Extracting body frame molecular geometry from ultrafast diffraction gas-phase experiments through coherent ensemble anisotropy.

Ultrafast electron and x-ray diffraction from molecular gases both aim to retrieve sub-picosecond and sub-nanometer intramolecular dynamics. These measurements record time-dependent pair-correlation distributions: histograms of all atomic pairwise distances in the molecule. With unlabelled distances alone, the geometry can rarely be retrieved uniquely without the aid of complex excited state dynamics simulations. Here we show a novel method that uses coherent rotational wave packets to better retrieve the molecular frame geometry. We derive a relation between the measured ensemble laboratory frame anisotropy and the molecule’s pairwise distances and molecular frame angles which otherwise remain inaccessible without extensive simulation. With this expression we retrieve the molecular geometry with both the atomic pairwise distances and the angles in the molecular frame.  We do this using a monte-carlo markov chain approach that avoids the need for complex excited-state simulations. We demonstrate this method in the asymmetric top molecule NO2.