5.4.1 Electron Density and Electron Spin Density
Transferability Viewed Through the Eye of the Source
Function Tool: The Case of N-alkyl Radicals
A cornerstone of chemistry is the atomic group transferability paradigm, deduced
from a plethora of experimental facts and corroborated on a firm quantitative basis,
for a large variety of group properties, by the Quantum Theory of Atoms in
Molecules [5]. The Source Function descriptor may be then conveniently exploited
to add further insight. On the one hand, the SF tool is capable to distinguish
between perfect transferability, implying that the electron density of a group is fully
transferable among a series of chemically related compounds, from the case of
compensatory transferability, where a constant value for a group property is only
achieved through compensatory effects [2, 6]. On the other hand, the occurrence of
perfect transferability of a group property, say for instance the value of the electron
density at a bcp within the group, not only implies a transferable SF contribution
from the atoms forming the group, but also that the sum of contributions to that
density from the remaining atoms or group of atoms in the system remains constant,
no matter the size of the system. This clearly adds further (chemical) information on
how perfect transferability realizes.
Terminal methyl groups in n-alkanes, past ethane, are known to be fully
transferable [5] as they show several properties (energy, electron population, volume and spectroscopic responses) that remain constant regardless the length of the
carbon chain. The transferability of the electron distribution in the methyl group is
so good that a constant value for the electron density at its unique C–H bcp is also
observed, past ethane. Such transferability realizes because of a constant SF contribution from the CH 3 group and a constant SF external contribution from the
remaining atoms in the chain, no matter its length [1, 2].
To verify whether this holds true also for SDD, CH 3 (CH 2 ) n CH 2
• n-alkyl radicals
[95] with n = 1–3, at fully optimized geometries and in their most stable conformations were considered. These correspond for all systems to the C[p] orbital,
housing the unpaired electron in the terminal CH 2
• group, being almost eclipsed
with respect to one of its β C–H bonds. Wavefunctions were calculated at the
UPBE1PBE/6-311 + G(d,p) level, using the Gaussian-09 code. Spin contamination
annihilated wavefunctions [IOP(5/14 = 2), pop = noab] were used for both
geometry optimization and SF S analysis. Integration of the spin density over the
basin of the terminal CH 2
• group typically shows that more than 91 % of the excess
α density lies in this group and essentially on the C (90 %), the second most
important contribution (6 %) coming from the eclipsed β-hydrogen atom mentioned
above.
Figure 5.2 compares the electron density [top, (a)] and the electron spin density
[middle, (b)] transferability at the C–H bcp of the terminal CH 2
• group for all
considered radicals.
The former transferability is confirmed to occur also in the n-alkyl radicals, and
with similar mechanisms to those operative in the corresponding alkanes.
5 Exploring Chemistry Through the Source Function …
119
Transferability Viewed Through the Eye of the Source
Function Tool: The Case of N-alkyl Radicals
A cornerstone of chemistry is the atomic group transferability paradigm, deduced
from a plethora of experimental facts and corroborated on a firm quantitative basis,
for a large variety of group properties, by the Quantum Theory of Atoms in
Molecules [5]. The Source Function descriptor may be then conveniently exploited
to add further insight. On the one hand, the SF tool is capable to distinguish
between perfect transferability, implying that the electron density of a group is fully
transferable among a series of chemically related compounds, from the case of
compensatory transferability, where a constant value for a group property is only
achieved through compensatory effects [2, 6]. On the other hand, the occurrence of
perfect transferability of a group property, say for instance the value of the electron
density at a bcp within the group, not only implies a transferable SF contribution
from the atoms forming the group, but also that the sum of contributions to that
density from the remaining atoms or group of atoms in the system remains constant,
no matter the size of the system. This clearly adds further (chemical) information on
how perfect transferability realizes.
Terminal methyl groups in n-alkanes, past ethane, are known to be fully
transferable [5] as they show several properties (energy, electron population, volume and spectroscopic responses) that remain constant regardless the length of the
carbon chain. The transferability of the electron distribution in the methyl group is
so good that a constant value for the electron density at its unique C–H bcp is also
observed, past ethane. Such transferability realizes because of a constant SF contribution from the CH 3 group and a constant SF external contribution from the
remaining atoms in the chain, no matter its length [1, 2].
To verify whether this holds true also for SDD, CH 3 (CH 2 ) n CH 2
• n-alkyl radicals
[95] with n = 1–3, at fully optimized geometries and in their most stable conformations were considered. These correspond for all systems to the C[p] orbital,
housing the unpaired electron in the terminal CH 2
• group, being almost eclipsed
with respect to one of its β C–H bonds. Wavefunctions were calculated at the
UPBE1PBE/6-311 + G(d,p) level, using the Gaussian-09 code. Spin contamination
annihilated wavefunctions [IOP(5/14 = 2), pop = noab] were used for both
geometry optimization and SF S analysis. Integration of the spin density over the
basin of the terminal CH 2
• group typically shows that more than 91 % of the excess
α density lies in this group and essentially on the C (90 %), the second most
important contribution (6 %) coming from the eclipsed β-hydrogen atom mentioned
above.
Figure 5.2 compares the electron density [top, (a)] and the electron spin density
[middle, (b)] transferability at the C–H bcp of the terminal CH 2
• group for all
considered radicals.
The former transferability is confirmed to occur also in the n-alkyl radicals, and
with similar mechanisms to those operative in the corresponding alkanes.
5 Exploring Chemistry Through the Source Function …
119