The potential energy curves for the ground state of SO and ClO molecules as well as their corresponding molecular ions have been computed using the multi-reference configuration interaction (MRCI) method with aug-cc-PVXZ (X=D,T,Q) basis sets. The MRCI energies are extrapolated to the complete basis sets limit with Feller's method. The equilibrium geometries and disassociation energies also have been determined. The analytical potential energy functions of these states have been fitted using Murrell-Sorbie function and least square fitting method. Based on the analytical potential energy functions, the vibrational levels have been determined by solving Schrdinger equation of nuclear motion, and corresponding spectroscopic constants accurately calculated respectively. The present values for the spectroscopic constants of each state are compared with the other theoretical and the experimental values currently available.