A systematic semiempirical study of information inequalities for the vibrational levels of a diatomic molecule for the example of the ground electronic state of 7Li2

Abstract

A systematic study of the dependences of information inequalities relating the variance, Fisher information, and Shannon entropy power in the coordinate and momentum spaces (the Cramer–Rao, Stam, Bialynicki–Birula–Mycielsky–Beckner, and other inequalities) on the vibrational quantum number of a diatomic molecule is performed for the first time. These dependences are calculated for the ground electronic state of the 7Li2 molecule using the semiempirical data available in the literature on the many-parameter potential curve of this state. Specific features of these dependences have been analyzed, their essentially nonmonotonic behavior was revealed, and not only quantitative, but also qualitative, distinctions between these dependences were observed. These results were compared with the results of our calculation in the classical mechanics approximation, and significant (up to a factor of 3.5) discrepancies between these data were observed not only for low-lying, but also for highly excited vibrational levels that are close to the dissociation limit. The results obtained can be used in quantum informatics, analysis of an intramolecular structure and the interaction processes involving the vibrational states of diatomic molecules.