Imaging molecules from within: Ultrafast angstrom-scale structure determination of molecules via photoelectron holography using free-electron lasers

A scheme based on (i) upcoming brilliant x-ray free-electron laser (FEL) sources, (ii) innovative energy and angular-dispersive large-area electron imagers, and (iii) the well-known photoelectron holography is elaborated that provides time-dependent three-dimensional structure determination of small to medium-sized molecules with Angstrom spatial and femtosecond time resolution. Inducing molecular dynamics, wave-packet motion, dissociation, passage through conical intersections, or isomerization by a pump pulse this motion is visualized by the x-ray FEL probe pulse launching keV photoelectrons within a few femtoseconds from specific and well-defined sites, deep core levels of individual atoms, inside the molecule. On their way out, the photoelectrons are diffracted generating a hologram on the detector that encodes the molecular structure at the instant of photoionization, thus providing femtosecond snapshot images of the molecule from within. Detailed calculations in various approximations of increasing sophistication are presented and three-dimensional retrieval of the spatial structure of the molecule with Angstrom spatial resolution is demonstrated. Due to the large photoabsorption cross sections the method extends x-ray-diffraction-based time-dependent structure investigations envisioned at FEL's to new classes of samples that are not accessible by any other method. Among them are dilute samples in the gas phase such as aligned, oriented, or conformer-selected molecules, ultracold ensembles and/or molecular or cluster objects containing mainly light atoms that do not scatter x rays efficiently.