Accurate studies of dissociation energies and vibrational energies on alkali metals

This paper studies full vibrational spectra {{}$E_upsilon ${}} andmolecular dissociation energies $D_e$ by using conventionalleast-squares (LS) fitting and an algebraic method (AM) proposedrecently for 10 diatomic electronic states of ${ }^7$Lileast-squares method, algebraicmethod, vibrational energy, dissociation energyProject supported by the NationalNatural Science Foundation of China (Grant No 10774105) and theScience Foundation of the Chinese Educational Ministry.3190, 3420This paper studies full vibrational spectra {{}$E_upsilon ${}} andmolecular dissociation energies $D_e$ by using conventionalleast-squares (LS) fitting and an algebraic method (AM) proposedrecently for 10 diatomic electronic states of ${ }^7$Lileast-squares method, algebraicmethod, vibrational energy, dissociation energyProject supported by the NationalNatural Science Foundation of China (Grant No 10774105) and theScience Foundation of the Chinese Educational Ministry.3190, 3420This paper studies full vibrational spectra {{}$E_upsilon ${}} andmolecular dissociation energies $D_e$ by using conventionalleast-squares (LS) fitting and an algebraic method (AM) proposedrecently for 10 diatomic electronic states of ${ }^7$Li$_2 $, Na$_2$,NaK and NaLi molecules based on some known experimental vibrationalenergies in a subset [$E_upsilon ^{exp t} $] respectively. Studiesshow that: (1) although both the full AM spectrum {{}$E_upsilon^{rm AM} ${}} and the LS spectrum {{}$E_upsilon ^{rm LS} ${}}can reproduce the known experimental energies in [$E_upsilon ^{expt} $], the {{}$E_upsilon ^{rm AM} ${}} is superior to the{{}$E_upsilon ^{rm LS} ${}} in that the high-lying AM vibrationalenergies which may not be available experimentally have better ormuch better accuracy than those LS counterparts in {{}$E_upsilon^{rm LS} ${}}, and so is the AM dissociation energy $D_e^{rm AM}$; (2) the main source of the errors in the data obtained by usingthe LS fitting is that the fitting which is just a pure mathematicalprocess does not use any physical criteria that must be satisfied bythe full vibrational spectrum, while the AM method does. This studysuggests that when fitting or solving a physical equation using a setof source data, it is important not only to apply a propermathematical tool, but also to use correct physical criteria whichmeasure the physical properties of the data, kick out those datahaving bigger errors, and impose conditional convergence on thenumerical process.