Theoretical schemes to evaluate electronic coupling elements for triplet-triplet annihilation (TTA) processes are proposed using fragment molecular orbital-linear combination of molecular orbital methods. Combining them with the Marcus formula, we estimate rate constants of TTA for 9,10-diphenylanthracene (DPA). We also performed molecular dynamics simulations of diffusion of DPAs in solution to estimate rate constants of molecular encounter in an assumed diffusion-controlled reaction. On the basis of the calculated rate constants, the mechanism of TTA process for DPAs in solution are discussed.