The stable isomers of the higher fullerenes C 76 and C 84 with D 2 symmetry as well as the basic fullerenes C 60 and C 70 were isolated from carbon soot and characterized by the new and advanced methods, techniques, and processes. The validity of several semiempirical, ab initio, and DFT theoretical calculations in predicting the general pattern of IR absorption and the vibrational frequencies, as well as the molecular electronic structure of the C 76 and C 84 isomers of D 2 symmetry, is confirmed, based on recent experimental results. An excellent correlation was found between the previously reported theoretical data and the recently obtained experimental results for these molecules over the relevant spectral range for the identification of fullerenes. These results indicate that there are no errors in the calculations in the significant spectral regions, the assumptions that were based on previous comparisons with partial experimental results. Isolated fullerenes are important for their applications in electronic and optical devices, solar cells, optical limiting, sensors, polymers, nanophotonic materials, diagnostic and therapeutic agents, health and environment protection, and so forth.