Prototype of cell for quantum cellular automata: Multimode vibronic model for a two-electron mixed valence molecular square

Multimode vibronic model for the two-electron square-planar mixed valence cluster is developed and applied to analysis of localization-delocalization phenomenon. The model involves interaction of the excess electrons both with "breathing" (Piepho-Krausz-Schatz- PKS-type) vibrations and with the intercenter vibrations modulating electron transfer integrals. We demonstrate that the coupling with two B1g-vbrations can be substituted by the effective coupling with the "interaction mode". As a result, complex three-mode vibronic problem proves to be reduced to the two-mode problem involving the interaction mode of B1g-symmetry having hybrid nature and pure intercenter A1g-vibration. The analysis of minima of the lower adiabatic potential surface shows that the two vibrations produce competitive effects on the localization-delocalization properties. Thus, the dominating coupling with B1g-vibration is shown to form the double-well adiabatic potential surface, with the electronic pair in each minimum being predominantly localized on one of diagonals of the square, while the dominating coupling with the A1g-mode gives rise to single-well surface describing fully delocalized electronic pair. Finally, keeping in mind applications of square-planar two-electron clusters as molecular cells in quantum cellular automata we reveal the role of different vibrations in the shape of cell-cell response function.