The geometry and the electronic structure of tetracyclo[18.104.22.168(2,6).0(3,10)]deca-4,8diene (hypostrophene) molecule were investigated by ab initio and DFT/B3LYP methods using the 6-31G(d) and 6-311G(d) basis sets. The double bonds of hypostrophene molecule are endo pyramidalized. The cationic intermediates and products formed in the addition reaction have been studied by HF/6-311G(d), HF/6-311G(d, p), B3LYP/6-311G(d) and B3LYP/6-311++G(2d, p)//B3LYP/6-311G(d) methods. The solvent effect was evaluated using the conducting polarized continuum model (CPCM). The bridged chloronium cation was more stable than the U-type cation. Considering that the bridged cation does not isomerize into the more unstable U-type cation, it is not possible for U-type product to be obtained in the reaction. The bridged chloronium cation transformed into the more stable N-type cation and the N-type product was obtained via this cation. The thermodynamic stability of the exo,exo and exo,endo isomers of the N-type dichloride molecule were almost identical. The N-type product was 12.201 kcal/mol (CPCM-B3LYP/6-311++G(2d,p)//B3LYP/6-311G(d)) more stable than the U-type product.