《Table 1 Different calculated rovibrational energies from different selec-tions》

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《Method for studying diatomic rovibrational spectra at a given vibrational state》

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In order to show the influence of different selections and how the physical criteria work，Table 1 lists 10 different calculated rovibrational energies for the（υ=28，J=50）state of the39K7Li-C1Σ+system，which will be discussed in detail in the next section.For comparison，the first line of this table gives the result of the best selection in this study and shows that the error between the AMr（v）and the experiment-based energy is less than 0.001 cm-1.However，Selection 2（No.2）gives a completely wrong rovibrational level not only because of its huge error compared to the experimental value but also because the energy is higher than the upper limit Emax（J=50）=3694.664 cm-1（listed in Table S8 of the Supporting information online）.Selections 3 to 6 also give large differences from the experimental data，and after careful examination in Table S8，it can be found that the energies of these selections do not meet the physical criteria of eq.（9）or（10）.Selections 7 to 9 give relatively better results，but not as good as the first one.As illustrated in our previous work[21]，these errors usually result from the“butterfly effect”of experimental errors in different selections.It is worth noting that，although the last selection（No.10）generates the exact rovibrational energy for the（υ=28，J=50）state，its rovibrational energies for other rotational states are less accurate than the first selection.For instance，the error of Selection 1for the（υ=28，J=0）state is also less than 0.001 cm-1，but that of selection 10 is more than 100 times greater than this.As a matter of fact，for each vibrational state，there are hundreds of concrete requirements from the physical criteria in the AMr（v）to ensure the reliability of its prediction.