The Rotating Morse–Pekeris Oscillator Revisited

Abstract

The Morse–Pekeris oscillator model for the calculation of the vibration–rotation energy levels of diatomic molecules is revisited. This model is based on the realization of a second-order exponential expansion of the centrifugal term about the minimum of the vibrational Morse oscillator and the subsequent analytical resolution of the resulting approximate radial eigenvalue equation for the rotating Morse oscillator. It is, however, possible to develop the Morse–Pekeris model by transforming the second-order exponential expansion of the rotating Morse oscillator into an effective Morse oscillator and by then taking advantage of the well-known solutions for the Morse oscillator. Such a transformation can be carried out in a straightforward and instructive way merely by making a suitable change of variable of the internuclear coordinate. In addition, this alternative method allows us to correct the Morse–Pekeris model by simple use of first-order perturbation theory. The efficiency of this treatment is demonstrated by carrying out a numerical application to the H2 molecule.

Morse potential in relativistic contexts from generalized momentum operator, Pekeris approximation revisited and mapping

“…Figure 1: Effective Morse potential (in units of hω) of the H 2 molecule in function of the dimensionless parameter r/a 0 [55]. For comparing the KG and the Dirac cases we have taken the same values of l = 0, 1, 2, 3, 4, 5 with the spin total for the Dirac case obeying the relation j = 1/2 + l for all l. We can see that the presence of the spin increases the effective potential barrier.…”

Derivation of Morse Potential Function

“…The Morse potential has been introduce to accurately describe the vibrational spectra of diatomic molecules and is widely used in chemistry texts as a model for anharmonic nuclear motion and bond dissociation: [1][2][3][4] V M orse = D[1 − exp(−β∆r)] 2 (1)…”

“…The Schrödinger equation can be solved analytically with either the Morse or harmonic potential. 3 While the solution with the harmonic potential is most often discussed in the undergraduate physical chemistry courses, the solution with the Morse potential provides a more realistic description of chemical bond, including the bond dissociation and anharmonicity in the vibrational spectra (Figure 1). Therefore, the Morse potential is introduced in most of the physical chemistry, quantum chemistry, and spectroscopy text books.…”

Empirical quality criteria for the approximation of the electronic term of a diatomic molecule by the Morse formula

“…In publications, the authors highly appreciate the usefulness of this potential [2,4,10,50,62,63,64,66], the importance is often emphasized by its mention in the titles of articles. In the university teaching of molecular spectroscopy and physical chemistry, Morse's potential is given considerable attention, including in laboratory practice, and didactic materials are regularly published in specialized journals [82][83][84][85][86][87][88][89]. At the same time, in the manuals, the question is presented according to the established standardfor example, its presentation at the stage of initial analysis [90,91] does not differ much from recent monographs and textbooks [92].…”