The recently reported photoswitching of diarylethene derivative molecules bridging carbon nanotube (CNT) contacts is theoretically analyzed. The short lifetime of the lowest unoccupied molecular orbital (LUMO) indicates that neither the open nor closed form of the molecule can be photoexcited into a charge-neutral excited state for any appreciable length of time preventing photochromic ring opening. Analysis of the highest occupied molecular orbital (HOMO) and LUMO lifetimes also suggests that photoexcitation results in oxidation of the molecules. This either reduces the quantum yield of photochromic ring closing, or it gives rise to the possibility of oxidative ring closing. Analysis of the resistance values and energy levels indicates that the HOMO energy levels of the closed isomers relevant for transport must lie within a few k(B)T of the CNT Fermi level. For armchair contacts, the change in resistance with isomer or substituent group is the result of shifts in the energy level of the molecular HOMO. The coupling of the molecular HOMO to the CNT contacts is insensitive to the isomer type or substituent group. For zigzag CNTs, the conductance is dominated by surface states at the Fermi level on the cut ends of the CNTs so that the conductance is relatively insensitive to the isomer type, and the conductance switching ratio is low. Multiple bridging molecules can interact coherently, resulting in energy splitting, shifting, and interference that cause a nonlinear change in conductance with increasing numbers of molecules. Instead of a factor of 3 increase in conductance expected for three independent channels, a factor of 10(3) increase in conductance is obtained for three bridging molecules.