Robust Approach to Estimating the Stoichiometric Ratio of Supramolecular Complexes Using the Volume of Cross-Peaks in 2D Asynchronous Spectra and the Jonckheere–Terpstra Test

Estimation of the stoichiometric ratio of a supramolecular aggregate formed by different compounds is very important in elucidating the structure and function of the aggregate. Many spectroscopic methods used to estimate the stoichiometric ratios of coordination complexes become invalid when characteristic peaks of the aggregate overlap with peaks of compounds that form the aggregate. Previously, we combined the asynchronous orthogonal sample design with Job’s method to address the abovementioned problem. However, the interference of noise may lead to incorrect results. Herein, a new method has been developed. In the generation of corresponding Job’s curve, the intensity of a cross peak at a single apex is replaced by the volume of the cross peak. Since most noise is canceled in the calculation of the volume of the cross peak, resultant Job’s curve is robust to noise. Moreover, the Jonckheere–Terpstra statistical test, a famous nonparametric method to detect whether the data has an upward or downward trend, could further reduce the risk of yielding incorrect results caused by noise. We have applied this approach to two real-world examples (resveratrol/β-Cyclodextrin (β-CD) and N, N-diethyl-N′-benzoylthiourea (DEBT)/Cu2+) with satisfactory results. The method described in this paper provides a robust way to measure the stoichiometric ratio in supramolecular systems.准确估算不同化合物形成的超分子聚集体的化学计量比，对于阐明该聚集体的结构与功能具有重要意义。诸多用于测定配位配合物化学计量比的光谱学方法，在聚集体特征峰与构成聚集体的单体化合物峰发生重叠时便会失效。此前本团队将异步正交样品设计（Asynchronous Orthogonal Sample Design）与约布法（Job’s method）相结合以解决上述问题，但噪声干扰仍可能导致结果失真。本文提出一种全新方法：在生成对应约布曲线（Job’s curve）时，以交叉峰体积替代单一顶点处的交叉峰强度。由于交叉峰体积的计算过程可抵消大部分噪声，所得约布曲线对噪声具备较强的鲁棒性。此外，容克赫尔-特普斯特拉统计检验（Jonckheere–Terpstra statistical test）作为一种经典的非参数趋势检测方法，可进一步降低由噪声引发结果错误的风险。我们将该方法应用于两个实际研究体系：白藜芦醇/β-环糊精（β-CD）与N,N-二乙基-N'-苯甲酰基硫脲（DEBT）/Cu²+，均取得了令人满意的结果。本文所提出的方法为超分子体系化学计量比的精准测定提供了一种可靠且稳健的解决方案。