Free energy barrier for molecular motions in bistable [2]rotaxane molecular electronic devices

Donor-acceptor binding of the π-electron-poor cyclophane cyclobis(paraquat-ρ-phenylene) (CBPQT ⁴⁺) with the π-electron-rich tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP) stations provides the basis for electrochemically switchable, bistable [2]rotaxanes, which have been incorporated and operated within solid-state devices to form ultradense memory circuits (ChemPhysChem 2002, 3, 519-525; Nature 2007, 445, 414-417) and nanoelectromechanical systems. The rate of CBPQT ⁴⁺ shuttling at each oxidation state of the [2]rotaxane dictates critical write-and-retention time parameters within the devices, which can be tuned through chemical synthesis. To validate how well computational chemistry methods can estimate these rates for use in designing new devices, we used molecular dynamics simulations to calculate the free energy barrier for the shuttling of the CBPQT ⁴⁺ ring between the TTF and the DNP. The approach used here was to calculate the potential of mean force along the switching pathway, from which we calculated free energy barriers. These calculations find a turn-on time after the rotaxane is doubly oxidized of ∼10 ^-7 s (suggesting that the much longer experimental turn-on time is determined by the time scale of oxidization). The return barrier from the DNP to the TTF leads to a predicted lifetime of 2.1 s, which is compatible with experiments.