The potential energy curve of the Cl 2(X1Σg+) is investigated by the highly accurate valence internally contracted multireference configuration interaction (MRCI) approach in combination with the largest correlation-consistent basis set, aug-cc-pV6Z, in the valence range. The theoretical spectroscopic parameters and the molecular constants of three isotopes, 35Cl2, 35Cl37Cl and 37Cl2, are studied. For the 35Cl2 (X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are obtained to be 2.3921 eV, 2.4264 eV, 0.19939 nm, 555.13 cm-1 , 2.6772 cm-1 , 0.001481 cm-1 and 0.24225 cm-1 , respectively. For the 35Cl37Cl(X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are calculated to be 2.3918 eV, 2.4257 eV, 0.19939 nm, 547.68 cm-1 , 2.6234 cm-1 , 0.00140 cm-1 and 0.23572 cm-1 , respectively. And for the 37C2 (X1Σg+), the values of D0 , De , Re , ωe , ωeχe , αe and Be are obtained to be 2.3923 eV, 2.4257 eV, 0.19939 nm, 540.06 cm-1 , 2.5556 cm-1 , 0.00139 cm-1 and 0.22919 cm-1 , respectively. These spectroscopic results are in good agreement with the available experimental data. With the potential of Cl2 molecule determined at the MRCI/aug-cc-pV6Z level of theory, the total of 59 vibrational states is predicted for each isotope when the rotational quantum number J equals zero (J = 0). The theoretical vibrational levels, classical turning points, inertial rotation and centrifugal distortion constants are determined when J = 0, which are in excellent accordance with the available experimental findings.