  We consider circular currents in molecular wires with loop substructures
studied within simple tight-binding models. Previous studies of this issue have
focused on specific molecular structures. Here we address several general
issues. First we consider the quantitative definition of a circular current and
adopt a definition that identified the circular component of a loop current as
the sole source of the magnetic field induced in the loop. The latter may be
associated with the field at the loop center, with the magnetic moment
associated with this field or with the total magnetic flux threading the loop.
We show that all three definitions yield an identical measure of the loop
current. Secondly, we study dephasing effects on the loop current and the
associated induced magnetic field. Finally, we consider circular currents in
several molecular structures: benzene, azulene, naphthalene and anthracene and
show that circular currents occur generically in such structures and can be, in
certain voltage ranges, considerably larger than the net current through the
molecule, and are furthermore quite persistent to normal thermal dephasing.
