Fullerenes containing a trimetallic nitride template (TNT) within the cage are a particularly interesting class of endohedral metallofullerenes. Not only are the cage properties modified by the presence of the incarcerated group but, almost uniquely among endohedral metallofullerenes, they are quite stable. Furthermore, they can be produced in multimilligram quantities, and these amounts should increase in the future. The electronic effect of the TNT is such that some fullerenes of sizes and symmetry that are otherwise relatively unstable become available for investigation.[1] The general formula of these TNT endohedral metallofullerenes is A 3Àn B n N@C k (n = 0-3; A,B = group III, IV, and rare-earth metals; k = 68, 78, and 80) with the archetypal examples of: Sc 3 N@C 80 , [2,3] Sc 3 N@C 68 , [4] and Sc 3 N@C 78 .[5] The structures of Sc 3 N@C 78 , Sc 3 N@C 80 , and Sc 3 N@C 68 are displayed in Figure 1.Special attention has been paid to lutetium-based TNT endohedral metallofullerenes, Lu 3Àn A n N@C 80 (n = 0-2; A = Gd, Ga, and Ho), because they may prove useful as multifunctional contrast agents for X-ray, magnetic resonance imaging, and radiopharmaceuticals.[6] The aim of this research is to use methods based on density functional theory (DFT) to answer the questions: How can the stability of the TNT endohedral metallofullerenes be predicted? Which fullerene cages between C 60 and C 84 will be capable of encapsulating TNTs? Aihara and co-workers proposed the bond resonance energy (BRE) [7] to be an indicator of the particular stabilization of free fullerene cages when they encapsulate metal units.[8] However, this method was not a predictive tool because it could not answer whether or not new cages will be capable of encapsulating TNTs.Up to now, only four carbon cages have been capable of encapsulating TNT units: D 3 -C 68 :6140, D 3h' -C 78 :5, D 5h -C 80 :6 and I h -C 80 :7. All these cages, except C 68 , satisfy the isolatedpentagon rule (IPR). But it is interesting to see that in all cases the empty IPR fullerene isomers isolated so far are different from the carbon cages found in isolable TNT endohedral metallofullerenes. The incorporation of a TNT into the fullerene results in an electron transfer from the metal atoms to the carbon cage, in other words, the formation of a stable ion pair. It should be noted that these fullerene cages are produced only when they are negatively charged by the encapsulated species. Theoretical calculations indicated that the thermodynamic stability of a fullerene molecule depends heavily on the negative charge that resides on it. [9] The bond between the nitride and the cage is markedly defined by the ionic model Sc 3 N 6+ @C k 6À (k = 68, 78, and 80).[10] From the geometric point of view, although the free Sc 3 N molecule is pyramidal, this fragment has a planar structure inside the fullerene cage. When the Sc 3 N unit is