Entanglement of electrons and nuclei: 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 and then generate an exact separable expression for the entangled molecular wave function. A most compact approximation with a minimum number of terms is obtained via Singular Value Decomposition. LiH and N₂ are used as an illustration: the two differ in their adiabatic electronic dynamics in the energy range accessible by a UV pulse.