Full vibrational spectra of some electronic states of NaLi molecule using a difference converging method

For most diatomic electronic states, it is very difficult to obtain the accurate vibrational spectra of the highly-excited states directly by using the modern experimental techniques and quantum theories. Based on the general expression of diatomic molecular vibrational energy, the difference converging method (DCM) is used to give a new analytical expression in this paper. By using ten known vibrational energies, the full vibrational spectra, the vibrational spectroscopic constants of the highly-excited states, and the dissociation energy can be predicted for a diatomic electronic state. In this study, the full vibrational spectra of the electronic states 31Π, 41Π and A1Σ+ of NaLi molecule are studied with the DCM and the new formula. Results show that all the vibrational levels given in the experiments can be reproduced with an error rate less than 0.02 percent in our study. In addition, By comparing with the reported experimental results, we find 26, 45 and 31 new vibrational levels for 31Π, 41Π and A1Σ+ of NaLi molecule, respectively.