The potential energy curve (PEC) of HI(X 1 Σ + ) molecule is studied using the complete active space self-consistent field method followed by the highly accurate valence internally contracted multireference configuration interaction approach at the correlation-consistent basis sets, aug-cc-pV6Z for H and aug-cc-pV5Z-pp for I atom. Using the PEC of HI(X 1 Σ + ), the spectroscopic parameters of three isotopes, HI(X 1 Σ + ), DI(X 1 Σ + ) and TI(X 1 Σ + ), are determined in the present work. For

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... HI(X 1 Σ + ), the values of D 0 , De, Re, ωe, ωeχe, αe and Be are 3.1551 eV, 3.2958 eV, 0.16183 nm, 2290.60 cm −1 , 40.0703 cm −1 , 0.1699 cm −1 and 6.4373 cm −1 , respectively; for the DI (X 1 Σ + ), the values of D 0 , De, Re, ωe, ωeχe, αe and Be are 3.1965 eV, 3.2967 eV, 0.16183 nm, 1626.8 cm −1 , 20.8581 cm −1 , 0.0611 cm −1 and 3.2468 cm −1 , respectively; for the TI (X 1 Σ + ), the values of D 0 , De, Re, ωe, ωeχe, αe and Be are of 3.2144 eV, 3.2967 eV, 0.16183 nm, 1334.43 cm −1 , 14.0765 cm −1 , 0.0338 cm −1 and 2.1850 cm −1 , respectively. These results accord well with the available experimental results. With the PEC of HI(X 1 Σ + ) molecule obtained at present, a total of 19 vibrational states are predicted for the HI, 26 for the DI, and 32 for the TI, when the rotational quantum number J is equal to zero (J = 0). For each vibrational state, vibrational level G(υ), inertial rotation constant Bυ and centrifugal distortion constant Dυ are determined when J = 0 for the first time, which are in excellent agreement with the experimental results.