P Æ2 . At P Æ5 the central saddle SL splits into a central (red) paratropic vortical SL,
and two saddle SLs lying on the Tr v ðxzÞ plane orthogonal to that of the molecule.
These saddle SLs change index sign at two points with coordinates (x ¼ Æ1:10,
y ¼ 0, z ¼ Æ1:07) bohr, and the emerging diatropic vortex lines end up at P Æ1 . Two
cages are found, each about one C nucleus. These patterns consist of a set of SLs
merging at P Æ3 and P Æ4 (two paratropic vortical, two saddle SLs, and a central
portion of diatropic vortical SL). All the branchings fulfill the Gomes theorem,
Eq. (7.59).
Fig. 7.10 Display of the current density vector in the plane containing the nuclei of ethylene. The
applied magnetic field is orthogonal to the plot plane and directed outward. Atom positions are
marked by crosses. The maximum modulus is 1.84 (cut to 0.25) au and the step between two
consecutive contours is 0.025 au. Contours of the magnetic shielding density R
H
xx , Eq. (7.81), of
hydrogen nucleus on the molecular plane of ethylene are represented in red. Solid (dashed) red
lines denote positive (negative) values
184
P. Lazzeretti