Our interest in this article is prompted by the problem of the vibronic self-trapping of charge polarized states in the four-dot molecular quantum cellular automata (mQCA), a paradigm for nanoelectronics, in which binary information is encoded in charge configuration of the mQCA cell. We report the evaluation of the electronic states and the adiabatic potentials of mixed-valence (MV) systems in which two electrons (or holes) are shared among four sites. These systems are exemplified by the two

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... inds of tetra–ruthenium (2Ru(II)+ 2Ru(III)) clusters (assembled as two coupled Creutz–Taube dimers) for which molecular implementation of mQCA was proposed. The tetra–ruthenium clusters include two holes shared among four sites and correspondingly we employ the model which takes into account the electron transfer processes as well as the Coulomb repulsion in the different instant positions of localization. The vibronic self-trapping is considered within the conventional vibronic Piepho, Krausz and Schatz (PKS) model adapted to the bi-electronic MV species with the square topology. This leads to a complicated vibronic problems (21A1g + 1B1g + 1B2g + 1Eu) ⊗ (b1g + eu) and (3A2g + 3B1g + 23Eu) ⊗ (b1g + eu) for spin-singlet and spin-triplet states correspondingly. The adiabatic potentials are evaluated with account for the low lying Coulomb levels in which the antipodal sites are occupied, the case just actual for utilization in mQCA. The conditions for the vibronic localization in spin-singlet and spin-triplet states are revealed in terms of the two actual transfer pathways parameters and strength of the vibronic coupling.