To determine the geometries of the most stable hept-C(62)X(2) (X = F, Cl, and Br) isomers, all 967 possible hept-C(62)F(2) isomers have been orderly optimized using AM1, HF/STO-3G, B3LYP/3-21G, and B3LYP/6-31G* methods, and chlorofullerenes and bromofullerenes, which are isostructural with five most stable hept-C(62)F(2) isomers, were regarded as candidates of the most stable isomer, and optimized at the B3LYP/6-31G* level. The results reveal that 2,9- and 9,62-hept-C(62)X(2) (X = F, Cl, and Br) are the two most stable isomers with slight energy difference. The halogenation releases strain energy of hept-C(62), and all halogenated fullerenes are more chemically stable than hept-C(62) with lower E(HOMO) and higher E(LUMO). All five most stable hept-C(62)X(2) (X = F, Cl, and Br) isomers are energetically favorable, and their thermodynamic stability decreases along with the increase of sizes of addends. Only hept-C(62)F(2) isomers show high thermodynamic stability, and they are potentially synthesized in experiments. 59,62-squ-C(62)X(2) (X = F, Cl, and Br) were computed for comparison, and they are found to be more stable than their heptagon-containing isomers.