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<p>We analyze angle-dependent potential-energy functions recently proposed for the study of diatomic molecules. Although the corresponding Schrödinger equation is separable and the resulting eigenvalues are mathematically consistent, we show that the underlying model lacks physical validity within the Born-Oppenheimer framework. In particular, the introduction of an ad hoc angular contribution leads to singular behavior and breaks the expected rotational invariance of an isolated diatomic system. Furthermore, we demonstrate that the use of spectroscopic parameters such as the equilibrium distance and dissociation energy becomes inconsistent when the potential depends on the angular coordinate. We conclude that these models may at best be regarded as purely formal or toy models with no direct connection to molecular spectroscopy.</p>

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Comment on “Modified \(\ell \)-states of diatomic molecules subject to central potentials plus an angle-dependent potential”

  • 期刊论文

  • 发表日期：

    2026年5月18日

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  • Francisco M. Fernández

摘要

We analyze angle-dependent potential-energy functions recently proposed for the study of diatomic molecules. Although the corresponding Schrödinger equation is separable and the resulting eigenvalues are mathematically consistent, we show that the underlying model lacks physical validity within the Born-Oppenheimer framework. In particular, the introduction of an ad hoc angular contribution leads to singular behavior and breaks the expected rotational invariance of an isolated diatomic system. Furthermore, we demonstrate that the use of spectroscopic parameters such as the equilibrium distance and dissociation energy becomes inconsistent when the potential depends on the angular coordinate. We conclude that these models may at best be regarded as purely formal or toy models with no direct connection to molecular spectroscopy.