Singlet exciton fission, a process that converts one singlet exciton to a pair of triplet excitons has the potential to enhance the efficiency of both bulk heterojunction and dye-sensitized solar cells and is understood in crystals but not well understood in molecules Previous studies have identified promising building blocks for singlet fission in molecular systems but little work has investigated how these individual chromophores should be combined to maximize triplet yield We consider the effects of chemically connecting two chromophores to create a coupled chromophore pair and compute how various structural choices alter the thermodynamic and kinetic parameters likely to control singlet fission yield We use density functional theory to compute the electron transfer matrix element and the thermodynamics of fission for several promising chromophore pairs and find a trade-off between the desire to maximize this element and the desire to keep the singlet fission process exoergic We identify promising molecular systems for singlet fission and suggest future experiments