Fullerene chemistry is a field of organic chemistry devoted to the chemical properties of fullerenes.Research in this field is driven by the need to functionalize fullerenes and tune their properties. For example fullerene is notoriously insoluble and adding a suitable group can enhance solubility. By adding a polymerizable group, a fullerene polymer can be obtained. Functionalized fullerenes are divided into two classes:
exohedral with substituents outside the cage
endohedral fullerenes with trapped molecules inside the cage.
Chemical properties of fullerenes.
Fullerene or C60 is soccer-ball-shaped or Ih with 12 pentagons and 20 hexagons. According to Euler's theorem these 12 pentagons are required for closure of the carbon network consisting of n hexagons and C60 is the first stable fullerene because it is the smallest possible to obey this rule. In this structure none of the pentagons make contact with each other. Both C60 and its relative C70 obey this so-called isolated pentagon rule (IPR). The next homologue C84 has 24 IPR isomers of which several are isolated and another 51,568 non-IPR isomers. Non-IPR fullerenes have thus far only been isolated as endohedral fullerenes such as Tb3N@C84 with two fused pentagons at the apex of an egg-shaped cage
Because of the molecule's spherical shape the carbon atoms are highly pyramidalized, which has far-reaching consequences for reactivity. It is estimated that strain energy constitutes 80% of the heat of formation. The conjugated carbon atoms respond to deviation from planarity by orbital rehybridization of the sp² orbitals and pi orbitals to a sp2.27 orbital with a gain in p-character. The p lobes extend further outside the surface than they do into the interior of the sphere and this is one of the reasons a fullerene is electronegative. The other reason is that the empty low-lying pi* orbitals also have high s character.
The double bonds in fullerene are not all the same. Two groups can be identified: 30 so-called [6,6] double bonds connect two hexagons and 60 [5,6] bonds connect a hexagon and a pentagon. Of the two the [6,6] bonds are shorter with more double-bond character and therefore a hexagon is often represented as a cyclohexatriene and a pentagon as a pentalene or radialene.
Fullerenes tend to react as electrophiles. An additional driving force is relief of strain when double bonds become saturated. Key in this type of reaction is the level of functionalization i.e. monoaddition or multiple additions and in case of multiple additions their topological relationships (new substituents huddled together or evenly spaced).
Fullerenes react as electrophiles with a host of nucleophiles in nucleophilic additions. The intermediary formed carbanion is captured an electrophile. Examples of nucleophiles are Grignard reagents and organolithium reagents. For example the reaction of C60 with methylmagnesium chloride stops quantitatively at the penta-adduct with the methyl groups centered around a cyclopentadienyl anion which is subsequently protonated . Another nucleophilic reaction is the Bingel reaction.
Fullerene reacts with chlorobenzene and aluminium chloride in a Friedel-Crafts alkylation type reaction. In this hydroarylation the reaction product is the 1,2-addition adduct (Ar-CC-H) .
The [6,6] bonds of fullerenes react as dienes or dienophiles in cycloadditions for instance Diels-Alder reactions. 4-membered rings can be obtained by [2+2]cycloadditions for instance with benzyne. An example of a 1,3-dipolar cycloaddition to a 5-membered ring is the Prato reaction.
Fullerenes are easily hydrogenated by several methods with C60H18 and C60H36 being most studied hydrofullerenes. However, completely hydrogenated C60H60 is only hypothetical because of large strain. Highly hydrogenated fullerenes are not stable, prolonged hydrogenation of fullerenes by direct reaction with hydrogen gas at high temperature conditions results in collapse of cage structure with formation of polycyclic aromatic hydrocarbons.
Although more difficult than reduction, oxidation of fullerene is possible for instance with oxygen and osmium tetraoxide
Fullerenes react in electrophilic additions as well. The reaction with bromine can add up to 24 bromine atoms to the sphere. The record holder for fluorine addition is C60F48. According to in silico predictions the as yet elusive C60F60 may have some of the fluorine atoms in endo positions (pointing inwards) and may resemble a tube more than it does a sphere 
Fullerenes react with carbenes to methanofullerenes