Molecular structures of Dy(3)N@C(78) and Tm(3)N@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 M(3)N@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 Sc(3)N cluster is planar in the earlier reported Sc(3)N@C(78) (D(3)h: 24,109) clusterfullerenes, relatively large Y(3)N and Lu(3)N 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 Y(3)N@C(78) and Lu(3)N@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 Tm(3)N@C(78) and the major isomer of Dy(3)N@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.