C 2h , the same as in the absence of field), shows a “dust” of (3, ±1) stagnation points:
as there is no Tr v plane, SLs do not occur. These isolated SPs correspond to local
saddle-nodes and diamagnetic or paramagnetic foci, see Figs. 1 and 2 of Ref. [102].
An analogous situation was found for planar H 3 BO 3 , with C 3h magnetic symmetry:
the stagnation graph consists of isolated stagnation points because of the absence of
Tr v planes, see Figs. 3 and 4 of Ref. [102]. Also the stagnation graph of the current
density vector field in distorted ethene C 2 H 4 , with magnetic symmetry D 2 ðC 2 Þ
consists of a “dust” of (3, ±1) SPs. Accordingly, plots of the current density vector
field contain only two symmetry-connected spiralling streamlines, see Figs. 5 and 6
of Ref. [102].
Fig. 7.8 Perspective view of an intermediate portion of the current density vector field in ethene
C 2 H 4 , with magnetic symmetry D 2h ðC 2h Þ, showing the bifurcation at points P Æ2 of the central
diamagnetic vortex into two vortices flowing about the C–H bonds. The uniform external magnetic
field B is applied in the direction of the C–C bond, coincident with the z axis. The sequence of
vortex-saddle splittings documented by the SG of Fig. 7.7 is fully contained within the streamline
surface, and is not visible
182
P. Lazzeretti
as there is no Tr v plane, SLs do not occur. These isolated SPs correspond to local
saddle-nodes and diamagnetic or paramagnetic foci, see Figs. 1 and 2 of Ref. [102].
An analogous situation was found for planar H 3 BO 3 , with C 3h magnetic symmetry:
the stagnation graph consists of isolated stagnation points because of the absence of
Tr v planes, see Figs. 3 and 4 of Ref. [102]. Also the stagnation graph of the current
density vector field in distorted ethene C 2 H 4 , with magnetic symmetry D 2 ðC 2 Þ
consists of a “dust” of (3, ±1) SPs. Accordingly, plots of the current density vector
field contain only two symmetry-connected spiralling streamlines, see Figs. 5 and 6
of Ref. [102].
Fig. 7.8 Perspective view of an intermediate portion of the current density vector field in ethene
C 2 H 4 , with magnetic symmetry D 2h ðC 2h Þ, showing the bifurcation at points P Æ2 of the central
diamagnetic vortex into two vortices flowing about the C–H bonds. The uniform external magnetic
field B is applied in the direction of the C–C bond, coincident with the z axis. The sequence of
vortex-saddle splittings documented by the SG of Fig. 7.7 is fully contained within the streamline
surface, and is not visible
182
P. Lazzeretti