Structure Determination from Single Molecule Ultrafast X-Ray Scattering using Three Photons per Image

Cooperation and Financial Support: SFB 755 - Nanoscale Photonic Imaging

Schematic depiction of the three-photon correlation using an exemplary synthetic single molecule scattering images of Crambin with ca. 20 coherently scattered photons. In the detector plane kxky the recorded photons are grouped into triplets, each of which is characterized by distances k1,k2,k3 to the detector center (orange lines) and the angles and 𝛃 between the respective photons (orange circular arcs).

The main challenges of single molecule scattering experiments are the unknown random orientation of the molecule in each shot and the extremely low signal to noise ratio due to the very low expected photon count per scattering image, typically well below the number of over 100 photons required by available analysis methods. Photon correlations are a summary statistic of the scattering images that can be collected from few photons without the need to determine the corresponding molecular orientations of each image.

We have developed a correlation-based approach that can determine the molecular structure de novo from as few as three coherently scattered photons per image. The method expresses Fourier intensities with spherical harmonics expansion that facilitate the analytic calculation of the three-photon correlations.

A Monte Carlo simulated annealing approach is used to solve the inverse problem of finding an intensity that fits the experimentally observed triple correlations. The size of the search space is reduced by using information from the analytic inversion of the two-photon correlation and the electron density is retrieved by applying an iterative phase retrieval method to the determined intensity.

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von Ardenne, B.; Mechelke, M.; Grubmüller, H.: Structure determination from single molecule X-ray scattering with three photons per image. Nature Communications 9, 2375 (2018)

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