Spectroscopic techniques are very essential tools in studying electronic structures, spectroscopic constants and energetic properties of diatomic molecules. These techniques are also required for parametrization of new method based on theoretical analysis and computational calculations. In this research, we apply the proper quantization rule in spectroscopic study of some diatomic molecules by solving the Schrödinger equation with two solvable quantum molecular systems-Tietz-Wei and shifted Deng-Fan potential models for their approximate nonrelativistic energy states via an appropriate approximation to the centrifugal term. We show that the energy levels can be determined from its ground state energy. The beauty and simplicity of the method applied in this study is that, it can be applied to any exactly as well as approximately solvable models. The validity and accuracy of the method is tested with previous techniques via numerical computation for H$_2$ and CO diatomic molecules. The result also include energy spectrum of 5 different electronic states of NO and 2 different electronic state of ICl.
On the universality of spectroscopic constants of diatomic molecules
我们通过机器学习的方法，证明了双原子分子的平衡距离，谐波振动频率和结合能是普遍相关的。特别是，光谱常数之间的关系是有效的独立的分子键。然而，它们强烈地依赖于组成原子的基团和周期。结果表明，利用分子内原子的基团和周期，可以预测光谱常数，其精度为$\lesssim 5\%$。最后，当采用{ \it ab initio}和密度泛函理论（DFT）电子结构方法的光谱常数时，满足相同的普适关系。
Algebraic Determination of Spectral Characteristics of Rovibrational States of Diatomic Molecules. I. Diagram Technique for Determination of Vibrational Dependences of Matrix Elements
Relativistic ab initio study on the spectroscopic and radiative properties of the lowest states and modeling of the optical cycles for the LiFr molecule
Interatomic potentials, electric properties, and spectroscopy of the ground and excited states of the Rb_2 molecule: Ab initio calculations and effect of a non-resonant field
