Studies on full vibrational spectra and dissociation energies of some diatomic molecular electronic states using algebraic approaches

Hidden physics in molecular rovibrational spectrum

An algebraic method for rotational energies (AMr) is proposed to unearth the rotational spectrum {ɛJ} and the rovibrational interaction energies ευJint that are hidden in the rovibrational energies EυJ. The applications to the excited electronic state a3Σu+ of 7Li2 and the ground state X1Σ+ of NaF molecules show that: (1) the rotational energies ɛJ of the lighter 7Li2 molecule have better accuracies than the widely used rigid rotor rotational energies εJrr particularly for the lowest two rotational states, while the rigid rotor model produces satisfied rotational energies for the heavier NaF molecule and (2) the attractive rovibrational interaction energies ευJint stabilize a molecular rovibrational system.

A variational algebraic method used to study the full vibrational spectra and dissociation energies of some specific diatomic systems

The algebraic method (AM) proposed by Sun et al. is improved to be a variational AM (VAM) to offset the possible experimental errors and to adapt to the individual energy expansion nature of different molecular systems. The VAM is used to study the full vibrational spectra {Eυ} and the dissociation energies De of (4)HeH(+)-X(1)Σ(+), (7)Li2-1(3)Δg,Na2-C(1)Πu,NaK-7(1)Π, Cs2-B(1)Πu and (79)Br2-β1g((3)P2) diatomic electronic states. The results not only precisely reproduce all known experimental vibrational energies, but also predict correct dissociation energies and all unknown high-lying levels that may not be given by the original AM or other numerical methods or experimental methods. The analyses and the skill suggested here might be useful for other numerical simulations and theoretical fittings using known data that may carry inevitable errors.