While most of CO-bound hemes are easily photodissociated with a quantum yield of nearly unity, we occasionally encounter a CO-heme which appears hardly photodissociable under the ordinary measurement conditions of resonance Raman spectra using CW laser excitation and a spinning cell. This study aims to understand such hemes theoretically, that is, the excited-state properties of the five-coordinate heme-CO adduct (5cH) as well as the 6c heme-CO adduct (6cH) with a weak axial ligand. Using a hybrid density functional theory, we scrutinized the properties of the ground and excited spin states of the computational models of a 5cH and a water-ligated 6cH (6cH-H(2)O) and compared these properties with those of a photodissociable imidazole-ligated 6cH (6cH-Im). Jahn-Teller softening for the Fe-C-O bending potential in the a(1)-e excited state was suggested. The excited-state properties of 6cH-Im and 5cH were further studied with time-dependent DFT theory. The reaction products of 6cH-Im and 5cH were assumed to be quintet and triplet states, respectively. According to the time-dependent DFT calculations, the Q excited state of 6cH-Im, which is initially a pure pi-pi state, crosses the Fe-CO dissociative state (2A') without large elongation of the Fe-CO bond. In contrast, the Q state of the 5cH does not cross the Fe-CO dissociative state but results in the formation of the excited spin state with a bent Fe-C-O. Consequently, photoisomerization from linear to bent Fe-C-O in the 5cH is a likely mechanism for apparent nonphotodissociation.