  We generalize the quantum waveguide approach to H\"uckel or tight-binding
models relevant to unsaturated $\p$ molecular devices. A Landauer-like formula
for the current density through {\em internal} bonds is also derived which
allows for defining a local conductance. The approach is employed to study
internal circular currents in two-terminal rings. We show how to predict the
occurrence and the nature of large vortex currents in coincidence with
vanishingly small currents in the leads. We also prove a remarkably simple
formula for the onset of a vortex regime.
