Dealing with the hidden unphysical constraint and the butterfly effect in spectrum computations

Since the order in the diatomic potential (or vibrational energy) expansion may be different from state to state, the algebraic method (AM) proposed by Sun et al. (J Mol Spectrosc 2002; 215: 93-105) is modified to adapt to the individual nature of different energy expansions by changing an original fixed order to a flexible one. The modified AM with a flexible order can be used to deal with the possible “butterfly effect” that may happen in spectroscopic computations, and it is applied to study the full vibrational spectra {Eυ} and the dissociation energies De for L7i2−23Σg+, K2−31Πg, Cs2−33∑g+, KLi−X1∑+, and RbCs−X1Σ+ electronic states. The results not only reproduce the known experimental vibrational energies, but also correctly predict the dissociation energies and all unknown energies that have not been obtained for these electronic states using the original AM. These facts demonstrate that the modified AM are good for many more diatomic systems by using the proper order of each corresponding diatomic state.

► We find that “butterfly effect” may happen in molecular spectroscopic computations. ► We modify our algebraic method (AM) to adapt to different diatomic systems. ► Modified AM can predict the full vibrational spectra rationally and precisely.