Electronic structures and stability rules of tetrahedral fullerenes

According to the topologies of tetrahedral (T, Td and Th) fullerenes, we have calculated the electronic structures of these molecules by means of our proposed method for Hückel chemistry calculation. According to the number of carbon atoms, the tetrahedral fullerenes are divided into three classes: Class 1 with n = 12N, Class 2 with n = 12N + 4 and Class 3 with n = 12N + 8, where n is the number of carbon atoms and N is a non-negative integer determined by group properties. From the calculated results, we have found: the molecules of Class 1 are closed-shell, those of Class 2 are open shell and those of Class 3 are open shell or pseudo-closed shell.