by the calculated average magnetizability n av ¼ À86:5 Â 10
À29 J T
−2 , the cubane
cage can be considered a hallmark of face-centred paramagnetism [116].
Pentaprismane constitutes another example of molecules designed and synthesized by chemists to give pleasure through their abstract beauty. Besides, it is
endowed with noticeable magnetic properties, interpretable [117] via the theoretical
tools outlined in this chapter. A perspective view of the SG of the pentaprismane
molecule in a spatially uniform magnetic field parallel to the C 5 symmetry axis, i.e.,
at right angles to the five-membered face, is shown in Fig. 7.28. The magnetic
symmetry is D 5h ðC 5h Þ, Eq. (7.82).
Fig. 7.25 Perspective view of the stagnation graph of the current density vector field in cubane
C 8 H 8 . The uniform external magnetic field B ¼ 3 B z is perpendicular to opposite square faces of
the C 8 H 8 cage ( 3 is the unit vector in the direction of the z axis through the centre). Green (red)
lines denote diatropic (paratropic) vortices, saddle lines are blue
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201
À29 J T
−2 , the cubane
cage can be considered a hallmark of face-centred paramagnetism [116].
Pentaprismane constitutes another example of molecules designed and synthesized by chemists to give pleasure through their abstract beauty. Besides, it is
endowed with noticeable magnetic properties, interpretable [117] via the theoretical
tools outlined in this chapter. A perspective view of the SG of the pentaprismane
molecule in a spatially uniform magnetic field parallel to the C 5 symmetry axis, i.e.,
at right angles to the five-membered face, is shown in Fig. 7.28. The magnetic
symmetry is D 5h ðC 5h Þ, Eq. (7.82).
Fig. 7.25 Perspective view of the stagnation graph of the current density vector field in cubane
C 8 H 8 . The uniform external magnetic field B ¼ 3 B z is perpendicular to opposite square faces of
the C 8 H 8 cage ( 3 is the unit vector in the direction of the z axis through the centre). Green (red)
lines denote diatropic (paratropic) vortices, saddle lines are blue
7 Topology of Quantum Mechanical Current Density …
201