A comprehensive statistical approach to identify correct types of cross-peaks based on their symmetric feature

Cross-peak signature patterns in two-dimensional (2D) asynchronous spectra are a useful tool for revealing the deeper physicochemical characteristics of intermolecular interactions. Various interferences such as noise can cause problems in recognizing the correct type of cross-peaks. The symmetrical characteristics of the cross-peaks may offer an intrinsic criterion for distinguishing between different types of cross-peaks. When intermolecular interaction only brings about a shift in the characteristic peak of a solute, we found that the resultant cross-peaks possess a mirror symmetry. However, such a symmetry may not be directly observable in the 2D asynchronous spectrum covered by severe noise. To solve this problem, a comprehensive approach to identify the symmetry is developed. Firstly, a method to locate the mirror is proposed. Then, the Kolmogorov-Smirnov test and Bayesian analysis are used to obtain the probability of the existence of mirror symmetry in the cross-peak group. The approach is showcased in three model systems and a real-world example (the benzene/I₂ system), which demonstrates that the approach is helpful in assigning the correct type of cross-peak under difficult situations.