# Universal information-entropic inequalities for Franck-Condon factors of diatomic molecules

## TL;DR

This paper derives new entropic inequalities for Franck-Condon factors in diatomic molecules, revealing hidden correlations in vibronic spectra through probabilistic and information-theoretic analysis.

## Contribution

It introduces novel entropic inequalities for FCFs using joint probability distributions and Hermite polynomials, advancing understanding of molecular vibronic correlations.

## Key findings

- Derived explicit entropic inequalities for FCFs.
- Linked inequalities to hidden correlations in vibronic spectra.
- Provided probabilistic representations of FCFs.

## Abstract

New entropic inequalities are obtained for Franck-Condon factors (FCF-s) of diatomic molecules in adiabatic harmonic oscillator approximation. The probability distributions associated with FCF-s of diatomic molecules are presented in the form of joint-probability distributions of either two or three random variables. In view of this representation information inequalities corresponding to subadditivity condition is found and in case of harmonic oscillator approximation is obtained in explicit form of new inequalities for Hermite polynomials. Physical meaning of obtained entropic-information inequalities as characteristics of hidden correlations in vibronic spectra of the molecules is studied.