Ten (0, 0) critical points lying on the C–C bond direction are found in the SG of
the energetically stable rotamer with D 2h ðC 2h Þ symmetry in Fig. 7.7. The current
density vector field is shown in Fig. 7.8. Denoting by P Æi ; i ¼ 1; 2 . . . 5; branching
points on opposite sides of, and equally spaced from, the origin in the centre of
mass (CM), they are P Æ1 at ±0.47, P Æ2 at ±0.52, P Æ3 at ±0.92, P Æ4 at ±1.54, and
P Æ5 at ±2.60, with distances in bohr. The C nuclei are located at ±1.24 bohr from
CM. The P Æ1 and P Æ2 SPs are separated by a short segment (0.05 bohr) of
saddle-type SL, which can be observed by magnifying the figure [102].
The primary diatropic vortex SL branches out at two (0, 0) critical points (too far
to be seen in Fig. 7.7) into a set of three SLs on the plane of the nuclei: a central
(blue) saddle SL and two (green) vortical SLs crossing the C–H bonds. These vortex
lines become saddle-type at points with coordinates (x ¼ 0; y ¼ Æ1:05; z ¼ Æ0:86)
bohr, where the i topological index changes from −1 to +1. The saddle SLs merge at
Fig. 7.9 Perspective view of the stagnation graph of the current density vector field induced by a
magnetic field B B 1 normal to the yz plane of the nuclei of ethylene. Green (red) lines denote
diamagnetic (paramagnetic) vortices, saddle lines are blue. Isolated blue points mark ð3; Æ1Þ
saddle-nodes, isolated green (red) points denote ð3; Æ1Þ diamagnetic (paramagnetic) foci
7 Topology of Quantum Mechanical Current Density …
183
the energetically stable rotamer with D 2h ðC 2h Þ symmetry in Fig. 7.7. The current
density vector field is shown in Fig. 7.8. Denoting by P Æi ; i ¼ 1; 2 . . . 5; branching
points on opposite sides of, and equally spaced from, the origin in the centre of
mass (CM), they are P Æ1 at ±0.47, P Æ2 at ±0.52, P Æ3 at ±0.92, P Æ4 at ±1.54, and
P Æ5 at ±2.60, with distances in bohr. The C nuclei are located at ±1.24 bohr from
CM. The P Æ1 and P Æ2 SPs are separated by a short segment (0.05 bohr) of
saddle-type SL, which can be observed by magnifying the figure [102].
The primary diatropic vortex SL branches out at two (0, 0) critical points (too far
to be seen in Fig. 7.7) into a set of three SLs on the plane of the nuclei: a central
(blue) saddle SL and two (green) vortical SLs crossing the C–H bonds. These vortex
lines become saddle-type at points with coordinates (x ¼ 0; y ¼ Æ1:05; z ¼ Æ0:86)
bohr, where the i topological index changes from −1 to +1. The saddle SLs merge at
Fig. 7.9 Perspective view of the stagnation graph of the current density vector field induced by a
magnetic field B B 1 normal to the yz plane of the nuclei of ethylene. Green (red) lines denote
diamagnetic (paramagnetic) vortices, saddle lines are blue. Isolated blue points mark ð3; Æ1Þ
saddle-nodes, isolated green (red) points denote ð3; Æ1Þ diamagnetic (paramagnetic) foci
7 Topology of Quantum Mechanical Current Density …
183