Prospect of retrieving vibrational wave function by single-object scattering sampling

The exact shape of wave functions has never been directly measured because an ensemble measurement is often overwhelmed by the contributions of highly populated configurations. In this work, we explore the possibility of directly obtaining vibrational wave functions by single-object scattering sampling (SOSS) using intense, ultrashort X-ray pulses provided by X-ray free electron lasers. Previously, single-molecule diffraction experiments using femtosecond X-ray pulses have been proposed with the prospect of determining three-dimensional structure of macromolecules without the need of single-crystal samples. In contrast to the previous proposals, SOSS is designed for obtaining the structural variations of constantly fluctuating molecules by sampling many single-shot, single-object scattering patterns. From the simulations on iodine molecules adopting various pulse characteristics and molecular parameters, we were able to reconstruct vibrational wave functions of molecular iodine and found that SOSS is feasible under appropriate experimental conditions.