All properties of molecules--from binding and excitation energies to their geometry--are determined by the highly correlated initial-state wavefunction of the electrons and nuclei. Details of these correlations can be revealed by studying the break-up of these systems into their constituents. The fragmentation might be initiated by the absorption of a single photon, by collision with a charged particle or by exposure to a strong laser pulse: if the interaction causing the excitation is sufficiently understood, the fragmentation process can then be used as a tool to investigate the bound initial state. The interaction and resulting fragment motions therefore pose formidable challenges to quantum theory. Here we report the coincident measurement of the momenta of both nuclei and both electrons from the single-photon-induced fragmentation of the deuterium molecule. The results reveal that the correlated motion of the electrons is strongly dependent on the inter-nuclear separation in the molecular ground state at the instant of photon absorption.