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.