Effects of electron transfer network topology on functioning of quantum cellular automata based on mixed-valence two-electron molecular squares

Molecular quantum cellular automata (QCA) devices are typically based on the square planar two-electron mixed valence (MV) molecules playing the role of QCA cells. The functional properties of such cells are determined by the Coulomb repulsion between the two excess electrons, which stabilize antipodal charge configurations that encoding binary information. The inner sphere electron transfer of the excess electrons transforming different charge configurations into each other, as well as by the vibronic coupling, which tends to localize the mobile charges. Previously, the most topical and theoretically complex case of arbitrary Coulomb repulsion has been considered by implying essential restricting assumptions on the network of the electron transfer pathways. Therefore, the electron transfer occurring along the sides of the molecular square has been taken into account. Meanwhile, the effects of diagonal transfer have been discussed only for the limiting case of strong intracell Coulomb repulsion, which is peculiar to predominantly ionic compounds that are unlikely to be relevant to the MV cells. Here, we go beyond these simplifying assumptions and consider the general situation when all electron transfer pathways are involved, providing arbitrary interrelations between the key electronic and vibronic parameters. By solving the adiabatic and quantum-mechanical three-mode vibronic problems, we reveal the influence of electron transfer network topology on key properties of QCA, such as the stabilization of different spin-states in the free and interacting cells, the extent of localization of the pair of excess electrons, the shape of the cell-cell response functions, and the heat release necessarily occurring in the course of the non-adiabatic switching cycle.