The central component of the programmable molecular switch demonstrated recently by Stoddart and Heath is [2]rotaxane, which consists of a cyclobis-(paraquat-p-phenylene) ring-shaped shuttle [(CBPQT(4+))(PF6-)(4)] encircling a finger and moving between two stations on the finger: tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP). We report here a quantum mechanics (QM) study of the mechanism by which movement of the ring (and in turn the on-off switching) is controlled by the oxidation-reduction process. We use B3LYP density functional theory to describe how oxidation of the [2]rotaxane components (in using Poisson-Boltzmann continuum-solvation theory for acetonitrile solution) induces the motions associated with switching (translation of the ring). These calculations support the proposal that oxidation occurs on TTF, leading to repulsion between two positive charge centers (TTF2+ and CBPQT(4+)) that drives the CBPQT(4+) ring from the TTF2+ station toward the neutral DNP station. The theory also supports the experimental observation that the first and second oxidation potentials are nearly the same (separated by 0.09 eV in the QM). This excellent agreement between the QM and experiment suggests that QM can be useful in designing new systems.