Current-density pathways in figure-eight-shaped octaphyrins

We have calculated the current density induced by an external magnetic field in a set of figure-eight-shaped expanded porphyrinoids. The studied octaphyrins can be divided into three classes (N2, N4, and N6) based on the number of the inner hydrogen atoms of the pyrrole rings. Using the Runge-Kutta method, the current density is split into diatropic and paratropic contributions that are analyzed separately. The calculations show that one common ring current consists of two rather independent pathways. Each of them follows the outer side of the molecular frame of one half of the molecule and passes to the inner side of the frame on the other half. The ring-current pathways are similar to the ones for [12]infinitene. However, the current density of the octaphyrins is more complex having many branching points and pathways. Vertical through-space current-density pathways pass in the middle of the molecules through a plane that is parallel to the figure-eight-shaped view of the molecules when the magnetic field is perpendicular to the plane. The isolectronic N2 and the N4 dication sustain a weak paratropic ring current inside the molecule, which is also observed in the ¹H NMR magnetic shielding constant of the inner hydrogen atoms. The diatropic current-density contribution dominates in the studied molecules. For the N4 and N6 molecules, the global current-density pathways are only diatropic and N6 sustains the strongest global diatropic current-density flux of 13.2 nA T^-1.