NMR晶体结构测定的贝叶斯方法
A Bayesian approach to NMR crystal structure determination
摘要：
核磁共振（NMR）光谱特别适合于确定粉末形式的分子和材料的结构。结构测定通常通过寻找实验观察到的NMR化学位移与候选结构之间的最佳匹配来进行。候选构型的化学位移传统上是通过电子结构方法计算的，最近则是通过机器学习预测的。然而，确定的可靠性取决于预测的偏移中的误差。在这里，我们提出了一个贝叶斯框架，用于确定实验晶体结构的识别的信心，在电子结构方法中的典型错误的知识的基础上。我们还扩展了最近开发的ShiftML机器学习模型，包括评估其预测的不确定性。本文介绍了六种有机分子晶体结构的测定方法。我们严格评估的结构测定的可靠性，促进了引入可视化的候选配置之间的相似性，在他们的化学位移和他们的结构。我们还表明，通常使用的值计算$^{13}$ C移位的错误被低估，更准确，自洽确定的不确定性使得有可能使用$^{13}$ C移位，以提高结构测定的准确性。
英文摘要：
Nuclear Magnetic Resonance (NMR) spectroscopy is particularly well-suited to determine the structure of molecules and materials in powdered form. Structure determination usually proceeds by finding the best match between experimentally observed NMR chemical shifts and those of candidate structures. Chemical shifts for the candidate configurations have traditionally been computed by electronic-structure methods, and more recently predicted by machine learning. However, the reliability of the determination depends on the errors in the predicted shifts. Here we propose a Bayesian framework for determining the confidence in the identification of the experimental crystal structure, based on knowledge of the typical error in the electronic structure methods. We also extend the recently-developed ShiftML machine-learning model, including the evaluation of the uncertainty of its predictions. We demonstrate the approach on the determination of the structures of six organic molecular crystals. We critically assess the reliability of the structure determinations, facilitated by the introduction of a visualization of the of similarity between candidate configurations in terms of their chemical shifts and their structures. We also show that the commonly used values for the errors in calculated $^{13}$C shifts are underestimated, and that more accurate, self-consistently determined uncertainties make it possible to use $^{13}$C shifts to improve the accuracy of structure determinations.
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