Vibronic interaction and its role in the occurrence of possible superconductivity in the monoanions of phenanthrene-edge-type aromatic hydrocarbons are studied. The vibrational frequencies and the vibronic coupling constants are computed and analyzed and the electron-phonon coupling constants are estimated. The results for phenanthrene-edge-type hydrocarbons are compared with those for acene-edge-type hydrocarbons. The lowest frequency mode and the C-C stretching modes of 1400-1600 cm(-1) afford large electron-phonon coupling constants in the monoanions of acene- and phenanthrene-edge-type hydrocarbons. The total electron-phonon coupling constants decrease with an increase in the number of carbon atoms in both acene- and phenanthrene-edge-type hydrocarbons, but those for the monoanions of phenanthrene-edge-type hydrocarbons are larger than those for the monoanions of acene-edge-type hydrocarbons. Possible superconducting transition temperatures T(c)s for the monoanions are estimated. The monoanions of phenanthrene-edge-type hydrocarbons would have higher T(c)s than the monoanions of acene-edge- type hydrocarbons if phenanthrene-edge-type hydrocarbons exhibit superconductivity. These results suggest that molecular edge structures as well as molecular sizes have relevance to the strength of electron-phonon coupling and T(c)s. The fragment molecular-orbital method (FMO) method successfully characterizes the distinct electronic structures of the two small polynuclear aromatic hydrocarbons (PAHs) with different type of edges such as anthracene and phenanthrene.