A novel analytic potential function applied to diatomic molecules based on cosine function

A new method on constructing analytical potential energy functions is presented,and an analytical potential energy function applied to both neutral diatomic molecules and charged diatomic molecular ions is obtained.The potential energy function is examined by 25 examples of eight different basic kinds of diatomic molecules or ions,namely homonuclear ground-state for neutral diatomic molecules H2-X1∑+g,homonuclear excitation-state for neutral diatomic molecule C2-d1∑+u,homonuclear ground-state for charged diatomic molecules O+2-X2∏g,homonuclear excitation-state for charged diatomic molecules N+2-B2∑+u,heternuclear ground-state for neutral diatomic molecules PuO-X1∑+g,heternuclear excitation-state neutral diatomic molecular ion PbS-A1∑+,heternuclear ground-state for charged diatomic molecules(BC)-X3∏,heternuclear excitation-state for charged diatomic molecules CS+-A2∏,etc.The theoretical values of the vibrational energy level of molecules calculated by the potential energy function are compared with RKR(Rydberg-Klein-Rees)or experimental data.As a consequence,all the results are in high-precision consistent with RKR data.