Complete determination of molecular orbitals by measurement of phase symmetry and electron density

Several experimental methods allow measuring the spatial probability density of electrons in atoms, molecules and solids, that is, the absolute square of the respective single-particle wave function. But it is an intrinsic problem of the measurement process that the information about the phase is generally lost during the experiment. The symmetry of this phase, however, is a crucial parameter for the knowledge of the full orbital information in real space. Here, we report on a key experiment that demonstrates that the phase symmetry can be derived from a strictly experimental approach from the circular dichroism in the angular distribution of photoelectrons. In combination with the electron density derived from the same experiment, the full quantum mechanical wave function can thus be determined experimentally.