  We present a way of partly reincorporate the effects of the localized bonding
electrons on the dynamics of their itinerant counterparts in Hubbard-like
Hamiltonians. This is done by relaxing the constraint that the former should be
entirely frozen in the chemical bonds between the underlying lattice sites
through the employment of a Born-Oppenheimer-like ansatz for the wavefunction
of the whole electronic system. Accordingly, the latter includes itinerant as
well as bonding electron coordinates. Going beyond the adiabatic approximation,
we show that the net effect of virtual transitions of bonding electrons between
their ground and excited states is to furnish the itinerant electrons with an
effective inter-electronic momentum-momentum interaction. Although we have
applied these ideas to the specific case of rings, our assumptions can be
generalized to higher dimensional systems sharing the required properties of
which we have made use herein.
