By means of density functional theory methods together with statistical thermodynamic analysis, the C-82 monometallofullerenes including special heterogeneous triangular clusters were theoretically probed for the first time. Despite having analogous structures, the YCN@C-82 and TbCN@C-82 series exhibit dissimilar thermodynamic stabilities, which lead to different components of experimental products. Significant relationship between the thermodynamic stabilities and geometry structures of C-82 metallofullerenes is disclosed. Studies of the electronic configurations of MCN@C-82 species not only explain their redox potentials but also recover complicated interaction mechanisms within them. In addition, predictions of the optical spectra of observed MCN@C-82 species coincide with experimental detections well, indicating that simulations for other structures will be helpful for future characterization of these cyanoclusterfullerenes.