The geometry and the electronic structure of tricyclo[126.96.36.199(2,5)]dodeca-1,5-diene (TCDD) molecule were investigated by DFT/B3LYP and DFT/B3PW91 methods using the 6-311G(d,p) and 6-311++G(d,p) basis sets. The double bonds of TCDD molecule are syn-pyramidalized. The structure of pi-orbitals and their mutual interactions for TCDD molecule were investigated. The cationic intermediates and products formed in the addition reaction have been studied by B3LYP/6-311G(d,p) and B3LYP/6-311++G(2d,p) methods. The solvent effect was evaluated using the conducting polarized continuum model (CPCM). The bridged bromonium cation was more stable than the U-type cation. The N-type products was 18.011 kcal/mol (CPCM-B3LYP/6-311++G(2d,p)//B3LYP/6-311G(d,p)) more stable than the U-type product. The reason for the skeletal structure of U-type being more unstable compared to the N-type is mainly due to the former having highly rigid cyclobutane rings. The configurations (molecular charge-transfer complex, transition states and intermediate) corresponding to the stationary points (minima or saddle points) of potential energy surface of the addition reaction have been investigated using the B3LYP/6-311G(d,p) method. The reaction is realized so as to follow the direction where transannular cross (N-type) bonding of double bonds (formation of C2-C6 bond) occur and more stable skeletal structure (N-type product) is obtained.