Full geometric optimization of tricyclo[126.96.36.199(2.5)]deca-3,7-diene (TDD) has been done by DFT/B3LYP methods and the structure of the molecule was investigated. Cyclobuten double bond (I) of molecule is syn pyramidalized, and bicyclookten double bond (II) is also exo pyramidalized. The double bond (I) is more pyramidalized than the double bond (II) and it has higher reactivity. The TDD-Br-2 system has been investigated by B3LYP/6-311++G(d,p) method and their stable configurations have been determined. The cationic intermediates and products obtained as a result of the addition reaction has been studied using B3LYP/6-311G(d,p) and B3LYP/6-311++G(d,p) methods. Bridged bromonium cation is more stable than U-type cation. Considering that the bridged cation does not isomerize to the less stable U-type cation, it is not possible for the U-type product to be obtained in the reaction. The bridged bromonium cation transformed into the more stable N-type cation and the N-type product was obtained via this cation. The thermodynamic stability of the anti, exo and anti, endo isomers of N-type dibromide molecule were almost identical. N-type product is 11.759 kcal mol more stable than U-type product.