Theoretical Hints to Optimize Energy Dissipation and Cell–Cell Response in Quantum Cellular Automata Based on Tetrameric and Bidimeric Cells

This article is largely oriented towards the theoretical foundations of the rational design of molecular cells for quantum cellular automata (QCA) devices with optimized properties. We apply the vibronic approach to the analysis of the two key properties of such molecular cells, namely the cell–cell response and energy dissipation in the course of the non-adiabatic switching of the electric field acting on the cell. We consider two kinds of square planar cells, namely cells represented by a two-electron tetrameric mixed valence (MV) cluster and bidimeric cells composed of two one-electron MV dimeric half-cells. The model includes vibronic coupling of the excess electrons with the breathing modes of the redox sites, electron transfer, intracell interelectronic Coulomb repulsion, and also the interaction of the cell with the electric field of polarized neighboring cells. For both kinds of cells, the heat release is shown to be minimal in the case of strong delocalization of excess electrons (weak vibronic coupling and/or strong electron transfer) exposed to a weak electric field. On the other hand, such a parametric regime proves to be incompatible with a strong nonlinear cell–cell response. To reach a compromise between low energy dissipation and a strong cell–cell response, we suggest using weakly interacting MV molecules with weak electron delocalization as cells. From this point of view, bidimeric cells are advantageous over tetrameric ones due to their smaller number of electron transfer pathways, resulting in a lower extent of electron delocalization. The distinct features of bidimeric cells, such as their two possible mutual arrangements (“side-by-side” and “head-to-tail”), are discussed as well. Finally, we briefly discuss some relevant results from a recent ab initio study on electron transfer and vibronic coupling from the perspective of the possibility of controlling the key parameters of molecular QCA cells.