There are four parts in this dissertation. Part one briefly describe the importance of the potentials of diatomic molecular ions and two kinds of theoretical methods used to study diatomic ion potentials: the numerical method and the analytical potential function method. Part two introduces the energy consistent method for ion (ECMI) which is developed from the ECM method. In part three the potential energy curves of several electronic states of some homonuclear diatomic molecular ions are studied by using the ECMI. Part four is our conclusion. Studies show that the ECMI is an excellent method which produces accurate potentials for these ionic states, and that the ECMI not only obtain accurate potentials near equilibrium internuclear distance, but also generate correct potential data in the ionic asymptotic and dissociation region where other methods may fail or may give less accurate results.
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