The large discrepancy on the SFs percentages arises from the three order of magnitude larger s value at NBCC.
In Ref. [94] we showed that interpretation of SF S values may be largely
enhanced when they are decomposed into a magnetic and into a reaction or relaxation contribution, the former being due to the magnetic natural orbital(s)
density and the second one to the remaining natural orbitals density. Magnetic
orbital(s) are easily obtained through diagonalization of the first order density
matrix and identified by picking up the orbital(s) with occupations equal to or very
close to 1. Technical details and a full discussion of the mentioned decomposition
scheme are reported in Ref. [94] and in its supplementary information.
Interestingly, the magnetic contribution, though being due only to an α-density,
does not always lead to an α-effect, but may also result in an overall decrease of the
spin density at a given rp. Likewise, the reaction contribution may either concur or
counteract the magnetic one in determining the SDD at the rp. For n-alkyl radicals,
the situation is very simple as there is only one magnetic natural orbital, whose
effect is made visible in Figs. 5.3c and 5.4b for the case of n-butyl radical and for
the two examined rps. The role of the reaction contribution may be assessed from
the difference of (b) and (c) SF S values in Fig. 5.3 and, analogously, of (a) and
(b) SF S values in Fig. 5.4. One observes that the magnetic orbital density plays the
major role and that the remaining relaxation density moderately (from 5 to 20 % in
magnitude) concur to the effects produced by the former density, for both rps.
These effects may be either of α or of β nature for both densities, but always agree
in their nature in this case, at least for the more significant contributions.
5.5 Concluding Remarks
In this chapter, we reviewed two recent developments of the Source Function
analysis and illustrated a couple of novel applications thereof, which emphasize the
ability of this descriptor to retrieve interesting and non trivial chemical insights.
We first showed that, analogously to what already reported for planar mono- and
polycyclic aromatic hydrocarbons, the Source Function tool is able to detect subtle
electron delocalization effects also in the non-planar and less conventional hydrocarbons, like the homotropylium cation and the 1,6-methano[10]annulene, where
the usual σ/π separation does no longer apply. The analysis of such systems has
been made by dissecting the electron density values at bond critical points in terms
of Source Function contributions from the bonded atoms, their next neighbouring
carbon atoms and the other carbon atoms in the system and by comparing the nature
of such dissection with that obtained for more conventional, π-conjugated, planar
reference compounds. Clear, quantitative footprints of through space and through
bond homoconjugation mechanisms have been so identified for the homotropylium
cation, along with similarities and differences, relative to benzene, in the way
electron conjugation realizes in the unsaturated moiety of its C atom linkage. In the
case of the 1,6-methano[10]annulene, comparison with source contributions
5 Exploring Chemistry Through the Source Function …
123
In Ref. [94] we showed that interpretation of SF S values may be largely
enhanced when they are decomposed into a magnetic and into a reaction or relaxation contribution, the former being due to the magnetic natural orbital(s)
density and the second one to the remaining natural orbitals density. Magnetic
orbital(s) are easily obtained through diagonalization of the first order density
matrix and identified by picking up the orbital(s) with occupations equal to or very
close to 1. Technical details and a full discussion of the mentioned decomposition
scheme are reported in Ref. [94] and in its supplementary information.
Interestingly, the magnetic contribution, though being due only to an α-density,
does not always lead to an α-effect, but may also result in an overall decrease of the
spin density at a given rp. Likewise, the reaction contribution may either concur or
counteract the magnetic one in determining the SDD at the rp. For n-alkyl radicals,
the situation is very simple as there is only one magnetic natural orbital, whose
effect is made visible in Figs. 5.3c and 5.4b for the case of n-butyl radical and for
the two examined rps. The role of the reaction contribution may be assessed from
the difference of (b) and (c) SF S values in Fig. 5.3 and, analogously, of (a) and
(b) SF S values in Fig. 5.4. One observes that the magnetic orbital density plays the
major role and that the remaining relaxation density moderately (from 5 to 20 % in
magnitude) concur to the effects produced by the former density, for both rps.
These effects may be either of α or of β nature for both densities, but always agree
in their nature in this case, at least for the more significant contributions.
5.5 Concluding Remarks
In this chapter, we reviewed two recent developments of the Source Function
analysis and illustrated a couple of novel applications thereof, which emphasize the
ability of this descriptor to retrieve interesting and non trivial chemical insights.
We first showed that, analogously to what already reported for planar mono- and
polycyclic aromatic hydrocarbons, the Source Function tool is able to detect subtle
electron delocalization effects also in the non-planar and less conventional hydrocarbons, like the homotropylium cation and the 1,6-methano[10]annulene, where
the usual σ/π separation does no longer apply. The analysis of such systems has
been made by dissecting the electron density values at bond critical points in terms
of Source Function contributions from the bonded atoms, their next neighbouring
carbon atoms and the other carbon atoms in the system and by comparing the nature
of such dissection with that obtained for more conventional, π-conjugated, planar
reference compounds. Clear, quantitative footprints of through space and through
bond homoconjugation mechanisms have been so identified for the homotropylium
cation, along with similarities and differences, relative to benzene, in the way
electron conjugation realizes in the unsaturated moiety of its C atom linkage. In the
case of the 1,6-methano[10]annulene, comparison with source contributions
5 Exploring Chemistry Through the Source Function …
123