Equivalence of the Wei potential model and Tietz potential model for diatomic molecules

Abstract

By employing the dissociation energy and the equilibrium bond length for a diatomic molecule as explicit parameters, we generate improved expressions for the well-known Rosen-Morse, Manning-Rosen, Tietz, and Frost-Musulin potential energy functions. It is found that the well-known Tietz potential function that is conventionally defined in terms of five parameters [T. Tietz, J. Chem. Phys. 38, 3036 (1963)] actually only has four independent parameters. It is shown exactly that the Wei [Phys. Rev. A 42, 2524 (1990)] and the well-known Tietz potential functions are the same solvable empirical function. When the parameter h in the Tietz potential function has the values 0, +1, and -1, the Tietz potential becomes the standard Morse, Rosen-Morse, and Manning-Rosen potentials, respectively.

Molecular energies of the improved Rosen−Morse potential energy model

“…In 2012, Jia et al 33 presented a more convenient form of the original Rosen−Morse potential energy function: (2) U RM (r) ϭ D eͩ 1 Ϫ e ␣r e ϩ 1 e ␣r ϩ 1 ͪ 2 where ␣ = 2/d, D e is the dissociation energy, and r e is the equilibrium bond length. Here, one term, 1 2 D e ͑e 4r e /d ϩ 1͒, has been added to the original Rosen−Morse potential (eq.…”

Improved expressions for the Schiöberg potential energy models for diatomic molecules

“…We obtained improved expressions for the standard ManningRosen potential energy function and Rosen-Morse potential energy function, which are given by, respectively [35,36],…”

“…The Frost-Musulin potential energy function [8] for diatomic molecules can be expressed as [36], U FM ðrÞ ¼ D e 1 À ðr þ ar e r À ar 2 e Þe ÀaðrÀreÞ r ! :…”

“…We showed that a simple version of the Schiöberg empirical potential function and the well-known Manning-Rosen potential energy function are the same empirical function [35], and the Wei potential energy function and the Tietz potential energy functions are also the same solvable empirical function [36]. Motivated by these works about the equivalence of some empirical potential energy functions, we attempt to investigate generally the equivalence of two versions of the Schiöberg potential energy function and the Rosen-Morse potential function and Manning-Rosen potential function.…”

Molecular energies of the improved Tietz potential energy model

“…18 The Tietz potential is more realistic than the Morse potential 19 in the description of molecular dynamics at moderate and high rotation-vibrational quantum numbers. 20 By using the least-squares Z test method of Murrell and Sorbie, 21 Royappa et al 22 27 proposed a more convenient form of the original Tietz potential energy function (eq. 1).…”