To increase performance of organic solar cells, the optimization of the electron-accepting fullerenes has received less attention. Here, an electronic structure study of a novel covalently linked C60-C70-heterodimer in blend with the polymer PCDTBT (poly[9-(1-octylnonyl)-9H-carbazole-2,7-diyl]-2,5-thiophenediyl-2,1,3-benzothiadiazole-4,7-diyl-2,5-thiophenediyl) is presented. Upon optical excitation of polymer:heterodimer solid films, the unpaired electron is shared between both C60 and C70 cages. In contrast, in the solution the electron is localized on one half of the dimer. Electronic structure calculations reveal that for the C60-C70-heterodimer two nearly isoenergetic minima exist, essentially the cis and trans conformers, which are separated by a thermodynamically accessible rotational barrier. In the cis conformation, the edge-to-edge distance between the two cages is ca. 4 Å and an unpaired electron is shared between two dimer halves, while in the trans conformation the separation between the fullerene cages is larger and favors electron localization on one half of the heterodimer. By comparison with the experimental data, it is concluded that the cis conformation is preferable in films, and the trans conformation in solution. Modification of the linking molecular bridge opens the possibility to influence the electronic properties of fullerene dimers, which in turn may have an impact on the charge carrier generation efficiency in solar cells.