An analytical formula for predicting high-lying rovibrational term values of CaO molecule

Abstract

The Sun’s difference converging method is successfully extended to calculate the rovibrational term values of diatomic molecules in this study. Similarly, a new analytical formula is derived from the idea of differentiation and the diatomic molecular total energy expression given by Herzberg including high-order rotational spectral constants such as $L_{\upsilon }$, $P_{\upsilon }$, $Q_{\upsilon }$, and $S_{\upsilon }$, which cannot be obtained experimentally and theoretically. This formula is more concise and convenient than the Herzberg’s expression and can correctly predict the high-lying excitation rovibrational term values without any spectral constants and only using 10 known experimental term values with a set of physical criteria for a vibrational level of diatomic molecule. The formula is applied to research the rovibrational term values of vibrational levels $\upsilon =0$ andc $\upsilon =3$ in the A$^{\mathrm {1}}\Sigma ^{\mathrm {+}}$ electronic state of CaO molecule in this work. The results show that the correct values of the unknown rotational states up to$J \quad =$ 80 for each vibrational level are predicted by using the formula This study provides important reference data for the related research areas of CaO.