A new approach to generate a two-dimensional asynchronous spectrum with improved signal-to-noise ratio using multiple two-trace two-dimensional spectra.

In this paper, a new approach is proposed to construct a two-dimensional (2D) asynchronous spectrum with a much-improved signal-to-noise level. The method produces a total number of sub-2D asynchronous spectra via a two-trace two-dimensional method (2T2D method) using n one-dimensional (1D) spectra. The final 2D asynchronous spectrum is a linear combination of this set of sub-2D asynchronous spectra with optimized combinatorial coefficients. The signs of the sub-2D asynchronous spectra are aligned to be consistent, thereby preventing undesirable cancellation of signals among different sub-2D asynchronous spectra. Suitable combinatorial coefficients derived via the Lagrange multiplier method equalize the noise variance across different sub-2D asynchronous spectra, allowing the noise to be effectively canceled out upon co-adding these sub-2D asynchronous spectra. The method is exemplified in two real-world examples. Firstly, we probed the interaction between Nd3+ and 4-tert-butylcalix[4]arene at the water/CH2Cl2 interface. The corresponding cross-peaks in the 2D asynchronous spectrum generated using the conventional method are obscured by heavy noise. However, a 2D asynchronous spectrum with well-defined cross-peak patterns is obtained using the new method from the same set of 1D spectra. The method also improved the quality of the 2D asynchronous spectrum in the benzene/I2 system. Overall, these results demonstrate that the OC-2T2D method excels at extracting highly subtle spectral variations that would otherwise be obscured by noise in conventional 2D asynchronous spectra.