Recent developments in high-repetition-rate x-ray free electron lasers (XFELs) such as the European XFEL and the LSCS-II, combined with coincidence measurements using the COLTRIMS-reaction microscope, are now opening a door to realize the long-standing dream of creating molecular movies of photo-induced chemical reactions in gas-phase molecules. In this paper, we propose a new theoretical method to experimentally visualize the dissociation of diatomic molecules via time-resolved polarization-averaged molecular-frame photoelectron angular distribution (PA-MFPAD) measurements using the COLTRIMS-reaction microscope and the two-color XFEL pump–probe set-up. We used first- and second-order scattering theory within the muffin-tin approximation, which is valid for a sufficiently high kinetic energy of photoelectrons, typically above 100eV, and for long bond lengths. This leads to a simple extended x-ray absorption fine structure (EXAFS)-type formula for the forward and backward scattering peaks in the PA-MFPAD structure. This formula relies only on three semi-empirical parameters obtainable from the time-resolved measurements. It can be used as a ‘bond length ruler’ on experimental results. The accuracy and applicability of the new ruler equation are numerically examined against the PA-MFPADs of CO²⁺ calculated with full-potential multiple scattering theory as a function of the C–O bond length reported in the preceding work (Ota etal J. Phys. B: At. Mol. Opt.). The bond lengths retrieved from the PA-MFPADs via our EXAFS-like formula coincide within an accuracy of 0.1 with the original C–O bond lengths used in the reference ab initio PA-MFPADs. We expect time-resolved PA-MFPADs to become a new attractive tool to make molecular movies visualizing intramolecular reactions.

欧洲 XFEL 和 LSCS-II 等高重复率 X 射线自由电子激光器 (XFEL) 的最新发展，结合使用 COLTRIMS 反应显微镜的巧合测量，现在为实现长期存在的梦想在气相分子中创建光致化学反应的分子电影。在本文中，我们提出了一种新的理论方法，通过使用 COLTRIMS 反应显微镜和双色 XFEL 泵的时间分辨偏振平均分子框架光电子角分布 (PA-MFPAD) 测量实验可视化双原子分子的解离– 探针设置。我们在松饼锡近似中使用了一阶和二阶散射理论，这对于足够高的光电子动能是有效的，通常高于 100eV，和长键长。这导致 PA-MFPAD 结构中前向和后向散射峰的简单扩展 X 射线吸收精细结构 (EXAFS) 型公式。该公式仅依赖于可从时间分辨测量中获得的三个半经验参数。它可以用作实验结果的“键长尺”。新标尺方程的准确性和适用性针对 CO 的 PA-MPFAD 进行了数值检验²⁺使用全电位多次散射理论计算，作为先前工作中报告的 C-O 键长的函数（Ota等人 J. Phys. B：At. Mol . Opt.）。通过我们的类似 EXAFS 的公式从 PA-MFPAD 检索到的键长与参考ab initio PA-MFPAD 中使用的原始 C-O 键长在 0.1 的精度内重合。我们希望时间分辨 PA-MFPADs 成为一种新的有吸引力的工具，使分子电影可视化分子内反应。