patterns in naphthalene and homotropylium cation, has enabled us to disentangle
the signatures of the ‘classical’ electron delocalization scheme, involving circulation of π electrons along the 10MR hydrocarbon chain, from those due to the
homoconjugative mechanism, which takes place essentially through space and
largely involves the two allylic, short bridge bonds.
Both discussed cases confirm that the Source Function picture nicely complies
with that provided by more sophisticated instruments based on the pair density, like
the delocalization indices. But the Source Function has, possibly, an advantage as it
may also reveal chemically relevant asymmetries in the electron delocalization
processes. It has been shown how these asymmetries disclose the non equivalence
of the delocalization effects between two atoms directly or indirectly connected
along a sequence of bonds or the different magnitudes of such effects when moving
perpendicularly to a bond and in opposite directions relative to the bond critical
point.
Secondly, we briefly reviewed the recent extension of the Source Function to the
electron spin density. Similarly to the case of the electron density, such development enables one to see the electron spin density at any point in the space in terms
of source contributions from the remaining points. The influence of each atom or
group of atoms in determining the spin polarization at any point can be then
quantified by integrating these local sources within atomic basins. It becomes so
possible to evaluate whether an atom or group of atoms concurs with or counteracts
the paramagnetic centre(s) in determining the local valence spin polarization at a
given point and whether it does so in a relevant or negligible measure. At the same
time, competing or cooperating spin propagation mechanisms can be disentangled.
Decomposition of source function contributions into a magnetic and into a relaxation term adds further precious chemical insight and largely facilitates their
interpretation. The magnetic contribution, though associated to an α-density only,
may still result in both an overall increase or decrease of the spin density at a given
point. The relaxation contribution may then either concur or counteract the effect of
the magnetic term.
We have concluded our chapter by analysing whether the spin density properties
are as transferable as are the electron density properties in a series of n-alkyl
radicals. We have convincingly shown that this is actually the case, but also that the
transferability of the two fields realizes in a quite distinct manner and one that
strongly depends on where the field is reconstructed through the Source Function
contributions. For instance, when the electron density or its spin counterpart are
reconstructed at the C–H bcp of a terminal CH 2
• group one finds that the electron
density at such point is largely determined by the atoms of the terminal group, and
with the remaining atoms providing only a small, constant contribution, regardless
the length of the chain. Instead, in the case of the spin density, the overall α
contribution from the terminal CH 2
• group is more than compensated for by an
overall β and constant contribution arising from the remaining part of the molecule.
Spin transferability at the bcp is thus ensured through a combination of opposing α
and β contributions of similar magnitude. Quite different is the case for the spin
density reconstruction at the non bonded charge concentration located above the
124
C. Gatti et al.
the signatures of the ‘classical’ electron delocalization scheme, involving circulation of π electrons along the 10MR hydrocarbon chain, from those due to the
homoconjugative mechanism, which takes place essentially through space and
largely involves the two allylic, short bridge bonds.
Both discussed cases confirm that the Source Function picture nicely complies
with that provided by more sophisticated instruments based on the pair density, like
the delocalization indices. But the Source Function has, possibly, an advantage as it
may also reveal chemically relevant asymmetries in the electron delocalization
processes. It has been shown how these asymmetries disclose the non equivalence
of the delocalization effects between two atoms directly or indirectly connected
along a sequence of bonds or the different magnitudes of such effects when moving
perpendicularly to a bond and in opposite directions relative to the bond critical
point.
Secondly, we briefly reviewed the recent extension of the Source Function to the
electron spin density. Similarly to the case of the electron density, such development enables one to see the electron spin density at any point in the space in terms
of source contributions from the remaining points. The influence of each atom or
group of atoms in determining the spin polarization at any point can be then
quantified by integrating these local sources within atomic basins. It becomes so
possible to evaluate whether an atom or group of atoms concurs with or counteracts
the paramagnetic centre(s) in determining the local valence spin polarization at a
given point and whether it does so in a relevant or negligible measure. At the same
time, competing or cooperating spin propagation mechanisms can be disentangled.
Decomposition of source function contributions into a magnetic and into a relaxation term adds further precious chemical insight and largely facilitates their
interpretation. The magnetic contribution, though associated to an α-density only,
may still result in both an overall increase or decrease of the spin density at a given
point. The relaxation contribution may then either concur or counteract the effect of
the magnetic term.
We have concluded our chapter by analysing whether the spin density properties
are as transferable as are the electron density properties in a series of n-alkyl
radicals. We have convincingly shown that this is actually the case, but also that the
transferability of the two fields realizes in a quite distinct manner and one that
strongly depends on where the field is reconstructed through the Source Function
contributions. For instance, when the electron density or its spin counterpart are
reconstructed at the C–H bcp of a terminal CH 2
• group one finds that the electron
density at such point is largely determined by the atoms of the terminal group, and
with the remaining atoms providing only a small, constant contribution, regardless
the length of the chain. Instead, in the case of the spin density, the overall α
contribution from the terminal CH 2
• group is more than compensated for by an
overall β and constant contribution arising from the remaining part of the molecule.
Spin transferability at the bcp is thus ensured through a combination of opposing α
and β contributions of similar magnitude. Quite different is the case for the spin
density reconstruction at the non bonded charge concentration located above the
124
C. Gatti et al.