Triplet exciton transfer (TET) and triplet-triplet annihilations (TTAs) anthracene derivatives, namely, one of the polymorphs of 9,10-bis(triisopropylsilylethynyl)anthracene (TIPS-ANTp) and 1,2,3,4-tetrafluoro-5,8-bis(trimethylsilylethynyl)anthracene (F4-TMS-ANT), are analyzed theoretically. The electronic couplings for TET and TTA are evaluated by means of the diabatization scheme in conjunction with the time-dependent density functional theory and the multireference second-order Moller-Plesset method. The TET rate is estimated on the basis of Fermi's golden rule considering the Franck-Condon factor of intramolecular modes. TTA is analyzed by means of quantum dynamics calculations with the multiconfiguration time-dependent Hartree method. TET in the cofacially stacked F4-TMS-ANT is faster than that of the slip-stacked TIPS-ANTp. In the anthracene derivatives, a singlet exciton is lower in energy than a pair of triplets. F4-TMS-ANT can exhibit an ultrafast TTA via the superexchange pathway mediated by higher lying charge transfer (CT) states, owing to strong electronic couplings. In contrast, TIPS-ANTp exhibits an inefficient TTA via the direct pathway with a small two-electron coupling. The cofacial stacking decreases the energy gap to the intermediate CT states, thereby facilitating TET and TTA via the superexchange pathway.