  Fermi--L\"owdin orbitals (FLO) are a special set of localized orbitals, which
have become commonly used in combination with the Perdew--Zunger
self-interaction correction (SIC) in the FLO-SIC method. The FLOs are obtained
for a set of occupied orbitals by specifying a classical position for each
electron. These positions are known as Fermi-orbital descriptors (FODs), and
they have a clear relation to chemical bonding. In this study, we show how FLOs
and FODs can be used to initialize, interpret and justify SIC solutions in a
common chemical picture, both within FLO-SIC and in traditional variational
SIC, and to locate distinct local minima in either of these approaches.
  We demonstrate that FLOs based on Lewis' theory lead to symmetry breaking for
benzene -- the electron density is found to break symmetry already at the
symmetric molecular structure -- while ones from Linnett's double-quartet
theory reproduce symmetric electron densities and molecular geometries.
Introducing a benchmark set of 16 planar, cyclic molecules, we show that using
Lewis' theory as the starting point can lead to artifactual dipole moments of
up to 1 Debye, while Linnett SIC dipole moments are in better agreement with
experimental values. We suggest using the dipole moment as a diagnostic of
symmetry breaking in SIC and monitoring it in all SIC calculations. We show
that Linnett structures can often be seen as superpositions of Lewis structures
and propose Linnett structures as a simple way to describe aromatic systems in
SIC with reduced symmetry breaking. The role of hovering FODs is also briefly
discussed.
