Molecular structures of Dy3N@C-78 and Tm3N@C-78 clusterfullerenes are addressed by the IR and Raman vibrational spectroscopic studies and density functional theory (DFT) computations. First, extensive semiempirical calculations of 2927 isomers of C-78 hexaanions followed by DFT optimization were applied to establish their relative stability. Then, DFT calculations of a series of M3N@C-78 (M = Sc, Y, Lu, La) isomers were performed which have shown that the stability order of the isomers depends on the cluster size. While the Sc3N cluster is planar in the earlier reported Sc3N@C-78 (D-3h: 24 109) clusterfullerene, relatively large Y3N and Lu3N clusters would be forced to be pyramidal inside this cage, which would result in their destabilization. Instead, these clusters remain planar in the nonisolated pentagon rule (non-IPR) C-2: 22 010 isomer making Y3N@C-78 and Lu3N@C-78 clusterfullerenes with this cage structure the most stable ones. Finally, on the basis of a detailed analysis of their IR and Raman spectra supplemented with DFT vibrational calculations, the recently isolated Tm3N@C-78 and the major isomer of Dy3N@C-78 are assigned to the non-IPR C-2: 22 010 cage structure. A detailed assignment of their experimental and computed IR and Raman spectra is provided to support this conclusion and to exclude other cage isomers.