In this article we focus on the study of spin effects in a single square-planar mixed-valence cell comprising two electrons and in coupled molecular cells for quantum cellular automata. Using the vibronic model we demonstrate that the polarizabilities of the cell are different in spin-singlet and spin-triplet states of the electronic pair. Based on this inference the concept of spin switching in molecular quantum cellular automata is proposed, and the conditions under which this effect is feasible are derived. In order to reveal these conditions we have performed a series of quantum-mechanical calculations of the vibronic energy levels of the isolated cell and of the cell subjected to the external polarizing field. To present the results in a descriptive way they are qualitatively discussed in terms of the adiabatic potential curves illustrating spin effects in switching cycle during operation in quantum cellular automata. The spin-switching effect stemming from the theoretical model is shown to be dependent on the relative strength of the intracell electronic interactions (Coulomb repulsion energies and electron transfer parameters) and vibronic coupling. This is expected to suggest a route for observation of spin switching in which the nonmagnetic vibronic ground state of the cell is changed to the magnetic one due to polarization induced in this cell by the neighboring one. The spin switching is shown to produce a significant effect on the cell-cell response function leading to the unusual stepwise shape of this function. Finally, we briefly discuss the systems in which favorable conditions for observation of the effect may exist and underline the importance of the topology of the network of oxidation centers.