Molecular-based quantum cellular automata (m-QCA), as an extension of quantum-dot QCAs, offer a novel alternative in which binary information can be encoded in the molecular charge configuration of a cell and propagated via nearest-neighbor Coulombic cell-cell interactions. Appropriate functionality of m-QCAs involves a complex relationship between quantum mechanical effects, such as electron transfer processes within the molecular building blocks, and electrostatic interactions between cells. The influence of structural distortions of single m-QCA are addressed in this paper within a minimal model using an diabatic-to-adiabatic transformation. We show that even small changes of the classical square geometry between driver and target cells, such as those induced by distance variations or shape distortions, can make cells respond to interactions in a far less symmetric fashion, modifying and potentially impairing the expected computational behavior of the m-QCA.