Double-Dimeric Versus Tetrameric Cells for Quantum Cellular Automata: A Semiempirical Approach to Evaluation of Cell-Cell Responses Combined with Quantum-Chemical Modeling of Molecular Structures

Quantum dot cellular automata is a computing paradigm based on transistor-free logic, which in turn relies on the idea of encoding binary information in bistable charge configurations of quantum dots and process information via Coulomb interactions. In the context of molecular implementation of quantum dot cellular automata, we have compared the properties of two possible kinds of molecular square cells, namely, cells tailored from two one-electron mixed valence dimers (double-dimeric cells) and a two-electron mixed valence tetramer. The physical model (based on the Hubbard-type Hamiltonian) of the cells involves the Coulomb interelectronic interaction, electron transfer, and vibronic coupling. We have demonstrated that the difference in the transfer pathways in the two types of cells gives rise to a considerable difference in their functional characteristics. Thus, the double-dimeric cell exhibits a more abrupt nonlinear cell-cell response, which is a prerequisite for the efficient functioning of quantum cellular automata. The difference in the cell-cell responses for the two kinds of cells is shown to be smaller for a weak electron transfer and/or strong vibronic coupling when the mobility of the electronic pair is strongly constrained. The dimeric and tetrameric systems, 1,4-dithia-hexane and crown ether 1,4,7,10-tetrathiacyclododecane, were selected as the molecular systems for the implementation of the proposed Hubbard-type analysis. This choice is prompted by the positive charge localization on the S-atoms, which are not connected covalently. We have performed the quantum-chemical calculations of the 1,4-dithia-compound with two S-atoms connected by a saturated carbon bridge CH₂CH₂ (proposed as a dimeric subunit) and the corresponding tetrameric structures of the crown ethers 1,4,7,10-tetrathiacyclododecane: parent neutral molecule, cation, and dication. The quantum-chemical estimations allowed us to quantitatively unveil the key parameters of the dimeric and tetrameric systems and to conclude that the proposed compounds can serve as cells with predominantly antipodal charge separation, which are potentially able to encode binary information.