The central component of the programmable molecular switch recently demonstrated by Stoddart and Heath is rotaxane, which consists of a cyclobis(paraquat-p-phenylene) shuttle (CBPQT(4+))(PF(6)(-))(4) (the ring) encircling a finger and moving between two stations, tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP). As a step toward understanding the mechanism of this switch, we report here its electronic structure using two flavors of density functional theory (DFT): B3LYP/6-31G and PBE/6-31G. We find that the electronic structure of composite rotaxane can be constructed reasonably well from its parts by combining the states of separate stations (TTF and DNP) with or without the (CBPQT)(PF(6))(4) shuttle around them. That is, the "CBPQT@TTF" state, (TTF)(CBPQT)(PF(6))(4)-(DNP), is described well as a combination of the (TTF)(CBPQT)(PF(6))(4) complex and free DNP, and the "CBPQT@DNP" state, (TTF)-(DNP)(CBPQT)(PF(6))(4), is described well as a combination of free TTF and the (DNP)(CBPQT)(PF(6))(4) complex. This allows an aufbau or a "bottom-up" approach to predict the complicated [n]rotaxanes in terms of their components. This should be useful in designing new components to lead to improved properties of the switches. A critical function of the (CBPQT(4+))(PF(6)(-))(4) shuttle in switching is that it induces a downshift of the frontier orbital energy levels of the station it is on (TTF or DNP). This occurs because of the net positive electrostatic potential exerted by the CBPQT(4+) ring, which is located closer to the active station than the four PF(6)(-)'s. This downshift alters the relative position of energy levels between TTF and DNP, which in turn alters the electron tunneling rate between them, even when the shuttle is not involved directly in the actual tunneling process. Based on this switching mechanism, the "CBPQT@TTF" state is expected to be a better conductor since it has better aligned levels between the two stations. A second potential role of the (CBPQT(4+))(PF(6)(-))(4) shuttle in switching is to provide low-lying LUMO levels. If the shuttle is involved in the actual tunneling process, the reduced HOMO-LUMO gap (from 3.6 eV for the isolated finger to 1.1 eV for "CBPQT@TTF" or to 0.6 eV for "CBPQT@DNP" using B3LYP) would significantly facilitate the electron tunneling through the system. This might occur in a folded conformation where a direct contact between free station and the shuttle on the other station is possible. When this becomes the main switching mechanism, we expect the "CBPQT@DNP" state to become a better conductor because its HOMO-LUMO gap is smaller and because its HOMO and LUMO are localized at different stations (HOMO exclusively at TTF and LUMO at CBPQT encircling DNP) so that the HOMO-to-LUMO tunneling would be through the entire molecule of rotaxane. Thus an essential element in designing these switches is to determine the configuration of the molecules (e.g., through self-assembled monolayers or incorporation of conformation stabilizing units).