The fullerenic structures include fullerenes having molecular weights less than that of C60 with the exception of C36 and fullerenes having molecular weights greater than C60. Examples include fullerenes C50, C58, C130, and C176. Fullerenic structure chemically bonded to a carbon surface is also disclosed along with a method for tethering fullerenes to a carbon material. The method includes adding functionalized fullerene to a liquid suspension containing carbon material, drying the suspension to produce a powder, and heat treating the powder.