The magnetic point groups for the tropilium cation, D 7h ðC 7h Þ, and
cyclo-octatetraenyl di-cation and di-anion, D 8h ðC 8h Þ, can also be constructed by the
Tavger-Zaitsev recipe [58, 98, 99], Eq. (7.71).
The electronic wavefunction of neutral and charged C n H n cyclic conjugated
molecules is characterized by sigma/pi separability for symmetry reasons, see, for
instance Ref. [15] and references therein. This feature is only preserved in the
presence of magnetic field perpendicular to the molecular r h plane. In these conditions, the magnetic response properties, e.g., magnetizability and nuclear magnetic shieldings, can be partitioned into separate contributions from r- and pelectrons. Analogously, the current density field J
B induced in neutral and charged
C n H n cyclic systems by a magnetic field B perpendicular to the molecular r h plane,
can be represented by the superposition of disjoined r- and p-contributions.
Accordingly, total properties can be rationalized in terms of separate pieces [15].
On the other hand, for B parallel to the molecular plane, r- and p-electron flow is
inextricably mixed.
A general quantum-mechanical procedure, referred to as continuous transformation of origin of the current density-diamagnetic zero (CTOCD-DZ) [3, 15, 71,
105], within the damped DZ2 variant [106, 107], has been employed, at the
Fig. 7.19 Streamlines of the current density vector field in methane CH 4 on a plane through the C
nucleus, normal to the uniform external magnetic field B parallel to the C 3 symmetry axis along a
CH bond. The (2, 0) stagnation points are identified via the stagnation graph of Fig. 7.18
192
P. Lazzeretti
cyclo-octatetraenyl di-cation and di-anion, D 8h ðC 8h Þ, can also be constructed by the
Tavger-Zaitsev recipe [58, 98, 99], Eq. (7.71).
The electronic wavefunction of neutral and charged C n H n cyclic conjugated
molecules is characterized by sigma/pi separability for symmetry reasons, see, for
instance Ref. [15] and references therein. This feature is only preserved in the
presence of magnetic field perpendicular to the molecular r h plane. In these conditions, the magnetic response properties, e.g., magnetizability and nuclear magnetic shieldings, can be partitioned into separate contributions from r- and pelectrons. Analogously, the current density field J
B induced in neutral and charged
C n H n cyclic systems by a magnetic field B perpendicular to the molecular r h plane,
can be represented by the superposition of disjoined r- and p-contributions.
Accordingly, total properties can be rationalized in terms of separate pieces [15].
On the other hand, for B parallel to the molecular plane, r- and p-electron flow is
inextricably mixed.
A general quantum-mechanical procedure, referred to as continuous transformation of origin of the current density-diamagnetic zero (CTOCD-DZ) [3, 15, 71,
105], within the damped DZ2 variant [106, 107], has been employed, at the
Fig. 7.19 Streamlines of the current density vector field in methane CH 4 on a plane through the C
nucleus, normal to the uniform external magnetic field B parallel to the C 3 symmetry axis along a
CH bond. The (2, 0) stagnation points are identified via the stagnation graph of Fig. 7.18
192
P. Lazzeretti