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We present a way of partly reincorporate the effects of the localized bondingelectrons on the dynamics of their itinerant counterparts in Hubbard-likeHamiltonians. This is done by relaxing the constraint that the former should beentirely frozen in the chemical bonds between the underlying lattice sitesthrough the employment of a Born-Oppenheimer-like ansatz for the wavefunctionof the whole electronic system. Accordingly, the latter includes itinerant aswell as bonding electron coordinates. Going beyond the adiabatic approximation,we show that the net effect of virtual transitions of bonding electrons betweentheir ground and excited states is to furnish the itinerant electrons with aneffective inter-electronic momentum-momentum interaction. Although we haveapplied these ideas to the specific case of rings, our assumptions can begeneralized to higher dimensional systems sharing the required properties ofwhich we have made use herein.

Effective momentum-momentum coupling in a correlated electronic system