For instance, assuming B along the C n axis, parallel to the z direction, the
magnetic group of benzene, the archetypal aromatic molecule, contains the symmetry elements listed in Eq. (7.80), that of cyclopropenyl cation, with n ¼ 3, is
given by Eq. (7.79), and that of the cyclobutadienyl dication, C 4 H
2 þ
4 , by Eq. (7.76).
Other interesting cyclic systems are the cyclopentadienyl anion, C 5 H
À
5 , belonging
to the symmetry group D 5h ðC 5h Þ, and the tropylium cation C 7 H
þ
7 . These systems
are regarded as aromatic on the magnetic criterion [15]. Using the nomenclature of
Eqs. (7.72)–(7.80),
D 5h f E 2C 5 2C
2
5
5C 2 r h 2S 5 2S
3
5 5r v g
C 5h E C 5 C
2
5
C
3
5
C
4
5
r h S 5 S
7
5
S
3
5 S
9
5
È
É
D 5h ðC 5h Þ E C 5 C
2
5
C
3
5
C
4
5
5TC 2 r h S 5 S
7
5 S
3
5
S
9
5 5Tr v
È
É
ð7:82Þ
Fig. 7.18 Perspective view
of the stagnation graph of the
current density vector field in
methane CH 4 . The uniform
external magnetic field B is
parallel to a C 3 symmetry axis
along a CH bond
7 Topology of Quantum Mechanical Current Density …
191