Accurate studies of dissociation energies and vibrational energies on alkali metals

This paper studies full vibrational spectra E_\upsilon and molecular dissociation energies D_\rm e by using conventional least-squares (LS) fitting and an algebraic method (AM) proposed recently for 10 diatomic electronic states of ^7Li_2 , Na_2, NaK and NaLi molecules based on some known experimental vibrational energies in a subset E_\upsilon ^\exp t respectively. Studies show 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 ^\exp t , the E_\upsilon ^\rm AM is superior to the E_\upsilon ^\rm LS in that the high-lying AM vibrational energies which may not be available experimentally have better or much better accuracy than those LS counterparts in E_\upsilon ^\rm LS , and so is the AM dissociation energy D_\rm e^\rm AM ; (2) the main source of the errors in the data obtained by using the LS fitting is that the fitting which is just a pure mathematical process does not use any physical criteria that must be satisfied by the full vibrational spectrum, while the AM method does. This study suggests that when fitting or solving a physical equation using a set of source data, it is important not only to apply a proper mathematical tool, but also to use correct physical criteria which measure the physical properties of the data, kick out those data having bigger errors, and impose conditional convergence on the numerical process.