A universal analytic potential function applied to diatomic molecules

In this paper, a new method on constructing analytical potential energy functions is presented, and from this a analytical potential energy function applied to both neutral diatomic molecules and charged diatomic molecular ions is obtained. This potential energy function includes three dimensionless undetermined parameters which can be determined uniquely by solving linear equations with the experimental spectroscopic parameters of molecules. The solutions of the dimensionless undetermined parameters are real numbers rather than complex numbers, this ensures that the analytical potential energy function has extensive universality. Finally, the potential energy function is examined with four kinds of diatomic molecules or ions homonuclear neutral diatomic molecule H
₂
(X
¹
Σ
_g
⁺
), homonuclear charged diatomic molecular ion, He
₂
⁺
(X
²
Σ
_u
⁺
) heternuclear neutral diatomic Molecule AlBr(A
¹
Π) and heternuclear charged diatomic Molecular ion BC
^-
(X
³
Π), as a consequence, good results are obtained.