An information-theoretical take on electron-nuclear wave packet dynamics

Applications of information-theoretic measures to a time-dependent coupled electron-nuclear system to analyze the dynamics and correlation between both particles are presented. For this, differential Shannon entropies that are derived from time-dependent coordinate-space and momentum-space probability densities are calculated. Two distinct scenarios are investigated: one exhibiting adiabatic Born-Oppenheimer dynamics and the other involving strong non-adiabatic transitions. The total and single-particle entropies, as well as the mutual information are analyzed and compared to semi-analytical expressions. The results reveal that in the adiabatic regime, correlations manifest differently in coordinate and momentum spaces, which is related to the formation of nodes. In the non-adiabatic case, entropies can be decomposed into state-specific contributions, revealing information about the transition between adiabatic states.