Entanglement of electrons and nuclei during ultrafast excitation: A most compact representation of the molecular wave function

Ultrafast pumping displaces both electrons and nuclei from equilibrium so that the wave function is a double sum of separable terms for the dynamics of the electrons and nuclei. We convert the double sum into a single one by a matricization of the wave function, that is equivalent to the Schmidt decomposition. If more than one term needs to be included in this sum, the wave functions exhibit entanglement of electrons and nuclei. We discuss generating the best exact separable expression for the entangled molecular wave function. Then an approximation with a minimum number of single terms is obtained via Singular Value Decomposition, SVD. Two contrasting examples, LiH and N2, are used as an illustration. In the energy range accessible by a UV excitation, the two differ in their adiabatic electronic dynamics. During the nuclear motion the singlet states of N2 remain bound while the states of LiH are dissociative.