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Currently, our general approach to retrieving molecular structures fromultrafast gas-phase diffraction heavily relies on complex ab initio electronicor vibrational excited state simulations to make conclusive interpretations.Without such simulations, inverting this measurement for the structuralprobability distribution is typically intractable. This creates a so-calledinverse problem. In this work, we develop a broadly applicable method thataddresses this inverse problem by approximating the molecular frame structure$|\Psi(\boldsymbol{R}, t)|^2$ distribution independent of these complexsimulations. We retrieve the vibronic ground state $|\Psi(\boldsymbol{R})|^2$for both simulated stretched NO$_2$ and measured N$_2$O. From measured N$_2$O,we observe 40 mAngstroms coordinate-space resolution from 3.75 inverseAngstroms reciprocal space range and poor signal-to-noise, a 50X improvementover traditional Fourier transform methods. In simulated NO$_2$, typical tohigh signal-to-noise levels predict 100--1000X resolution improvements, down to0.1 mAngstroms. By directly measuring the width of $|\Psi(\boldsymbol{R})|^2$,we open ultrafast gas-phase diffraction capabilities to measurements beyondcurrent analysis approaches. This method has the potential to effectively turngas-phase ultrafast diffraction into a discovery-oriented technique to probesystems that are prohibitively difficult to simulate.

communications physics

Applying Bayesian Inference and deterministic anisotropy to retrieve the  molecular structure $|\Psi(\boldsymbol{R})|^2$ distribution from gas-phase  diffraction experiments