The molecular structure of the ground electronic state (*X*^{2}*Σ*^{+}) of ^{35}ClF^{-} and ^{37}ClF^{-} molecular ions have been calculated using single and double substitution quadratic configuration interaction calculations with the triple contribution [QCISD(T)] method and the simple and double excitation coupled-cluster theory with noniterative treatment with the triple excitations [CCSD(T)] method in combination with the correlation consistent basis sets aug-cc-pVXZ (X=D, T, Q, 5). Basis set extrapolation procedures were employed to estimate the complete basis set limit using results obtained with the CCSD(T) method. The analytical potential energy curves for the ground state of the systems were determined by fitting the data of single point energy scans that were calculated at the CCSD(T)/aug-cc-pVXZ (X=D, T, Q, 5) level of theory. The obtained potential energy curves correctly described the configuration and dissociation energy of the molecular ion and was well reproduced by the Murrell-Sorbie function. The corresponding spectroscopic parameters for the ground states of ^{35}ClF^{-} and ^{37}ClF^{-} molecular ions were also deduced. Parallel computations were carried out for the neutral ClF radical on the same level of theory. The results were in good agreement with available experimental data. The consistency between our results and previously reported experimentally determined values demonstrated the feasibility of the theoretical approach performed in this work. The optimized equilibrium geometric parameters were further used to derive the electron affinities of the neutral ClF radical. The vertical detachment energy of ClF^{-} was also determined. Based on computation results for ClF^{-}, the vibrational levels and corresponding molecular constants for the *X*^{2}*Σ*^{+} states of ^{35}ClF^{-} and ^{37}ClF^{-} molecular ions were obtained by solving the radical Schr?dinger equation of the nuclear motion.