σ-π separation of the molecular orbital models does no
longer apply. In those two studies, descriptors like the electron-density-based bond
orders, the bond ellipticity and the degree of the alignment of axes uniquely
defining the plane of the π-electron distribution for each CC bond had for the first
time been introduced to quantify the extent of electron delocalization (and aromaticity). Successful applications of the method had then concerned several
interesting cases, like the assessment of potential homoaromatic conjugation in a
series of non planar cations, including the debated case of the homotropylium
cation [21, 22] or the characterization of competing electron conjugation pathways
in some 11,11-disubstituted 1,6-methane[10]annulenes [23, 24].
Though it had been unequivocally shown that the electron density bears recognizable signatures (of the effects) of electron delocalization, it later on became
progressively evident that its very mechanism is immediately related only to the
quantum-mechanical correlation among electron pairs. Such correlation had long
time before already been discussed, among others, by Mc Weeney [25] and Bader
and Stephens [26]. The so called exchange-correlation density, ρ 2,xc (r 1 , r 2 ), is an
useful tool to study such correlation. It measures the deviation between the true pair
density of a system and that given by the purely classical description of a product of
two independent electron densities, not subject to any Coulomb and Fermi correlation of electron motions. Use of the exchange-correlation density has led through
years to the definition of several electron delocalization descriptors, like the so
called delocalization indices (DI’s) [27], that provide an estimate of the number of
electrons pairs delocalized (shared) between two atoms Ω and Ω′, no matter
whether they are or they are not directly linked by a bond path. DI’s have been
largely employed to highlight delocalization effects and to quantify aromaticity, for
example through the so-called para-delocalization index PDI [28] or the Fermi Hole
Delocalization Density index, FHDD [29], which both represent global measures of
electron delocalization non homogeneity. The performance of such global aromaticity indicators has also been extensively compared with that of several other
aromaticity measures, less fundamental in nature and based instead on given,
indirect consequences of electron delocalization. The HOMA (Harmonic Oscillator
Model of Aromaticity) [30, 31] and NICS (Nucleus-Independent Chemical Shift)
[32, 33] indices, represent just two popular examples. HOMA exploits the increase
of the CC bond length equalization with increasing electron delocalization homogeneity, while NICS the supposedly different magnetic shielding of a magnetic test
dipole at the center of a conjugated ring in the presence of a diatropic (aromatic
system) or paratropic (antiaromatic system) ring current. Both indices have been
5 Exploring Chemistry Through the Source Function …
105