phosphole and arsole [111, 112], with lower C s ðC 1 Þ f E Tr g magnetic
symmetry.
The stagnation graphs of 1,3-cyclopentadiene, furan, pyrrole, and thiophene is
characterized by a similar pattern in the proximity of the CH 2 group or the
heterotom, i.e., the green truncated vortex line, denoting diamagnetic flow which
extends to the tail regions of the molecular domain. On crossing the plane of the
nuclei, for the first three compounds, this SL corresponds to saddle flow. A small
closed loop corresponding to two vortices flowing in opposite directions, which
characterizes a TV, is observed in front of it in pyrrole and thiophene. More
complicated patterns were found in the vicinity of the CH 2 moiety of
1,3-cyclopentadiene and nearby the oxygen atom in furan.
Another common feature constitutes the hallmark of all the five-membered
cyclic molecules in Fig. 7.22 and characterizes their peculiar magnetic response,
that is, the closed stagnation loop disconnected from the rest of the SG, passing
nearby the midpoint of the pentagon side opposite to the CH 2 group or the heteroatom. The green diamagnetic vortex line crossing the C–C bond and the red
paramagnetic vortex line, flowing in the vicinity of its centre of mass, are connected
to blue saddle lines by (0, 0) points, at which change of regime takes place. The
Gomes index of this disconnected piece is 0, as two lines with opposite ±1 index
emerge at each branching point.
The red portion of the stagnation loop crossing the molecular plane indicates,
according to the colour code of Fig. 7.22, the presence of a paramagnetic vortex,
which is actually observed in the streamline maps [111]. Its substantial difference
from that typical of D nh ðC nh Þ aromatics, corresponding to a vortical SL in between
two (0, 0) degenerate points on the main symmetry axis, i.e., belonging to a connected set of SLs, can hardly be overemphasized. Therefore, the disconnected
stagnation loop is the topological signature distinguishing five-membered heterocyclic molecules from the cyclic C n H n molecules to which they are frequently
associated. An analysis of diatropicity of pentatomic cyclic molecules, and a
comparison of their aromaticity (on the magnetic criterion) with benzene’s, should
not put aside these findings.
7.5.4 Cyclopropane
Chemists traditionally assumed that cyclopropane enjoys a peculiar combination of
properties referred to as r-aromaticity, which would be determined by r-electron
delocalization related to resonance and to strained geometry. In fact, the experimental average magnetizability n av of C 3 H 6 is much larger than that calculated from
additive Pascalian schemes. The enhanced anisotropy of n ab has been attributed to
the presence of r-electron ring currents induced by a magnetic field perpendicular
to the molecular plane, which would also cause upfield chemical shift in proton
magnetic resonance. This interpretation has been seriously questioned in recent
7 Topology of Quantum Mechanical Current Density …
197
symmetry.
The stagnation graphs of 1,3-cyclopentadiene, furan, pyrrole, and thiophene is
characterized by a similar pattern in the proximity of the CH 2 group or the
heterotom, i.e., the green truncated vortex line, denoting diamagnetic flow which
extends to the tail regions of the molecular domain. On crossing the plane of the
nuclei, for the first three compounds, this SL corresponds to saddle flow. A small
closed loop corresponding to two vortices flowing in opposite directions, which
characterizes a TV, is observed in front of it in pyrrole and thiophene. More
complicated patterns were found in the vicinity of the CH 2 moiety of
1,3-cyclopentadiene and nearby the oxygen atom in furan.
Another common feature constitutes the hallmark of all the five-membered
cyclic molecules in Fig. 7.22 and characterizes their peculiar magnetic response,
that is, the closed stagnation loop disconnected from the rest of the SG, passing
nearby the midpoint of the pentagon side opposite to the CH 2 group or the heteroatom. The green diamagnetic vortex line crossing the C–C bond and the red
paramagnetic vortex line, flowing in the vicinity of its centre of mass, are connected
to blue saddle lines by (0, 0) points, at which change of regime takes place. The
Gomes index of this disconnected piece is 0, as two lines with opposite ±1 index
emerge at each branching point.
The red portion of the stagnation loop crossing the molecular plane indicates,
according to the colour code of Fig. 7.22, the presence of a paramagnetic vortex,
which is actually observed in the streamline maps [111]. Its substantial difference
from that typical of D nh ðC nh Þ aromatics, corresponding to a vortical SL in between
two (0, 0) degenerate points on the main symmetry axis, i.e., belonging to a connected set of SLs, can hardly be overemphasized. Therefore, the disconnected
stagnation loop is the topological signature distinguishing five-membered heterocyclic molecules from the cyclic C n H n molecules to which they are frequently
associated. An analysis of diatropicity of pentatomic cyclic molecules, and a
comparison of their aromaticity (on the magnetic criterion) with benzene’s, should
not put aside these findings.
7.5.4 Cyclopropane
Chemists traditionally assumed that cyclopropane enjoys a peculiar combination of
properties referred to as r-aromaticity, which would be determined by r-electron
delocalization related to resonance and to strained geometry. In fact, the experimental average magnetizability n av of C 3 H 6 is much larger than that calculated from
additive Pascalian schemes. The enhanced anisotropy of n ab has been attributed to
the presence of r-electron ring currents induced by a magnetic field perpendicular
to the molecular plane, which would also cause upfield chemical shift in proton
magnetic resonance. This interpretation has been seriously questioned in recent
7 Topology of Quantum Mechanical Current Density …
197