The calculation results of the R-branch transition emission spectra of (0–0) band of the A 2 1 → X 2 1 transition system of SbNa molecule are presented in this paper. These R-branch high-lying transitional emission spectral lines are predicted by using the difference converging method (DCM). Our results show excellent agreement between DCM spectral lines and the experimental values, and the deviations are controlled within 0.0224 cm−1. What is more, based on the principle of over-determined linear equations, the prediction error is quantified in this work, which provides reliable theoretical support for our predicted DCM calculations. This work provides a lot of useful information for understanding the microstructure of SbNa molecule.

An analytical formula for the diatomic R-branch emission lines that was recently tested as a universal expression has been further modified based on the difference algebraic converging method. The tiny experimental line errors that may lead to amplified errors in the determination of high J lines were taken into account in the formula. Applications are presented for the R-branch emission spectra of (2-0), (3-1), (6-4), and (7-5) overtone bands of the ground electronic state of 12C16O. The rotational constants and band origins that are consistent with those reported previously are determined through the analytical formula for predicting frequency for emission lines up to J = 110. The results are shown to not only compare favorably with available lower J lines, but also generate reasonable higher J lines for the overtone bands, which agree with data from the HITRAN database and other works.