应用贝叶斯推断与确定性各向异性从气相衍射实验中反演分子结构$|Ψ(\boldsymbol{R})|^2$分布
Applying Bayesian Inference and deterministic anisotropy to retrieve the molecular structure $|Ψ(\boldsymbol{R})|^2$ distribution from gas-phase diffraction experiments
AI总结：
针对气相衍射结构反演依赖复杂模拟的逆问题，研究提出结合贝叶斯推断与确定性各向异性的方法，无需从头算模拟即可反演分子结构分布，实测分辨率较传统方法提升50倍，模拟高信噪比下提升可达100-1000倍，为探测难模拟体系提供新手段。
摘要：
当前，我们从超快气相衍射中反演分子结构的通用方法高度依赖复杂的从头算电子或振动激发态模拟才能得出确定性结论。若没有这类模拟，从该测量结果反推结构概率分布通常是不可解的，这便形成了所谓的逆问题。本研究中，我们开发了一种适用性广泛的方法，无需依赖这些复杂模拟，通过近似分子框架结构$|Ψ(\boldsymbol{R}, t)|^2$分布来解决该逆问题。我们分别对模拟的拉伸态NO₂与实测的N₂O反演了电子振动基态的$|Ψ(\boldsymbol{R})|^2$。针对实测N₂O样本，在倒易空间范围为3.75埃⁻¹且信噪比不佳的条件下，我们获得了40毫埃的坐标空间分辨率，较传统傅里叶变换方法提升了50倍。在模拟的NO₂体系中，典型的高信噪比水平预计可实现100至1000倍的分辨率提升，最低可达0.1毫埃。通过直接测量$|Ψ(\boldsymbol{R})|^2$的宽度，我们拓展了超快气相衍射的测量能力，使其突破了现有分析方法的局限。该方法有望将气相超快衍射切实转变为一种以发现为导向的技术，用于探测那些模拟难度极高的体系。
英文摘要：
Currently, our general approach to retrieving molecular structures from ultrafast gas-phase diffraction heavily relies on complex ab initio electronic or vibrational excited state simulations to make conclusive interpretations. Without such simulations, inverting this measurement for the structural probability distribution is typically intractable. This creates a so-called inverse problem. In this work, we develop a broadly applicable method that addresses this inverse problem by approximating the molecular frame structure $|Ψ(\boldsymbol{R}, t)|^2$ distribution independent of these complex simulations. We retrieve the vibronic ground state $|Ψ(\boldsymbol{R})|^2$ 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 inverse Angstroms reciprocal space range and poor signal-to-noise, a 50X improvement over traditional Fourier transform methods. In simulated NO$_2$, typical to high signal-to-noise levels predict 100--1000X resolution improvements, down to 0.1 mAngstroms. By directly measuring the width of $|Ψ(\boldsymbol{R})|^2$, we open ultrafast gas-phase diffraction capabilities to measurements beyond current analysis approaches. This method has the potential to effectively turn gas-phase ultrafast diffraction into a discovery-oriented technique to probe systems that are prohibitively difficult to simulate.
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