Structure, photoabsorption, and excited states of a covalently bonded porphyrin-fullerene dyad H2P-O34C(60) are studied using DFT and TD-DFT approaches. Charge transfer from the donor (porphyrin) to the acceptor (fullerene) and the excited-state geometrical relaxation are of special interest. An analysis of differences in the description of these delicate phenomena due to the different exchange-correlation functionals is presented. We compare the results given by LDA, GGA, and hybrid functionals (i.e., SVWN, PBE, B3LYP, and PBE0). The ground-state center-to-center (cc) equilibrium distance between the donor and the acceptor moieties is 6.3, 7.1, and 7.9 angstrom with SVWN, PBE, and B3LYP, respectively. The associated charge transfer of 0.15, 0.11, and 0.09 electrons is shown to depend on this distance but not directly on the functional itself. The same trend is seen in the HOMO-LUMO difference results, and further, in the lowest excitation energies, except for the hybrid functional calculations that yield the largest HOMO-LUMO gap and the highest energy for the lowest electronic excitation. The hybrid functionals were not found practical for excited-state conformational relaxation with the present computing resources. With LDA, the relaxation increases the cc distance by about 0.2 angstrom, which is associated with a 0.14 eV decrease in energy. As compared to the ground-state dipole moment of about 4 D, the relaxed excited-state charge-transfer complex dipole moment turns out to become about 20 D. A local excitation of the porphyrin donor is considered, as well, and based on all these results, the nature and interpretation of the photoinduced electron-transfer process is discussed.